- #1

Debdut

- 19

- 2

I have two functions ##\phi(t)=\cos(\omega t)## and ##f(t)=u(t)−u(t−k)## with ##f(t)=f(t+T)##, ##u(t)## is the unit step function.

The problem is to find Laplace transform of ##\phi(t) \cdot f(t)##.

I have tried convolution in frequency domain, but unable to solve it because of gamma functions. Also a doubt is arising about the limits of the convolution. Laplace transform of multiplication of simple functions and convolution of their individual transforms are not matching when taking limits like ##0 \rightarrow s## or ##s \rightarrow \infty## or ##0 \rightarrow \infty##.

I have also thought about integration by parts of ##\phi(t)f(t)e^{−st}## as its limits are known: ##0 \rightarrow \infty##. But value of a periodic function at infinity is undefined.

I am stuck, please help...

<Moderator's note: Member has been warned not to remove template.>

The problem is to find Laplace transform of ##\phi(t) \cdot f(t)##.

I have tried convolution in frequency domain, but unable to solve it because of gamma functions. Also a doubt is arising about the limits of the convolution. Laplace transform of multiplication of simple functions and convolution of their individual transforms are not matching when taking limits like ##0 \rightarrow s## or ##s \rightarrow \infty## or ##0 \rightarrow \infty##.

I have also thought about integration by parts of ##\phi(t)f(t)e^{−st}## as its limits are known: ##0 \rightarrow \infty##. But value of a periodic function at infinity is undefined.

I am stuck, please help...

<Moderator's note: Member has been warned not to remove template.>

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