kopia lustrzana https://github.com/gabrielegilardi/SignalFilters
save copy
Gabriele Gilardi
rodzic
c036881614
commit
cfa166d6d8
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@ -0,0 +1,178 @@
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import numpy as np
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measurements = np.array([5., 6., 7., 9., 10.])
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motion = np.array([1., 1., 2., 1., 1.])
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measurement_sigma = 4.
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motion_sigma = 2.
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mu = 0.
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sigma = 1000.
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# Measurement
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def Update( mean1, var1, mean2, var2 ):
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mean = (var2*mean1 + var1*mean2) / (var1 + var2)
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var = 1.0 / (1.0/var1 + 1.0/var2)
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return [mean, var]
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# Motion
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def Predict( mean1, var1, U, varU ):
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mean = mean1 + U
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var = var1 + varU
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return [mean, var]
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for n in range(len(measurements)):
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[mu, sigma] = Update(mu, sigma, measurements[n], measurement_sigma)
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print('Update : ', n, [mu, sigma])
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[mu, sigma] = Predict(mu, sigma, motion[n],motion_sigma)
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print('Predict: ', n, [mu, sigma])
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print(' ')
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print(Update(1,1,3,1))
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# -------------------------------------------------------
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import numpy as np
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measurements = [ 1., 2., 3. ]
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dt = 1.
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# Initial state (location and velocity)
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x = np.array([[ 0. ],
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[ 0. ]])
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# Initial uncertainty
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P = np.array([[ 1000., 0. ],
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[ 0., 1000. ]])
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# External motion
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U = np.array([[ 0. ],
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[ 0. ]])
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# Next state function
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F = np.array([[ 1., dt ],
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[ 0., 1. ]])
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# Measurement function
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H = np.array([[ 1., 0. ]])
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# Measurement uncertainty
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R = np.array([[ 1. ]])
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# Identity matrix
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I = np.eye(2)
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def filter(x, P):
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for z in (measurements):
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# Measurement
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Htra = H.T
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S = H.dot(P.dot(Htra)) + R
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Sinv = np.linalg.inv(S)
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K = P.dot(Htra.dot(Sinv))
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y = z - H.dot(x)
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xp = x +K.dot(y)
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Pp = P - K.dot(H.dot(P))
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# Prediction
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x = F.dot(xp) + U
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Ftra = F.T
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P = F.dot(Pp.dot(Ftra))
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print('x = ',x)
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print('P = ',P)
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filter(x, P)
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# -------------------------------------------------------
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import numpy as np
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# x0 = 4.
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# y0 = 12.
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# measurements = np.array([[ 5., 10. ],
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# [ 6., 8. ],
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# [ 7., 6. ],
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# [ 8., 4. ],
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# [ 9., 2. ],
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# [ 10., 0. ]])
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# x0 = -4.
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# y0 = 8.
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# measurements = np.array([[ 1., 4. ],
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# [ 6., 0. ],
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# [ 11., -4. ],
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# [ 16., -8. ]])
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# x0 = 1.
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# y0 = 19.
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# measurements = np.array([[ 1., 17. ],
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# [ 1., 15. ],
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# [ 1., 13. ],
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# [ 1., 11. ]])
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x0 = 1.
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y0 = 19.
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measurements = np.array([[ 2., 17. ],
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[ 0., 15. ],
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[ 2., 13. ],
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[ 0., 11. ]])
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# Time step
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dt = 0.1
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# Initial state (location and velocity)
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x = np.array([[ x0 ],
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[ y0 ],
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[ 0. ],
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[ 0. ]])
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# Initial uncertainty
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P = np.array([[ 0., 0., 0., 0. ],
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[ 0., 0., 0., 0. ],
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[ 0., 0., 1000., 0. ],
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[ 0., 0., 0., 1000. ]])
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# External motion
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U = np.array([[ 0. ],
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[ 0. ],
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[ 0. ],
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[ 0. ]])
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# Next state function
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F = np.array([[ 1., 0., dt, 0. ],
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[ 0., 1., 0., dt ],
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[ 0., 0., 1., 0. ],
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[ 0., 0., 0., 1. ]])
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# Measurement function
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H = np.array([[ 1., 0., 0., 0. ],
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[ 0., 1., 0., 0. ]])
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# Measurement uncertainty
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R = np.array([[ 0.1, 0. ],
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[ 0. , 0.1 ]])
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# Measurement vector
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z = np.zeros((2,1))
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def filter(x, P):
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for n in range(len(measurements)):
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z[0][0] = measurements[n][0]
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z[1][0] = measurements[n][1]
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# Prediction
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xp = F.dot(x) + U
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Ftra = F.T
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Pp = F.dot(P.dot(Ftra))
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# Measurement
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Htra = H.T
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S = H.dot(Pp.dot(Htra)) + R
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Sinv = np.linalg.inv(S)
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K = Pp.dot(Htra.dot(Sinv))
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y = z - H.dot(xp)
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x = xp +K.dot(y)
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P = Pp - K.dot(H.dot(Pp))
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# print(z)
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# print('x = ')
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# print(x)
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# print('P = ')
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# print(P)
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# print(' ')
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return x, P
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x_final, P_final = filter(x, P)
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print('x = ')
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print(x_final)
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print('P = ')
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print(P_final)
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@ -4,83 +4,95 @@ Class for filter/smooth data.
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Copyright (c) 2020 Gabriele Gilardi
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N = order/smoothing factor/number of past bars
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alpha = damping term
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References (both from John F. Ehlers):
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[1] "Cycle Analytics for Traders: Advanced Technical Trading Concepts".
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[2] "Signal Analysis, Filters And Trading Strategies".
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General b,a Generic case (param = [b; a])
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SMA N Simple Moving Average
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EMA N Exponential Moving Average
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PassBand P,delta Pass band filter
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StopBand P,delta Stop band filter
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InstTrendline alpha Instantaneous trendline
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GaussLow P,N Gauss, low pass (must be P > 1)
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ZEMA1 N,K,Vn Zero-lag EMA (type 1)
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ZEMA2 N,K Zero-lag EMA (type 2)
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LWMA N Linearly Weighted Moving Average
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MSMA N Modified Simple Moving Average
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MLSQ N Modified Least-Squares Quadratic
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GaussHigh P,N Gauss, high pass (must be P > 4)
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ButterOrig P,N Butterworth original, order N (2 or 3)
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ButterMod P,N Butterworth modified, order N (2 or 3)
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SuperSmoother P, N Super smoother
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SincFunction N Sinc function (N > 1, cut off at 0.5/N)
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X (n_samples, n_series) Dataset to filter
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b (n_b, ) Numerator coefficients
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a (n_a, ) Denominator coefficients
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Y (n_samples, n_series) Filtered dataset
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idx scalar First filtered element in Y
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n_samples Number of data to filter
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n_series Number of series to filter
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nb Number of coefficients (numerator)
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na Number of coefficients (denominator)
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Notes:
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- the filter is applied starting from index.
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- non filtered data are set equal to the original input, i.e.
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Y[0:idx-1,:] = X[0:idx-1,:]
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Filters (ref. [1])
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------------------
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Generic b, a Generic case
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SMA N Simple Moving Average
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EMA N Exponential Moving Average
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WMA N Weighted moving average
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MSMA N Modified Simple Moving Average
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MLSQ N Modified Least-Squares Quadratic (N = 5, 7, 9, 11)
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ButterOrig P, N Butterworth original (N = 2, 3)
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ButterMod P, N Butterworth modified (N = 2, 3)
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SuperSmoother P, N Super smoother (N = 2, 3)
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GaussLow P, N Gauss, low pass (P > 1)
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GaussHigh P, N Gauss, high pass (P > 4)
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Decycler P Decycler
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DecyclerOsc P1, P2 Decycle oscillator
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ZEMA1 N, K, Vn Zero-lag EMA (type 1)
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ZEMA2 N, K Zero-lag EMA (type 2)
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MEMA N, Ns Modified EMA (with cubic velocity extimation)
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PassBand P, delta Pass band filter
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StopBand P, delta Stop band filter
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InstTrendline alpha Instantaneous trendline
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SincFunction N Sinc function (N > 1, cut off at 0.5/N)
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Roofing P1, P2 Gauss,HP,2nd,P1 + Supersmoother,P2
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N Order/smoothing factor/number of previous samples
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alpha Damping term
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P, P1, P2 Cut-off/critical period (50% power loss, -3 dB)
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b Coefficients at the numerator
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a Coefficients at the denominator
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P Cut of period (50% power loss, -3 dB)
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N Order/smoothing factor
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K Coefficient/gain
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Vn Look back bar for the momentum
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delta Band centered in P and in percent
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(0.3 => 30% of P, = 0.3*P, if P = 10 => 0.3*10 = 3)
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alpha Damping term
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nt Times the filter is called (order)
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Ns Look back bar/skip factor
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"""
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import sys
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import numpy as np
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import utils as utl
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def filter_data(X, b, a):
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"""
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Applies a generic filter.
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Inputs:
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X (n_samples, n_series) Data to filter
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b Transfer response coefficients (numerator)
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a Transfer response coefficients (denominator)
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Outputs:
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Y Filtered data
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idx Index of the first element in Y filtered
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Notes:
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- the filter is applied from element 0 to len(X).
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- elements from 0 to (idx-1) are set equal to the original input.
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Applies a filter with transfer response coefficients <a> and <b>.
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"""
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n_samples, n_series = X.shape
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Nb = len(b)
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Na = len(a)
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idx = np.amax([0, Nb-1, Na-1])
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nb = len(b)
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na = len(a)
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idx = np.amax([0, nb - 1, na - 1])
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Y = X.copy()
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# Apply filter
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for i in range(idx, n_samples):
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tmp = np.zeros(n_series)
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# Contribution from [b] (numerator)
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for j in range(Nb):
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tmp = tmp + b[j] * X[i-j,:]
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for j in range(nb):
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tmp = tmp + b[j] * X[i-j,:] # Numerator term
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# Contribution from [a] (denominator)
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for j in range(1, Na):
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tmp = tmp - a[j] * Y[i-j, :]
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for j in range(1, na):
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tmp = tmp - a[j] * Y[i-j, :] # Denominator term
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# Filtered value
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Y[i,:] = tmp / a[0]
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return Y, idx
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@ -90,15 +102,24 @@ class Filter:
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def __init__(self, X):
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"""
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X (nel_X, ) Data to filter
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"""
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self.X = np.asarray(X)
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self.n_samples, self.n_series = X.shape
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self.idx = 0
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def Generic(self, b=1.0, a=1.0):
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"""
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Filter with generic transfer response coefficients <a> and <b>.
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"""
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b = np.asarray(b)
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a = np.asarray(a)
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Y, self.idx = filter_data(self.X, b, a)
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return Y
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def SMA(self, N=10):
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"""
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Simple moving average (type ???).
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Simple moving average (?? order, FIR, ?? band).
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"""
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b = np.ones(N) / N
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a = np.array([1.0])
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@ -107,20 +128,217 @@ class Filter:
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def EMA(self, N=10, alpha=None):
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"""
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Exponential moving average (type ???).
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Exponential moving average (?? order, IIR, pass ??).
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If <alpha> is not given it is determined as equivalent to a N-SMA.
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If not given, <alpha> is determined as equivalent to a N-SMA.
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"""
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if (alpha is None):
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alpha = 2.0 / (N + 1.0)
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b = np.array([alpha])
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a = np.array([1.0, alpha - 1.0])
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a = np.array([1.0, -(1.0 - alpha)])
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Y, self.idx = filter_data(self.X, b, a)
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return Y
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def WMA(self, N=10):
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"""
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Weighted moving average (?? order, FIR, pass ??).
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Example: N = 5 --> [5.0, 4.0, 3.0, 2.0, 1.0] / 15.0
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"""
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w = np.arange(N,0,-1)
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b = w / np.sum(w)
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a = np.array([1.0])
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Y, self.idx = filter_data(self.X, b, a)
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return Y
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def MSMA(self, N=10):
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"""
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Modified simple moving average (?? order, FIR, pass ??).
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Example: N = 4 --> [0.5, 1.0, 1.0, 1.0, 0.5] / 4.0
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"""
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w = np.ones(N+1)
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w[0] = 0.5
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w[N] = 0.5
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b = w / N
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a = np.array([1.0])
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Y, self.idx = filter_data(self.X, b, a)
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return Y
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def MLSQ(self, N=5):
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"""
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Modified simple moving average (?? order, FIR, pass ??).
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Only N = 5, 7, 9, and 11 are implemented. If not return the unfiltered
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dataset.
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"""
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if (N == 5):
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b = np.array([7.0, 24.0, 34.0, 24.0, 7.0]) / 96.0
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elif (N == 7):
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b = np.array([1.0, 6.0, 12.0, 14.0, 12.0, 6.0, 1.0]) / 52.0
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elif (N == 9):
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b = np.array([-1.0, 28.0, 78.0, 108.0, 118.0, 108.0, 78.0, 28.0, \
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-1.0]) / 544.0
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elif (N == 11):
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b = np.array([-11.0, 18.0, 88.0, 138.0, 168.0, 178.0, 168.0, \
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138.0, 88.0, 18.0, -11.0]) / 980.0
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else:
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Y = self.X.copy()
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return Y
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a = np.array([1.0])
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Y, self.idx = filter_data(self.X, b, a)
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return Y
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def ButterOrig(self, N=2, P=10):
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"""
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Butterworth original version (?? order, IIR, pass ??).
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Only N = 2 and 3 are implemented. If not return the unfiltered dataset.
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"""
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if (N == 2):
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beta = np.exp(-np.sqrt(2.0) * np.pi / P)
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alpha = 2.0 * beta * np.cos(np.sqrt(2.0) * np.pi / P)
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b = np.array([1.0, 2.0, 1.0]) * (1.0 - alpha + beta ** 2.0) / 4.0
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a = np.array([1.0, -alpha, beta ** 2.0])
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elif (N == 3):
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beta = np.exp(-np.pi / P)
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alpha = 2.0 * beta * np.cos(np.sqrt(3.0) * np.pi / P)
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b = np.array([1.0, 3.0, 3.0, 1.0]) \
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* (1.0 - alpha + beta ** 2.0) * (1.0 - beta ** 2.0) / 8.0
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a = np.array([1.0, - (alpha + beta ** 2.0), \
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(1.0 + alpha) * beta ** 2.0, - beta ** 4.0])
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else:
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Y = self.X.copy()
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return Y
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Y, self.idx = filter_data(self.X, b, a)
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return Y
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def ButterMod(self, N=2, P=10):
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"""
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Butterworth modified version (?? order, IIR, pass ??).
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Only N = 2 and 3 are implemented. If not return the unfiltered dataset.
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"""
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if (N == 2):
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beta = np.exp(-np.sqrt(2.0) * np.pi / P)
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alpha = 2.0 * beta * np.cos(np.sqrt(2.0) * np.pi / P)
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b = np.array([1.0 - alpha + beta ** 2.0])
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a = np.array([1.0, -alpha, beta ** 2.0])
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elif (N == 3):
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beta = np.exp(-np.pi / P)
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alpha = 2.0 * beta * np.cos(np.sqrt(3.0) * np.pi / P)
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b = np.array([1.0 - alpha * (1.0 - beta ** 2.0) - beta ** 4.0])
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a = np.array([1.0, - (alpha + beta ** 2.0), \
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(1.0 + alpha) * beta ** 2.0, - beta ** 4.0])
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else:
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Y = self.X.copy()
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return Y
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Y, self.idx = filter_data(self.X, b, a)
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return Y
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def SuperSmoother(self, N=2, P=10):
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"""
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SuperSmoother (?? order, IIR, pass ??).
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|
||||
Only N = 2 and 3 are implemented. If not return the unfiltered dataset.
|
||||
"""
|
||||
if (N == 2):
|
||||
beta = np.exp(-np.sqrt(2.0) * np.pi / P)
|
||||
alpha = 2.0 * beta * np.cos(np.sqrt(2.0) * np.pi / P)
|
||||
w = 1.0 - alpha + beta ** 2.0
|
||||
b = np.array([w, w]) / 2.0
|
||||
a = np.array([1.0, - alpha, beta ** 2.0])
|
||||
elif (N == 3):
|
||||
beta = np.exp(-np.pi / P)
|
||||
alpha = 2.0 * beta * np.cos(1.738 * np.pi / P)
|
||||
w = 1.0 - alpha * (1.0 - beta ** 2.0) - beta ** 4.0
|
||||
b = np.array([w, w]) / 2.0
|
||||
a = np.array([1.0, - (alpha + beta ** 2.0), \
|
||||
(1.0 + alpha) * beta ** 2.0, - beta ** 4.0])
|
||||
else:
|
||||
Y = self.X.copy()
|
||||
return Y
|
||||
Y, self.idx = filter_data(self.X, b, a)
|
||||
return Y
|
||||
|
||||
def GaussLow(self, P=2, N=1):
|
||||
"""
|
||||
Gauss low pass (IIR, N-th order, low pass).
|
||||
|
||||
Must be P > 1. If not return the unfiltered dataset.
|
||||
"""
|
||||
if (P < 2):
|
||||
Y = self.X.copy()
|
||||
return Y
|
||||
A = 2.0 ** (1.0 / N) - 1.0
|
||||
B = 4.0 * np.sin(np.pi / P) ** 2.0
|
||||
C = 2.0 * (np.cos(2.0 * np.pi/ P) - 1.0)
|
||||
alpha = (-B + np.sqrt(B ** 2.0 - 4.0 * A * C)) / (2.0 * A)
|
||||
b = np.array([alpha])
|
||||
a = np.array([1.0, - (1.0 - alpha)])
|
||||
Y = self.X.copy()
|
||||
for i in range(N):
|
||||
Y, self.idx = filter_data(Y, b, a)
|
||||
return Y, b, a
|
||||
|
||||
def GaussHigh(self, P=5, N=1):
|
||||
"""
|
||||
Gauss high pass (IIR, Nth order, high pass).
|
||||
|
||||
Must be P > 4. If not return the unfiltered dataset.
|
||||
"""
|
||||
if (P < 5):
|
||||
Y = self.X.copy()
|
||||
return Y
|
||||
A = 2.0 ** (1.0 / N) * np.sin(np.pi / P) ** 2.0 - 1.0
|
||||
B = 2.0 * (2.0 ** (1.0 / N) - 1.0) * (np.cos(2.0 * np.pi / P) - 1.0)
|
||||
C = - B
|
||||
alpha = (-B - np.sqrt(B ** 2.0 - 4.0 * A * C)) / (2.0 * A)
|
||||
b = np.array([1.0 - alpha / 2.0, -(1.0 - alpha / 2.0)])
|
||||
a = np.array([1.0, - (1.0 - alpha)])
|
||||
Y = self.X - self.X[0, :]
|
||||
for i in range(N):
|
||||
Y, self.idx = filter_data(Y, b, a)
|
||||
return Y, b, a
|
||||
|
||||
|
||||
|
||||
def Decycler(self, P=10):
|
||||
"""
|
||||
Decycler (?? order, IIR, pass ??). Gauss,HP,1st,P
|
||||
"""
|
||||
pass
|
||||
|
||||
# % Built subtracting high pass Gauss filter from 1 (only order 1)
|
||||
# case 'Decycler'
|
||||
# P = param(1);
|
||||
# [TMP,nLast] = FiltersBasic(IN,'GaussHigh',[P 1]);
|
||||
# OUT = IN - TMP;
|
||||
|
||||
def DecyclerOsc(self, Pmin=1, Pmax=5):
|
||||
"""
|
||||
Decycler (?? order, IIR, pass ??). Gauss,HP,2nd,Pmax - Gauss,HP,2nd,Pmin
|
||||
"""
|
||||
pass
|
||||
|
||||
# % (Gauss, HP, 2nd, Pmax - Gauss, HP, 2nd Pmin)
|
||||
# % Pmax = larger cut off period
|
||||
# % Pmin = smaller cut off period
|
||||
# case 'DecyclerOsc'
|
||||
# P1 = min(param);
|
||||
# P2 = max(param);
|
||||
# [TMP1,nLast] = FiltersBasic(IN,'GaussHigh',[P1 2]);
|
||||
# [TMP2,nLast] = FiltersBasic(IN,'GaussHigh',[P2 2]);
|
||||
# OUT = TMP2 - TMP1;
|
||||
|
||||
|
||||
|
||||
|
||||
def InstTrend(self, alpha=0.5):
|
||||
"""
|
||||
Instantaneous Trendline (2nd order, IIR, low pass, Ehlers.)
|
||||
Instantaneous Trendline (2nd order, IIR, low pass, Ehlers.).
|
||||
"""
|
||||
b = np.array([alpha - alpha ** 2.0 / 4.0, alpha ** 2.0 / 2.0,
|
||||
- alpha + 3.0 * alpha ** 2.0 / 4.0])
|
||||
|
|
@ -131,10 +349,6 @@ class Filter:
|
|||
def PassBand(self, P=5, delta=0.3):
|
||||
"""
|
||||
Pass Band (type ???).
|
||||
|
||||
P = cut-off period (50% power loss, -3 dB)
|
||||
delta = band centered in P and in percent
|
||||
(Example: 0.3 => 30% of P => 0.3*P, if P = 10 => 0.3*10 = 3)
|
||||
"""
|
||||
beta = np.cos(2.0 * np.pi / P)
|
||||
gamma = np.cos(4.0 * np.pi * delta) / P
|
||||
|
|
@ -147,9 +361,6 @@ class Filter:
|
|||
def StopBand(self, P=5, delta=0.3):
|
||||
"""
|
||||
Stop Band
|
||||
P = cut-off period (50% power loss, -3 dB)
|
||||
delta = band centered in P and in percent
|
||||
(Example: 0.3 => 30% of P => 0.3*P, if P = 10 => 0.3*10 = 3)
|
||||
"""
|
||||
beta = cos(2.0*pi/float(P))
|
||||
gamma = cos(2.0*pi*(2.0*delta)/float(P))
|
||||
|
|
@ -160,33 +371,15 @@ class Filter:
|
|||
Y, self.idx = Generalized(self.X, b, a)
|
||||
return Y
|
||||
|
||||
def GaussLow(self, P=2, N=1):
|
||||
"""
|
||||
Gauss Low (low pass, IIR, N-th order, must be P > 1)
|
||||
P = cut-off period (50% power loss, -3 dB)
|
||||
N = times the filter is called (order)
|
||||
"""
|
||||
P = np.array([2, P], dtype=int).max() # or error? warning?
|
||||
A = 2.0**(1.0/float(N)) - 1.0
|
||||
B = 4.0*sin(pi/float(P))**2.0
|
||||
C = 2.0*(cos(2.0*pi/float(P)) - 1.0)
|
||||
delta = sqrt(B**2.0 - 4.0*A*C)
|
||||
alpha = (-B + delta)/(2.0*A)
|
||||
b = np.array([alpha])
|
||||
a = np.array([1.0, -(1.0-alpha)])
|
||||
Y = np.copy(self.X)
|
||||
for i in range(N):
|
||||
Y, self.idx = Generalized(Y, b, a)
|
||||
return Y
|
||||
|
||||
def ZEMA1(self, N=10, K=1.0, Vn=5):
|
||||
def ZEMA1(self, N=10, alpha=None, K=1.0, Vn=5):
|
||||
"""
|
||||
Zero lag Exponential Moving Average (type 1)
|
||||
N = order/smoothing factor
|
||||
K = coefficient/gain
|
||||
Vn = look back bar for the momentum
|
||||
The damping term <alpha> is determined as equivalent to a N-SMA
|
||||
Zero lag Exponential Moving Average (type 1).
|
||||
|
||||
If not given, <alpha> is determined as equivalent to a N-SMA.
|
||||
"""
|
||||
if (alpha is None):
|
||||
alpha = 2.0 / (N + 1.0)
|
||||
alpha = 2.0 / (float(N) + 1.0)
|
||||
b = np.zeros(Vn+1)
|
||||
b[0] = alpha * (1.0 + K)
|
||||
|
|
@ -195,12 +388,47 @@ class Filter:
|
|||
Y, self.idx = Generalized(self.X, b, a)
|
||||
return Y
|
||||
|
||||
def Generalized(self, a, b):
|
||||
"""
|
||||
Generic filter with transfer response coefficients <a> and <b>
|
||||
"""
|
||||
b = np.asarray(b)
|
||||
a = np.asarray(a)
|
||||
Y, self.idx = filter_data(self.X, b, a)
|
||||
return Y
|
||||
|
||||
|
||||
# % Zero lag Exponential Moving Average (type 2)
|
||||
# % alpha is determined as equivalent to a N-SMA
|
||||
# case 'ZEMA2'
|
||||
# N = param(1);
|
||||
# alpha = 2/(N+1);
|
||||
# K = param(2);
|
||||
# b = alpha*(1+K);
|
||||
# a = [1 alpha*K-(1-alpha)];
|
||||
# [OUT,nLast] = GeneralizedFilter(IN,b,a,3);
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
# % Sinc function
|
||||
# case 'SincFunction'
|
||||
# N = param(1);
|
||||
# nel = 50;
|
||||
# k=1:nel-1;
|
||||
# b = [ 1/N sin(pi*k/N)./(pi*k) ];
|
||||
# a = 1;
|
||||
# [OUT,nLast] = GeneralizedFilter(IN,b,a,1);
|
||||
|
||||
# % Roofing filter: Gauss high pass 2nd order filter + SuperSmoother
|
||||
# % P1 = cut off period for GaussHigh
|
||||
# % P2 = cut off period for SuperSmoother
|
||||
# case 'Roofing'
|
||||
# P1 = param(1);
|
||||
# P2 = param(2);
|
||||
# [TMP,nLast] = FiltersBasic(IN,'GaussHigh',[P1 2]);
|
||||
# [OUT,nLast] = FiltersBasic(TMP,'SuperSmoother',[P2 1]);
|
||||
|
||||
|
||||
# % MEMA - Uses cubic velocity extimation
|
||||
# case 'MEMA'
|
||||
# N = param(1);
|
||||
# Ns = param(2);
|
||||
# alpha = 2/(N+1);
|
||||
# [Vel,Acc,nLast] = FiltersMak(IN,'Cubic',Ns);
|
||||
# for i = nLast:-1:1
|
||||
# OUT(i) = alpha*(IN(i)+Vel(i)/Ns) + (1-alpha)*OUT(i+1);
|
||||
# end
|
||||
|
|
|
|||
|
|
@ -3,15 +3,15 @@ Filters for time series.
|
|||
|
||||
Copyright (c) 2020 Gabriele Gilardi
|
||||
|
||||
|
||||
|
||||
ToDo:
|
||||
- use NaN/input values for points not filtered?
|
||||
- what to use as previous Y in recursive filters? i.e. set Y=X or set Y=0?
|
||||
- plot filtered data (utils, with generic number of arguments passed)
|
||||
- plot filter characteristics (utils)
|
||||
- return idx?
|
||||
- util to test filter (impulse, utils)
|
||||
- warning in filter when wrong order?
|
||||
- use self.a and self.b
|
||||
- remove a and b from plots
|
||||
- in comments write what filters do
|
||||
- is necessary to copy X for Y untouched?
|
||||
"""
|
||||
|
||||
import sys
|
||||
|
|
@ -31,7 +31,18 @@ n_samples = data.shape[0]
|
|||
data = data.reshape(n_samples, -1)
|
||||
|
||||
spx = flt.Filter(data)
|
||||
EMA = spx.EMA()
|
||||
print(EMA[0:5,:])
|
||||
|
||||
# args = (spx.X, spx.SMA(N=5), spx.EMA(alpha=0.7))
|
||||
# utl.plot_signals(args)
|
||||
# utl.plot_signals(args)
|
||||
|
||||
# alpha = 0.8
|
||||
# bb = np.array([alpha])
|
||||
# aa = np.array([1.0, alpha - 1.0])
|
||||
|
||||
|
||||
res, bb, aa = spx.GaussHigh(N=3, P=10)
|
||||
print(bb)
|
||||
print(aa)
|
||||
|
||||
utl.plot_frequency_response(bb, aa)
|
||||
utl.plot_lag_response(bb, aa)
|
||||
|
|
|
|||
|
|
@ -4,6 +4,7 @@ Utility functions for ????.
|
|||
Copyright (c) 2020 Gabriele Gilardi
|
||||
"""
|
||||
|
||||
from scipy import signal
|
||||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
|
|
@ -117,3 +118,346 @@ def plot_signals(signals):
|
|||
|
||||
plt.grid(b=True)
|
||||
plt.show()
|
||||
|
||||
|
||||
def plot_frequency_response(b, a=1.0):
|
||||
"""
|
||||
"""
|
||||
b = np.asarray(b)
|
||||
a = np.asarray(a)
|
||||
|
||||
w, h = signal.freqz(b, a)
|
||||
h_db = 20.0 * np.log10(abs(h))
|
||||
wf = w / (2.0 * np.pi)
|
||||
|
||||
plt.plot(wf, h_db)
|
||||
plt.axhline(-3.0, lw=1.5, ls='--', C='r')
|
||||
plt.grid(b=True)
|
||||
plt.xlim(np.amin(wf), np.amax(wf))
|
||||
plt.xlabel('$\omega$ [rad/sample]')
|
||||
plt.ylabel('$h$ [db]')
|
||||
plt.title('b = ' + np.array_str(np.around(b, decimals=2)) \
|
||||
+ ', a = ' + np.array_str(np.around(a, decimals=2)))
|
||||
plt.show()
|
||||
|
||||
|
||||
def plot_lag_response(b, a=1.0):
|
||||
"""
|
||||
"""
|
||||
b = np.asarray(b)
|
||||
a = np.asarray(a)
|
||||
|
||||
w, gd = signal.group_delay((b, a))
|
||||
wf = w / (2.0 * np.pi)
|
||||
|
||||
plt.plot(wf, gd)
|
||||
plt.grid(b=True)
|
||||
plt.xlim(np.amin(wf), np.amax(wf))
|
||||
plt.xlabel('$\omega$ [rad/sample]')
|
||||
plt.ylabel('$gd$ [samples]')
|
||||
plt.title('b = ' + np.array_str(np.around(b, decimals=2)) \
|
||||
+ ', a = ' + np.array_str(np.around(a, decimals=2)))
|
||||
plt.show()
|
||||
|
||||
|
||||
|
||||
# function [y,t] = interpSignal(x,n1,n2,varargin)
|
||||
# if (nargin == 4)
|
||||
# dt = varargin{1};
|
||||
# else
|
||||
# dt = 20;
|
||||
# end
|
||||
# N = length(x);
|
||||
# Ts = (n2-n1)/(N-1);
|
||||
# n = n1:Ts:n2;
|
||||
# t = n1:Ts/dt:n2;
|
||||
# nt = length(t);
|
||||
# y = zeros(1,nt);
|
||||
# for i = 1:nt
|
||||
# a = x.*sinc( (t(i)-n)/Ts );
|
||||
# y(i) = sum(a);
|
||||
# end
|
||||
# end
|
||||
|
||||
|
||||
# function [f] = plotFn(type,func,varargin)
|
||||
# % 0 Plot real function
|
||||
# % 1 Plot real/imag values
|
||||
# % 2 Plot real/imag values in polar form
|
||||
# % 3 Plot magnitude/phase
|
||||
|
||||
# clf
|
||||
# tiny = 1e-7;
|
||||
|
||||
# % Check if func is a function or data
|
||||
# if ( isa(func,"function_handle") )
|
||||
# N = varargin{1};
|
||||
# n = (0:N-1)';
|
||||
# f = func(n);
|
||||
# else
|
||||
# N = length(func);
|
||||
# n = (0:N-1)';
|
||||
# f = func;
|
||||
# end
|
||||
|
||||
# % Clean data
|
||||
# xRe = real(f);
|
||||
# xIm = imag(f);
|
||||
# xRe( abs(xRe) < tiny ) = 0;
|
||||
# xIm( abs(xIm) < tiny ) = 0;
|
||||
|
||||
# switch (type)
|
||||
|
||||
# % Plot real function
|
||||
# case 0
|
||||
|
||||
# stem(n,xRe,"b","filled")
|
||||
# xlim([n(1) n(N)])
|
||||
# grid on
|
||||
# xlabel("n")
|
||||
# ylabel("f")
|
||||
# box on
|
||||
|
||||
# % Plot real/imag function
|
||||
# case 1
|
||||
# subplot(2,1,1)
|
||||
# stem(n,xRe,"b","filled")
|
||||
# xlim([n(1) n(N)])
|
||||
# grid on
|
||||
# xlabel("n")
|
||||
# ylabel("Re")
|
||||
# box on
|
||||
# subplot(2,1,2)
|
||||
# stem(n,xIm,"b","filled")
|
||||
# xlim([n(1) n(N)])
|
||||
# grid on
|
||||
# xlabel("n")
|
||||
# ylabel("Im")
|
||||
# box on
|
||||
|
||||
# % Plot real/imag function in polar form
|
||||
# case 2
|
||||
# scatter(xRe,xIm,"b","filled")
|
||||
# maxRe = max( abs(xRe) );
|
||||
# maxIm = max( abs(xIm) );
|
||||
# m = max(maxRe,maxIm);
|
||||
# dx = 2*m/50;
|
||||
# text(xRe+dx,xIm,num2str(n))
|
||||
# xlim( [-m +m ])
|
||||
# ylim( [-m +m ])
|
||||
# axis("square")
|
||||
# grid on
|
||||
# hold on
|
||||
# plot([-m 0; +m 0],[0 -m; 0 +m],"k")
|
||||
# hold off
|
||||
# xlabel("Real")
|
||||
# ylabel("Imag")
|
||||
# box on
|
||||
|
||||
# % Plot magnitude/phase
|
||||
# case 3
|
||||
# xMa = sqrt( xRe.^2 + xIm.^2 );
|
||||
# xAr = atan2(xIm,xRe);
|
||||
# subplot(2,1,1)
|
||||
# stem(n,xMa,"b","filled")
|
||||
# xlim([n(1) n(N)])
|
||||
# grid on
|
||||
# xlabel("n")
|
||||
# ylabel("Magnitude")
|
||||
# box on
|
||||
# subplot(2,1,2)
|
||||
# stem(n,xAr,"b","filled")
|
||||
# xlim([n(1) n(N)])
|
||||
# ylim([-pi pi])
|
||||
# grid on
|
||||
# xlabel("n")
|
||||
# ylabel("Phase [rad]")
|
||||
# box on
|
||||
|
||||
# end
|
||||
|
||||
# end
|
||||
|
||||
|
||||
# function sP = SyntQT(P,type)
|
||||
# % Function: generate a random (synthetic) price curve
|
||||
# %
|
||||
# % Inputs
|
||||
# % ------
|
||||
# % P prices (for type equal to 'P' and 'R')
|
||||
# % normal distribution data (for type equal to 'N')
|
||||
# % P(1) = mean
|
||||
# % P(2) = std
|
||||
# % P(3) = length
|
||||
# % type type of generation
|
||||
# % P use returns from price
|
||||
# % R use returns normal distribution
|
||||
# % N use specified normal distribution
|
||||
# %
|
||||
# % Output
|
||||
# % ------
|
||||
# % sP generated synthetic prices
|
||||
|
||||
# % Check for number of arguments
|
||||
# if (nargin ~= 2)
|
||||
# fprintf(1,'\n');
|
||||
# error('Wrong number of arguments');
|
||||
# end
|
||||
|
||||
# switch(type)
|
||||
|
||||
# % Use actual returns from P to generate values
|
||||
# case 'P'
|
||||
# R = Price2ret(P,'S'); % "simple" method
|
||||
# sR = phaseran(R,1);
|
||||
|
||||
# % Use normal distribution to generate values
|
||||
# % (mean and std are from the actual returns of P)
|
||||
# case 'R'
|
||||
# R = Price2ret(P,'S'); % "simple" method
|
||||
# sR = normrnd(mean(R),std(R),length(R),1);
|
||||
|
||||
# % Use defined normal distribution to generate values
|
||||
# % P(1)=mean, P(2)=std, P(3)=length
|
||||
# case 'N'
|
||||
# sR = normrnd(P(1),P(2),P(3),1);
|
||||
|
||||
# otherwise
|
||||
# fprintf(1,'\n');
|
||||
# error('Type not recognized');
|
||||
|
||||
# end
|
||||
|
||||
# % Use 'simple' method and P0 = 1 to determine price
|
||||
# sP = Ret2price(sR,'S');
|
||||
|
||||
# end % End of function
|
||||
|
||||
|
||||
# % Input data
|
||||
# % ----------
|
||||
# % recblk: is a 2D array. Row: time sample. Column: recording.
|
||||
# % An odd number of time samples (height) is expected. If that is not
|
||||
# % the case, recblock is reduced by 1 sample before the surrogate
|
||||
# % data is created.
|
||||
# % The class must be double and it must be nonsparse.
|
||||
|
||||
# % nsurr: is the number of image block surrogates that you want to
|
||||
# % generate.
|
||||
|
||||
# % Output data
|
||||
# % ---------------------
|
||||
# % surrblk: 3D multidimensional array image block with the surrogate
|
||||
# % datasets along the third dimension
|
||||
|
||||
# % Example 1
|
||||
# % ---------
|
||||
# % x = randn(31,4);
|
||||
# % x(:,4) = sum(x,2); % Create correlation in the data
|
||||
# % r1 = corrcoef(x)
|
||||
# % surr = phaseran(x,10);
|
||||
# % r2 = corrcoef(surr(:,:,1)) % Check that the correlation is preserved
|
||||
|
||||
# % Carlos Gias
|
||||
# % Date: 21/08/2011
|
||||
|
||||
# % Reference:
|
||||
# % Prichard, D., Theiler, J. Generating Surrogate Data for Time Series
|
||||
# % with Several Simultaneously Measured Variables (1994)
|
||||
# % Physical Review Letters, Vol 73, Number 7
|
||||
|
||||
# function surrblk = phaseran(recblk,nsurr)
|
||||
|
||||
# % Get parameters
|
||||
# [nfrms,nts] = size(recblk);
|
||||
# if ( rem(nfrms,2) == 0 )
|
||||
# nfrms = nfrms-1;
|
||||
# recblk = recblk(1:nfrms,:);
|
||||
# end
|
||||
|
||||
# % Get parameters
|
||||
# len_ser = (nfrms-1)/2;
|
||||
# interv1 = 2:len_ser+1;
|
||||
# interv2 = len_ser+2:nfrms;
|
||||
|
||||
# % Fourier transform of the original dataset
|
||||
# fft_recblk = fft(recblk);
|
||||
|
||||
# % Create the surrogate recording blocks one by one
|
||||
# surrblk = zeros(nfrms,nts,nsurr);
|
||||
# for k = 1:nsurr
|
||||
# ph_rnd = rand([len_ser 1]);
|
||||
|
||||
# % Create the random phases for all the time series
|
||||
# ph_interv1 = repmat(exp(2*pi*1i*ph_rnd),1,nts);
|
||||
# ph_interv2 = conj(flipud( ph_interv1));
|
||||
|
||||
# % Randomize all the time series simultaneously
|
||||
# fft_recblk_surr = fft_recblk;
|
||||
# fft_recblk_surr(interv1,:) = fft_recblk(interv1,:).*ph_interv1;
|
||||
# fft_recblk_surr(interv2,:) = fft_recblk(interv2,:).*ph_interv2;
|
||||
|
||||
# % Inverse transform
|
||||
# surrblk(:,:,k)= real(ifft(fft_recblk_surr));
|
||||
# end
|
||||
|
||||
# end % End of function
|
||||
|
||||
|
||||
# function [Tv,Av] = SyntWave(P,varargin)
|
||||
# % Function: generate a multi-sinewave
|
||||
# %
|
||||
# % Inputs
|
||||
# % ------
|
||||
# % P = [ P1 P2 ... Pn ] Periods
|
||||
# % varargin = A, T, PH Amplitudes, time, phases
|
||||
# %
|
||||
# % A = [ A1 A2 ... An ] Amplitudes
|
||||
# % T = [ ts tf dt] Time info: from ts to tf with step dt
|
||||
# % PH = [PH1 PH2 ... PHn] Phases (rad)
|
||||
# %
|
||||
# % Outputs
|
||||
# % -------
|
||||
# % Av = SUM(1 to n) of [ A*sin(2*pi*f*t + PH) ]
|
||||
# % Tv Time (ts to tf with step dt)
|
||||
# %
|
||||
# % Default amplitudes are ones
|
||||
# % Default time is from 0 to largest period (1000 steps)
|
||||
# % Default phases are zeros
|
||||
|
||||
# % Check for arguments
|
||||
# if (nargin == 1)
|
||||
# np = length(P);
|
||||
# A = ones(1,np);
|
||||
# T = [0 max(P) max(P)/1000];
|
||||
# PH = zeros(1,np);
|
||||
# elseif (nargin == 2)
|
||||
# np = length(P);
|
||||
# A = varargin{1};
|
||||
# T = [0 max(P) max(P)/1000];
|
||||
# PH = zeros(1,np);
|
||||
# elseif (nargin == 3)
|
||||
# np = length(P);
|
||||
# A = varargin{1};
|
||||
# T = varargin{2};
|
||||
# PH = zeros(1,np);
|
||||
# elseif (nargin == 4)
|
||||
# np = length(P);
|
||||
# A = varargin{1};
|
||||
# T = varargin{2};
|
||||
# PH = varargin{3};
|
||||
# else
|
||||
# fprintf(1,'\n');
|
||||
# error('Wrong number of arguments');
|
||||
# end
|
||||
|
||||
# % Add all waves
|
||||
# Tv = T(1):T(3):T(2);
|
||||
# Av = zeros(1,length(Tv));
|
||||
# for j = 1:np
|
||||
# Av = Av + A(j)*sin(2*pi*Tv/P(j)+PH(j));
|
||||
# end
|
||||
|
||||
# end % End of function
|
||||
|
||||
|
||||
|
|
|
|||
Ładowanie…
Reference in New Issue