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Recent questions tagged discrete-fourier-transform

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TIFR ECE 2015 | Question: 2
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 $X(\omega)=\sum_{n=-\infty}^{\infty} x[n] e^{-j \omega n}$. Then the $\text{DTFT}$ ... zero only at one value of $\omega \in[-\pi, \pi]$ Its maximum value is larger than $1$ Its minimum value is less than $-1$ None of the above

admin asked in Calculus Dec 15, 2022

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GATE ECE 2016 Set 3 | Question: 35
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 to be computed in real time using the radix-$2$ decimation-in- ... by $1$ and $-1$) and the time required for addition/subtraction is negligible, then the maximum value of $N$ is _________

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

by Milicevic3306

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GATE ECE 2016 Set 2 | Question: 33
The Discrete Fourier Transform (DFT) of the $4$-point sequence $x\left [ n \right ]=\left \{ x\left [ 0 \right ],x\left [ 1 \right ], x\left [ 2 \right ], x\left [ 3 \right ] \right \}= \left \{ 3,2,3,4 \right \}$ ... $\left | \frac{X_{1}\left [ 8 \right ]}{X_{1}\left [ 11 \right ]} \right |$ is _________

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

by Milicevic3306

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GATE ECE 2015 Set 2 | Question: 44
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 ܺ$X_{2}(k)$ be $4$-point DFTs of $x_{1}[n]$ and $x_{2}[n]$, respectively. Another ... $4$-point inverse DFT of $X_{3}(k) = X_{1}(k)X_{2}(k).$ The value of $x_{3}[2]$ is ________.

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

by Milicevic3306

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GATE ECE 2014 Set 4 | Question: 45
The $N$-point DFT $X$ of a sequence $x[n]$, $0 \leq n \leq N-1$ is given by $X[k] = \frac{1}{\sqrt{N}} \Sigma_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N}nk}, \: \: \: 0 \leq k \leq N-1.$ Denote this relation as $X=DFT(x)$. For ... $x = \begin{bmatrix} 1 & 3 & 2 & 2 \end{bmatrix}$ $x = \begin{bmatrix} 1 & 2 & 2 & 3 \end{bmatrix}$

Milicevic3306 asked in Continuous-time Signals Mar 26, 2018

by Milicevic3306

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