Question

Question : 14 : Signals :

How to \(\color{red}{\text{Convolve}}\) these two signals given below:

\(\color{green}{x(t) = \begin{cases} t && 0 \lt t \le T \\ 0 && otherwise \end{cases}}\)

\(\color{blue}{h(t) = \begin{cases} 1 && 0 \lt t \le 2T \\ 0 && otherwise \end{cases}}\)

Answer 1

I have got a result, I just want to check it if it is true or not..

Answer 2

My result is :

\(y(t) = \begin{cases} 0 && t \lt 0 \\ \frac{1}{2}t^2 && 0 \le t \lt T\\ \frac{1}{2}T^2 && T \le t \lt 2T \\ -\frac{1}{2}t^2 + 2 \cdot t \cdot T - \frac{3}{2}T^2 && 2T \le t \lt 3T\\0 && t \gt 3T\end{cases}\)

Answer 3

But my book is giving all answers other than this.. :P

Answer 4

paaji u can use laplace transform

Answer 5

and thn take its inverse laplace

Answer 6

See, in Conventional exams, it comes that solve by using Convolution, then we should not try to use Fourier as well as Laplace Analysis if possible.. :)

Answer 7

Suppose you know Convolution, and you have not read Laplace or Fourier Analysis yet, then what will be your approach towards it?? :P

Will you wait till you learn Fourier And Laplace Transforms?? :P