Question

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 ______________

(a) y[k] = 1, for k = 0, 1 and 0 otherwise

(b) y[k] = 1, for k = 1 and -1 for k=-1

(c) y[k] = 1, for k = 0, 1 and -1 otherwise

(d) y[k] = 1, for k = 0, 1 and 0 otherwise

This question was posed to me in semester exam.

Asked question is from Discrete-Time Fourier Transform topic in chapter Fourier Transform of Signals and Systems

Answer 1

Correct answer is (a) y[k] = 1, for k = 0, 1 and 0 otherwise

For explanation I would say: 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.