discrete fourier transform

The relationship between any N-length sequence $x[n]$ and its corresponding N-point discrete Fourier transform $X[k]$ is defined as $X[k] = \mathcal{F}\{x[n]\}$. Another sequence $...

For a vector $$\overline x $$ = [x[0], x[1], ....., x[7]], the 8-point discrete Fourier transform (DFT) is denoted by $$\overline X $$ = DFT($$\overline x $$) = [X[0], X[1], .....,...

A finite duration discrete-time signal $x[n]$ is obtained by sampling a continuous - time signal $x(t)=\cos (200 \pi t)$ at sampling instants $t=\frac{n}{400}, n=0,1, \ldots ., 7$....

Let X[k] = k + 1, 0 ≤ k ≤ 7 be 8-point DFT of a sequence x[n], where X[k] = $$\sum\limits_{n = 0}^{N - 1} {x\left[ n \right]{e^{ - j2\pi nk/N}}} $$. The value (correct to two decim...

The Discrete Fourier Transform (DFT) of the 4-point sequence $$x\left[ n \right]$$= {x[0], x[1], x[2], x[3]} = {3, 2, 3, 4 } is x[k] = {X[0], X[1], X[2], X[3]} = {12, 2j, 0, -2j }...

Two sequences [a, b, c ] and [A, B, C ] are related as, $$\left[ {\matrix{ A \cr B \cr C \cr } } \right] = \left[ {\matrix{ 1 \cr 1 \cr 1 \cr } {\mkern 1mu} \,\matrix{ 1 \cr {W_3^{...

The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence $$\left\{ {1,\,0,\,2,\,3} \right\}$$ is

{x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence y (n) = $${1 \over N}\,\...