User:No4

From Wikipedia, the free encyclopedia

My name's Matej (EN: Matthew / Matt). I'm from Slovakia and currently I live in Czech Republic.


Time

n \in \mathbb{N}\,

k \in \mathbb{N}\,


f_{vz} \in \mathbb{R}_+ \,

t_s = \frac{1}{f_{vz}}\,

t = t_s \cdot n\,

y = function(t)\,


S = \left | DFT(y) \right\vert


n \in \mathbb{N}_0\,

x(n) \in \mathbb{R}\,

A(y) = \left | DHT(y) \right\vert


Y_k = \sum_{n=0}^{N-1} y_n e^{-\frac{2 \pi i}{N} k n} \quad \quad k = 0, \dots, N-1
y_n = \frac{1}{N} \sum_{k=0}^{N-1} Y_k e^{\frac{2\pi i}{N} k n} \quad \quad n = 0,\dots,N-1.


R_{yy}(j) = \sum_n y_n \overline{y}_{n-j} = IDFT(S(f))


Y(k) = \omega(k) \sum_{n=1}^N y(n) cos \frac{\pi(2n-1)(k-1)}{2N}

\quad k=1,...,N

\omega(k) = \begin{cases} \frac{1}{\sqrt{N}} & \quad k = 1 \\ \sqrt{\frac{2}{N}} & \quad 2 \leqq k \leqq N \end{cases}


y(k) = \sum_{k=1}^N \omega(k) Y(k) cos \frac{\pi(2n-1)(k-1)}{2N}

\quad n = 1,...,N

\omega(k) = \begin{cases} \frac{1}{\sqrt{N}} & \quad k = 1 \\ \sqrt{\frac{2}{N}} & \quad 2 \leqq k \leqq N \end{cases}


Y(k) = \sum_{n=1}^N y(n) sin \left (\pi \frac{kn}{N+1}\right )

\quad k=1,...,N

y(k) = \frac{2}{N+1} \sum_{n=1}^N Y(n) sin \left (\pi \frac{kn}{N+1}\right )

\quad k=1,...,N


\quad \Delta f

\quad \tau = \frac{1}{\Delta f}

\quad C(\tau)=IDFT(log(S(f)))

\quad C(\tau)=IDFT(ln(DFT(jf))) = IDFT(ln|DFT(f)| + j\varphi (f))