kopia lustrzana https://github.com/Dsplib/libdspl-2.0
127 wiersze
4.8 KiB
Plaintext
127 wiersze
4.8 KiB
Plaintext
\form#0:\[ e = \max \left( \frac{|x(k) - y(k)| }{ |x(k)|} \right), \quad \quad |x(k)| > 0, \]
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\form#1:\[ e = \max(|x(k) - y(k)| ), ~\qquad \quad~|x(k)| = 0, \]
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\form#2:$ e$
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\form#3:$ C_ord(x)$
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\form#4:\[ C_ord(x) = 2 x C_{ord-1}(x) - C_{ord-2}(x), \]
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\form#5:$ C_0(x) = 1 $
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\form#6:$ C_1(x) = x$
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\form#7:$ U_{ord}(x)$
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\form#8:\[ U_{ord}(x) = 2 x U_{ord-1}(x) - U_{ord-2}(x), \]
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\form#9:$ U_0(x) = 1 $
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\form#10:$ U_1(x) = 2x$
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\form#11:$ x = a + j b $
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\form#12:\[ |x|^2 = x x^* = a^2 + b^2. \]
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\form#13:\[ \textrm{Arccos}(x) = \frac{\pi}{2} - \textrm{Arcsin}(x) = \frac{\pi}{2} -j \textrm{Ln}\left( j x + \sqrt{1 - x^2} \right) \]
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\form#14:\[ \textrm{Arcsin}(x) = j \textrm{Ln}\left( j x + \sqrt{1 - x^2} \right) \]
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\form#15:\[ \textrm{cos}(x) = \frac{\exp(jx) + \exp(-jx)}{2} \]
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\form#16:\[ \textrm{Ln}(x) = j \varphi + \ln(|x|), \]
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\form#17:$\varphi$
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\form#18:\[ \textrm{sin}(x) = \frac{\exp(jx) - \exp(-jx)}{2j} \]
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\form#19:\[ y(k) = \sqrt{x(k)}, \qquad k = 0 \ldots n-1. \]
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\form#20:$ c = a * b$
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\form#21:$a$
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\form#22:$b$
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\form#23:$n = n_0 \times n_1 \times n_2 \times n_3 \times \ldots \times n_p \times m$
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\form#24:$n_i = 2,3,5,7$
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\form#25:$m $
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\form#26:\[ H(z) = \frac{\sum_{n = 0}^{N} b_n z^{-n}} {1+{\frac{1}{a_0}}\sum_{m = 1}^{M} a_m z^{-m}}, \]
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\form#27:$a_0$
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\form#28:$N=M=$
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\form#29:$s(t) = \sin(2\pi \cdot 0.05 t) + n(t)$
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\form#30:$n(t)$
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\form#31:$ n $
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\form#32:$ x(m) $
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\form#33:$ m = 0 \ldots n-1 $
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\form#34:\[ Y(k) = \sum_{m = 0}^{n-1} x(m) \exp \left( -j \frac{2\pi}{n} m k \right), \]
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\form#35:$ k = 0 \ldots n-1 $
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\form#36:$x(m)$
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\form#37:$n$
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\form#38:$Y(k)$
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\form#39:$ n^2 $
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\form#40:\[ y(k) = \sum_{m = 0}^{n-1} x(m) \exp \left( j \frac{2\pi}{n} m k \right), \]
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\form#41:$y(k)$
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\form#42:$ u = \textrm{cd}^{-1}(w, k)$
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\form#43:$ w $
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\form#44:$ k $
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\form#45:$ u = \textrm{sn}^{-1}(w, k)$
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\form#46:$ y = \textrm{cd}(u K(k), k)$
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\form#47:$ u $
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\form#48:$ k_i $
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\form#49:$ K(k) $
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\form#50:\[ K(k) = \frac{\pi}{2} \prod_{i = 1}^{\infty}(1+k_i), \]
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\form#51:$ k_0 = k$
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\form#52:\[ k_i = \left( \frac{k_{i-1}} { 1+\sqrt{1-k_{i-1}^2} } \right)^2 \]
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\form#53:$ k<1 $
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\form#54:$ y = \textrm{sn}(u K(k), k)$
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\form#55:\[ Y(k) = \frac{1}{N} \sum_{m = 0}^{n-1} x(m) \exp \left( j \frac{2\pi}{n} m k \right), \]
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\form#56:$ n = 725760 $
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\form#57:$725760 = 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 9 \cdot 16 $
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\form#58:$ n = 172804 = 43201 \cdot 4 $
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\form#59:$ n = 13 \cdot 17 \cdot 23 \cdot 13 = 66079 $
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\form#60:$\sqrt{2^{31}} = 46340.95$
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\form#61:$x_0$
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\form#62:$x_1$
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\form#63:$x(k) = x_0 + k \cdot dx$
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\form#64:$dx = \frac{x_1 - x_0}{n-1}$
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\form#65:$k = 0 \ldots n-1.$
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\form#66:$dx = \frac{x_1 - x_0}{n}$
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\form#67:$10^{x_0}$
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\form#68:$10^{x_1}$
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\form#69:$x(k) = 10^{x_0} \cdot dx^k$
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\form#70:$dx = \sqrt[n-1]{10^{x_1 - x_0}}$
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\form#71:$dx = \sqrt[n]{10^{x_1 - x_0}}$
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\form#72:$ H(j \omega) $
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\form#73:$ H(j \omega)$
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\form#74:$ H(s) $
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\form#75:\[ H(s) = \frac {\sum_{k = 0}^{N} b_k s^k} {\sum_{m = 0}^{N} a_m s^m}, \]
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\form#76:$ N $
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\form#77:$ s = j \omega $
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\form#78:$ \omega $
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\form#79:$H(s)$
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\form#80:$H(z)$
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\form#81:$ H \left(\mathrm{e}^{j\omega} \right) $
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\form#82:$ 2\pi $
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\form#83:$ \pi $
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\form#84:$ -\pi $
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\form#85:$ H \left(e^{j \omega} \right)$
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\form#86:\[ H(z) = \frac {\sum_{k = 0}^{N} b_k z^{-k}} {\sum_{m = 0}^{N} a_m z^{-m}}, \]
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\form#87:$N$
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\form#88:$z = e^{j \omega} $
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\form#89:$\omega$
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\form#90:$ 2 \pi-$
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\form#91:$2 \pi$
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\form#92:$-\pi$
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\form#93:$ \pi$
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\form#94:$ H \left(e^{j \omega} \right) = H^* \left(e^{-j \omega} \right)$
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\form#95:$\pi$
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\form#96:$ -R_p $
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\form#97:$ H(s)$
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\form#98:$-R_p$
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\form#99:$ R_p $
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\form#100:$-R_s$
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\form#101:$H(j\cdot 1) = -R_s$
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\form#102:\[ H(s) = \frac{\sum_{n = 0}^{N_z} b_n \cdot s^n}{\sum_{m = 0}^{N_p} a_m \cdot s^m} = \frac{\prod_{n = 0}^{N_z}(s-z_n)}{\prod_{m = 0}^{N_p} (s-p_m)} \]
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\form#103:$ F(s) $
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\form#104:$F(s)$
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\form#105:$Y(s) = (H \circ F)(s) = H(F(s))$
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\form#106:\[ H(s) = \frac{\sum\limits_{m = 0}^{n} b_m s^m}{\sum\limits_{k = 0}^{n} a_k s^k}, \quad F(s) = \frac{\sum\limits_{m = 0}^{p} d_m s^m}{\sum\limits_{k = 0}^{p} c_k s^k}, \quad Y(s) = \frac{\sum\limits_{m = 0}^{n p} \beta_m s^m}{\sum\limits_{k = 0}^{n p} \alpha_k s^k} \]
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\form#107:$Y(s) = (H \circ F)(s)$
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\form#108:\[ s \leftarrow \frac{1 - z^{-1}}{1 - z^{-1}}. \]
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\form#109:$\Omega$
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\form#110:\[ \Omega = \tan(\omega / 2). \]
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\form#111:\[ s(t) = \sum\limits_{n = 0}^{n_{\omega}-1} S(\omega_n) \exp(j\omega_n t) \]
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\form#112:$\omega_n$
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\form#113:$S(\omega_n)$
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\form#114:$ I_0(x)$
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\form#115:$ x $
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\form#116:$[0 \ 3]$
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\form#117:$ \textrm{sinc}(x,a) = \frac{\sin(ax)}{ax}$
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\form#118:\[ \textrm{Si}(x) = \int_{0}^{x} \frac{\sin(x)}{x} \, dx\]
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\form#119:$[-6\pi \ 6\pi]$
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\form#120:$a_{ij}$
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\form#121:$P_N(x)$
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\form#122:$N-$
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\form#123:\[ P_N(x) = a_0 + a_1 \cdot x + a_2 \cdot x^2 + a_3 \cdot x^3 + ... a_N \cdot x^N. \]
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\form#124:\[ P_N(x) = a_0 + x \cdot (a_1 + x \cdot (a_2 + \cdot ( \ldots x \cdot (a_{N-1} + x\cdot a_N) \ldots ))) \]
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\form#125:$10^{56}$
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