# Convolution of step signal 100 times that is 100 convolution

Convolution of step signal 100 times that is 100 convolution operations. The Laplace transform is ______________

A. $$\frac{1}{s^{100}}$$

B. $$\frac{1}{s^{50}}$$

C. 1

D. s^100

The question was asked in exam.

I’d like to ask this question from Problems on Initial and Final Value Theorem topic in portion Application of the Laplace Transform in Circuit Analysis of Network Theory

Right option is A. $$\frac{1}{s^{100}}$$

To elaborate: 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 100 convolutions = $$\frac{1}{s^{100}}$$.