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Test: Discrete-Time Fourier Transform


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10 Questions MCQ Test Signals and Systems | Test: Discrete-Time Fourier Transform

Test: Discrete-Time Fourier Transform for Electronics and Communication Engineering (ECE) 2023 is part of Signals and Systems preparation. The Test: Discrete-Time Fourier Transform questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Discrete-Time Fourier Transform MCQs are made for Electronics and Communication Engineering (ECE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Discrete-Time Fourier Transform below.
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Test: Discrete-Time Fourier Transform - Question 1

Given a discrete time signal x[k] defined by x[k] = 1, for -2 ≤ k ≤ 2 and 0, for |k| > 2. Then, y[k] = x[3k - 2] is ______________

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 1

y[k] = x [3k-2]
Now, y [0] = x [-2] = 1
Or, y [1] = x [1] = 1
Or, y [2] = x [4] = 0
∴ y[k] = 1, for k = 0, 1 and 0 otherwise.

Test: Discrete-Time Fourier Transform - Question 2

A discrete time signal is given as X [n]  The period of the signal X [n] is ______________

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 2

Given that, N1 = 18, N2 = 14
We know that period of X [n] (say N) = LCM (N1, N2)
∴ Period of X [n] = LCM (18, 14) = 126.

Test: Discrete-Time Fourier Transform - Question 3

F(t) and G(t) are the one-sided z-transforms of discrete time functions f(nt) and g(nt), the z-transform of ∑f(kt)g(nt-kt) is given by _____________

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 3

Given that F (t) and G (t) are the one-sided z-transforms.
Also, f (nt) and g (nt) are discrete time functions, which means that property of Linearity, time shifting and time scaling will be similar to that of continuous Fourier transform. Since, for a continuous Fourier transform, the value of ∑f(kt)g(nt-kt) is given by∑f(nt)g(nt)z-n.
∴ z-transform of ∑f(kt)g(nt-kt) is given by∑f(nt)g(nt)z-n.

Test: Discrete-Time Fourier Transform - Question 4

A Discrete signal is said to be even or symmetric if X(-n) is equal to __________

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 4

We know that any signal be it discrete or continuous is said to be even or symmetric when that signal f(x) = f (-x). Here given signal is X (n). It is a discrete time signal. So, the signal will be even symmetric if X (n) = X (-n).

Test: Discrete-Time Fourier Transform - Question 5

A discrete time signal is as given below 

The period of the signal X [n] is _____________

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 5

Given that, N1 = 4, N2 = 16, N3 = 8
We know that period of X [n] (say N) = LCM (N1, N2, N3)
∴ Period of X [n] = LCM (4, 16, 8) = 16.

Test: Discrete-Time Fourier Transform - Question 6

The time system which operates with a continuous time signal and produces a continuous time output signal is _________

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 6

DTF System operates with a discrete signal, on the other hand time invariant system is a system whose output does not depend explicitly on time. For continuous time system, the inputs as well as output both are CT signals.

Test: Discrete-Time Fourier Transform - Question 7

What is the steady state value of The DT signal F (t), if it is known that F(s)

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 7

The steady state value of the DT signal F(s) exists since all poles of the given Laplace transform have negative real part.
∴F (∞) = lims→0 s F(s)

= 0.

Test: Discrete-Time Fourier Transform - Question 8

A discrete time signal is as given below X [n] = cos (n/8) cos (πn/8)
The period of the signal X [n] is _____________

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 8

We know that for X [n] = X1 [n] × X2 [n] to be periodic, both X1 [n] and X2 [n] should be periodic with finite periods.
Here X2 [n] = cos (πn/8), is periodic with fundamental period as 8/n
But X1 [n] = cos (n/8) is non periodic.
∴ X [n] is a non-periodic signal.

Test: Discrete-Time Fourier Transform - Question 9

The system described by the difference equation y(n) – 2y(n-1) + y(n-2) = X(n) – X(n-1) has y(n) = 0 and n<0. If x (n) = δ(n), then y (z) will be?

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 9

Given equation = y (n) – 2y (n-1) + y (n-2) = X (n) – X (n-1) has y (n) = 0
For n = 0, y (0)2y (-1) + y (-2) = x (0) – x (-1)
∴ y(0) = x(0) – x(-1)
Or, y (n) = 0 for n<0
For n=1, y (1) = -2y (0) + y (-1) = x (1) – x (0)
Or, y (1) = x (1) – x (0) + 2x (0) – 2x (-1)
Or, y (1) = x (1) +x (0) – 2x (-1)
For n=2, y (2) = x (2) – x (1) + 2y (1) – y (0)
Or, y(2) = x(2) – x(1) + 2x(1) + 2x(0) – 4x(-1) – x(0) + x(-1)
∴y (2) = d (2) + d (1) + d (0) – 3d (-1).

Test: Discrete-Time Fourier Transform - Question 10

The Nyquist frequency for the signal x (t) = 3 cos 50πt + 10 sin 300πt – cos 100t is ___________

Detailed Solution for Test: Discrete-Time Fourier Transform - Question 10

We know that Nyquist frequency is twice the maximum frequency, i.e. fs = 2 fm.
The maximum frequency present in the signal is ωm = 300 π or fm = 150 Hz. Therefore the Nyquist frequency fs = 2 fm = 300 Hz.

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