- #1

- 809

- 0

The following is all in discrete time, n is an integer

We are given that:

[tex] h_2(n) = \delta ( n ) + \delta ( n-1 ) [/tex]

I want to find the convolution of h2[n]*h2[n].

I don't really understand how to solve this properly.

So,

[tex] y(n) = \Sigma_{k=-\infty}^{k=\infty} (\delta(n)+\delta(n-1)) \times (\delta(n-k)+\delta(n-k-1)) [/tex]

So the [tex] (\delta(n)+\delta(n-1)) [/tex] pulls out because it is constant.

So,

[tex] y(n) = (\delta(n)+\delta(n-1)) \Sigma_{k=-\infty}^{k=\infty} \delta(n-k)+\delta(n-k-1) [/tex]

How do I even solve this?

The book gets

h_2(n)*h_2(n) = [tex] \delta(n) + \2\delta(n-1) + \delta(n-2) [/tex]

I don't understand how they get this.

We are given that:

[tex] h_2(n) = \delta ( n ) + \delta ( n-1 ) [/tex]

I want to find the convolution of h2[n]*h2[n].

I don't really understand how to solve this properly.

So,

[tex] y(n) = \Sigma_{k=-\infty}^{k=\infty} (\delta(n)+\delta(n-1)) \times (\delta(n-k)+\delta(n-k-1)) [/tex]

So the [tex] (\delta(n)+\delta(n-1)) [/tex] pulls out because it is constant.

So,

[tex] y(n) = (\delta(n)+\delta(n-1)) \Sigma_{k=-\infty}^{k=\infty} \delta(n-k)+\delta(n-k-1) [/tex]

How do I even solve this?

The book gets

h_2(n)*h_2(n) = [tex] \delta(n) + \2\delta(n-1) + \delta(n-2) [/tex]

I don't understand how they get this.

Last edited: