Recent questions tagged discrete-fourier-transform

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

Let $x[n]=a^{\lfloor n \mid}$, ( $a$ is real, $0<a<1$ ) and the discrete time Fourier transform $\text{(DTFT)}$ of $x[n]$ is given by $X(\omega)=\sum_{n=-\infty}^{\infty}...

The $4$-point Discrete Fourier Transform (DFT) of a discrete time sequence $\{1,0,2,3\}$ is$[0,-2+2 j, 2,-2-2 j]$$[2,2+2 \mathrm{j}, 6,2-2 \mathrm{j}]$$[6,1-3 \mathrm{j},...

The first six points of the $8$-point $\text{DFT}$ of a real valued sequence are $5,1-\mathrm{j} 3,0,3-\mathrm{j} 4,0$ and $3+\mathrm{j} 4$. The last two points of the $\...

For a vector $\overline{x} = \left[ x [0], x , \dots, x[7] \right],$ the $\text{8-point}$ discrete Fourier transform $\text{(DFT)}$ is denoted by $\overline{X} = DFT (\ov...

A continuous-time speech signal $x_a(t)$ is sampled at a rate of $8\:kHz$ and the samples are subsequently grouped in blocks, each of size $N$. The DFT of each block is t...

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

Consider two real sequences with time-origin marked by the bold value, $$x_{1}[n] = \{\textbf{1},2,3,0\},\:\:x_{2}[n] = \{\textbf{1},3,2,1\}$$ Let ܺ$X_{1}(k)$ and ܺ$X_{2}...

The $N$-point DFT $X$ of a sequence $x[n]$, $0 \leq n \leq N-1$ is given by $$X[k] = \frac{1}{\sqrt{N}} \Sigma_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N}nk}, \: \: \: 0 \leq k...