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GATE 2019: Signal & System Quiz 10

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Question 1

An FIR system is described by the system function The system is

Question 2

A continuous-time speech signal xa(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-frequency FFT algorithm. If the processor performs all operations sequentially, and takes 20μs for computing each complex multiplication (including multiplications by 1 and −1) and the time required for addition/subtraction is negligible, then the maximum value of N is _____

Question 3

The DFT of a vector is the vector . Consider the product

The DFT of the vector is a scaled version of

Question 4

The Discrete Fourier Transform (DFT) of the 4-point sequence

If is the DFT of the 12-point sequence, the value of is_______.

Question 5

The N-point DFT X of a sequence

Denote this relation as X = DFT(x). For N = 4, which one of the following sequences satisfies DFT (DFT (x))=x ?

Question 6

{x(n)} is a real-valued periodic sequence with a period N. x(n) and x(k) from N– point. Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence  is
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Aug 22ESE & GATE EC