kopia lustrzana https://github.com/Dsplib/libdspl-2.0
424 wiersze
6.0 KiB
TeX
424 wiersze
6.0 KiB
TeX
\documentclass{article}
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\usepackage{ifthen}
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\usepackage{epsfig}
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\usepackage[utf8]{inputenc}
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\usepackage{newunicodechar}
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\newunicodechar{⁻}{${}^{-}$}% Superscript minus
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\newunicodechar{²}{${}^{2}$}% Superscript two
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\newunicodechar{³}{${}^{3}$}% Superscript three
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\pagestyle{empty}
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\begin{document}
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\[ e = \max \left( \frac{|x(k) - y(k)| }{ |x(k)|} \right), \quad \quad |x(k)| > 0, \]
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\pagebreak
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\[ e = \max(|x(k) - y(k)| ), ~\qquad \quad~|x(k)| = 0, \]
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\pagebreak
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$ e$
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\pagebreak
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\[ e = \max \left( \frac{|x(k) - y(k)|}{|x(k)|} \right), \quad \quad |x(k)| > 0, \]
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\pagebreak
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$ C_ord(x)$
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\pagebreak
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\[ C_ord(x) = 2 x C_{ord-1}(x) - C_{ord-2}(x), \]
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\pagebreak
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$ C_0(x) = 1 $
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\pagebreak
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$ C_1(x) = x$
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\pagebreak
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$ U_{ord}(x)$
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\pagebreak
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\[ U_{ord}(x) = 2 x U_{ord-1}(x) - U_{ord-2}(x), \]
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\pagebreak
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$ U_0(x) = 1 $
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\pagebreak
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$ U_1(x) = 2x$
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\pagebreak
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$ x = a + j b $
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\pagebreak
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\[ |x|^2 = x x^* = a^2 + b^2. \]
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\pagebreak
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\[ \textrm{Arccos}(x) = \frac{\pi}{2} - \textrm{Arcsin}(x) = \frac{\pi}{2} -j \textrm{Ln}\left( j x + \sqrt{1 - x^2} \right) \]
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\[ \textrm{Arcsin}(x) = j \textrm{Ln}\left( j x + \sqrt{1 - x^2} \right) \]
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\[ \textrm{cos}(x) = \frac{\exp(jx) + \exp(-jx)}{2} \]
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\[ \textrm{Ln}(x) = j \varphi + \ln(|x|), \]
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$\varphi$
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\[ \textrm{sin}(x) = \frac{\exp(jx) - \exp(-jx)}{2j} \]
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\pagebreak
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\[ y(k) = \sqrt{x(k)}, \qquad k = 0 \ldots n-1. \]
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\pagebreak
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$ c = a * b$
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\pagebreak
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$a$
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$b$
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\pagebreak
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$n = n_0 \times n_1 \times n_2 \times \ldots \times n_p \times m$
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\pagebreak
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$n_i = 2,3,5,7$
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\pagebreak
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$m $
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\pagebreak
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\[ H(z) = \frac{\sum_{n = 0}^{N} b_n z^{-n}} {1+{\frac{1}{a_0}}\sum_{m = 1}^{M} a_m z^{-m}}, \]
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\pagebreak
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$a_0$
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$N=M=$
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\pagebreak
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$H(z)$
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\pagebreak
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$s(t) = \sin(2\pi \cdot 0.05 t) + n(t)$
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$n(t)$
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$ n $
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\pagebreak
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$ x(m) $
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$ m = 0 \ldots n-1 $
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\pagebreak
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\[ Y(k) = \sum_{m = 0}^{n-1} x(m) \exp \left( -j \frac{2\pi}{n} m k \right), \]
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\pagebreak
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$ k = 0 \ldots n-1 $
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\pagebreak
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$x(m)$
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$n$
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$Y(k)$
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$ n^2 $
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\[ y(k) = \sum_{m = 0}^{n-1} x(m) \exp \left( j \frac{2\pi}{n} m k \right), \]
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$y(k)$
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$ u = \textrm{cd}^{-1}(w, k)$
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$ w $
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$ k $
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$ u = \textrm{sn}^{-1}(w, k)$
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\pagebreak
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$ y = \textrm{cd}(u K(k), k)$
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$ u $
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$ k_i $
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$ K(k) $
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\[ K(k) = \frac{\pi}{2} \prod_{i = 1}^{\infty}(1+k_i), \]
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$ k_0 = k$
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\pagebreak
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\[ k_i = \left( \frac{k_{i-1}} { 1+\sqrt{1-k_{i-1}^2} } \right)^2 \]
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$ k<1 $
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$ y = \textrm{sn}(u K(k), k)$
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\[ Y(k) = \frac{1}{N} \sum_{m = 0}^{n-1} x(m) \exp \left( j \frac{2\pi}{n} m k \right), \]
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$n = n_0 \times n_1 \times n_2 \times n_3 \times \ldots \times n_p \times m$
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$n = n_0 \times n_1 \times n_2 \ldots \times n_p \times m$
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$ n = 725760 $
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$725760 = 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 9 \cdot 16 $
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$ n = 172804 = 43201 \cdot 4 $
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$ n = 13 \cdot 17 \cdot 23 \cdot 13 = 66079 $
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$\sqrt{2^{31}} = 46340.95$
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\pagebreak
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$x_0$
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$x_1$
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\pagebreak
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$x(k) = x_0 + k \cdot dx$
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$dx = \frac{x_1 - x_0}{n-1}$
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$k = 0 \ldots n-1.$
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$dx = \frac{x_1 - x_0}{n}$
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$10^{x_0}$
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$10^{x_1}$
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$x(k) = 10^{x_0} \cdot dx^k$
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$dx = \sqrt[n-1]{10^{x_1 - x_0}}$
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\pagebreak
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$dx = \sqrt[n]{10^{x_1 - x_0}}$
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\pagebreak
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$ H(j \omega) $
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$ H(j \omega)$
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$ H(s) $
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\[ H(s) = \frac {\sum_{k = 0}^{N} b_k s^k} {\sum_{m = 0}^{N} a_m s^m}, \]
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\pagebreak
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$ N $
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\pagebreak
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$ s = j \omega $
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$ \omega $
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$H(s)$
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$ H \left(\mathrm{e}^{j\omega} \right) $
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$ 2\pi $
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$ \pi $
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$ -\pi $
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$ H \left(e^{j \omega} \right)$
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\pagebreak
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\[ H(z) = \frac {\sum_{k = 0}^{N} b_k z^{-k}} {\sum_{m = 0}^{N} a_m z^{-m}}, \]
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\pagebreak
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$N$
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\pagebreak
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$z = e^{j \omega} $
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$\omega$
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$ 2 \pi-$
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$2 \pi$
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$-\pi$
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$ \pi$
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$ H \left(e^{j \omega} \right) = H^* \left(e^{-j \omega} \right)$
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$\pi$
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$ -R_p $
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$ H(s)$
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\pagebreak
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$-R_p$
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$ R_p $
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\pagebreak
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$-R_s$
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$H(j\cdot 1) = -R_s$
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\pagebreak
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\[ H(s) = \frac{\sum_{n = 0}^{N_z} b_n \cdot s^n}{\sum_{m = 0}^{N_p} a_m \cdot s^m} = \frac{\prod_{n = 0}^{N_z}(s-z_n)}{\prod_{m = 0}^{N_p} (s-p_m)} \]
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\pagebreak
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\[ H(z) = \sum_{n = 0}^{ord} h_n z^{-n} \]
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$ F(s) $
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$F(s)$
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$Y(s) = (H \circ F)(s) = H(F(s))$
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\[ H(s) = \frac{\sum\limits_{m = 0}^{n} b_m s^m} {\sum\limits_{k = 0}^{n} a_k s^k}, \quad F(s) = \frac{\sum\limits_{m = 0}^{p} d_m s^m} {\sum\limits_{k = 0}^{p} c_k s^k}, \quad Y(s) = \frac{\sum\limits_{m = 0}^{n p} \beta_m s^m} {\sum\limits_{k = 0}^{n p} \alpha_k s^k} \]
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$Y(s) = (H \circ F)(s)$
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\[ s \leftarrow \frac{1 - z^{-1}}{1 - z^{-1}}. \]
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\pagebreak
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$\Omega$
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\[ \Omega = \tan(\omega / 2). \]
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\[ s(t) = \sum\limits_{n = 0}^{n_{\omega}-1} S(\omega_n) \exp(j\omega_n t) \]
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\pagebreak
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$\omega_n$
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$S(\omega_n)$
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\pagebreak
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$ I_0(x)$
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$ x $
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$[0 \ 3]$
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$ \textrm{sinc}(x,a) = \frac{\sin(ax)}{ax}$
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\[ \textrm{Si}(x) = \int_{0}^{x} \frac{\sin(x)}{x} \, dx\]
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\pagebreak
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$[-6\pi \ 6\pi]$
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$P_N(x)$
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$N-$
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\[ P_N(x) = a_0 + a_1 \cdot x + a_2 \cdot x^2 + a_3 \cdot x^3 + ... a_N \cdot x^N. \]
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\pagebreak
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\[ P_N(x) = a_0 + x \cdot (a_1 + x \cdot (a_2 + \cdot ( \ldots x \cdot (a_{N-1} + x\cdot a_N) \ldots ))) \]
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\pagebreak
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$10^{56}$
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\pagebreak
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$x(i)$
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$i = 0,1,\ldots n$
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\pagebreak
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$y(i)$
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\[ y(i) = k_x x(i) + d_x, \qquad k_x = \frac{h}{x_{\textrm{max}} - x_{\textrm{min}}}. \]
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\pagebreak
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$x_{\textrm{min}}$
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$x_{\textrm{max}}$
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$d_x$
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\pagebreak
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$h + d_x$
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\end{document}
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