Question

Convolution of step signal 49 times that is 49 convolution operations. The Laplace transform is ______________

(a) \(\frac{1}{s^{49}} \)

(b) \(\frac{1}{s^{50}} \)

(c) 1

(d) s^49

The question was posed to me during an online interview.

The origin of the question is Concept of Convolution topic in chapter Signal Transmission Through Linear Systems of Signals and Systems

Answer 1

Right option is (a) \(\frac{1}{s^{49}} \)

Easiest explanation: n times = u (t) * u (t) * …… * u (t)

Laplace transform of the above function = \(\frac{1}{s^n} \), where n is number of convolutions.

∴ Laplace transform for 49 convolutions = \(\frac{1}{s^{49}} \).