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GATE 2024 Signal & System Foundation Quiz 32

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Question 1

The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence

is denoted by

. Find the value of

is __________.

Question 2

The DFT of a real values signal x[n] is given as {4, 1 + 2j, 2 – 2j, 3 + j, –3, 3 – j, 2 + 2j, 1 – 2j}

Then the value of is______.

Question 3

The DFT of a real value signal is given as X[k] = {10, 2 + 3j, A, 3 – 2j, –5, B, 2 +4j, C}

Evaluate the values of A, B, C?

Question 4

X[k] is the 6-point DFT of x[n]={3,2,1,0,0,3} and

where Y[k] is the 6-point DFT of y[n] and

. Then y[n] ?

Question 5

4 point DFT of a real discreate – time signal x (n) of length 4 is given by

X[k], n = 0, 1, 2, 3 and k = 0, 1, 2, 3. It is given that x (o) = 5, x(1) = 1+j1, x(2) = 0

Then x(3) and x(0), respectively are

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Apr 13ESE & GATE EC