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For a vector $$\overline x$$ = [x[0], x[1], ....., x[7]], the 8-point discrete Fourier transform (DFT) is denoted by $$... GATE ECE 2022 The Fourier transform X(j$$\omega$$) of the signal$$x(t) = {t \over {{{(1 + {t^2})}^2}}}$$is ____________. GATE ECE 2022 Consider two 16-point sequences x[n] and h[n]. Let the linear convolution of x[n] and h[n] be denoted by y[n], while z[n... GATE ECE 2021 For an N-point FFT algorithm with N =$${2^m}$$which one of the following statements is TRUE? GATE ECE 2010 ## Marks 2 More The Discrete Fourier Transform (DFT) of the 4-point sequence$$x\left[ n \right]$$= {x[0], x[1], x[2], x[3]} = {3, 2,... GATE ECE 2016 Set 2 A continuous-time speech signal$${x_a}(t)$$is sampled at a rate of 8 kHz and the samples are subsequently grouped in ... GATE ECE 2016 Set 3 Consider two real sequences with time- origin marked by the bold value,$${x_1}\left[ n \right] = \left\{ {1,\,2,\,3,\,0...
GATE ECE 2015 Set 1
Two sequences [a, b, c ] and [A, B, C ] are related as, $$\left[ {\matrix{ A \cr B \cr C \cr } } \ri... GATE ECE 2015 Set 1 The N-point DFT X of a sequence x[n] 0 ≤ n ≤ N − 1 is given by$$X\left[ k \right] = {1 \over {\sqrt N }}\,\,\sum\lim...
GATE ECE 2014 Set 4
Consider a discrete time periodic signal x$$\left[ n \right]$$= $$\sin \left( {{{\pi n} \over 5}} \right)$$. Let ak be ...
GATE ECE 2014 Set 1
The DFT of a vector [a b c d] is the vector [α β γ δ ]. Consider the product The DFT of the vector [ p q r s] is a sc...
GATE ECE 2013
The first six points of the 8-point DFT of a real valued sequence are 5, 1 - j3, 0, 3- j4, 0 and 3+ j4. The last two p...
GATE ECE 2011
The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence $$\left\{ {1,\,0,\,2,\,3} \right\}$$ is
GATE ECE 2009
{x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT) ...
GATE ECE 2008

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