How do I calculate the impulse response?

How do I write the code in order to get the impluse response for the following equation:

y[n]=x[n]+x[n-1]+x[n-2]

Answer 1

[michael scheinfeild]

f=100;% frequanecy
fs=1000;
n=[1:1000]*f/fs;
u=ones(n,1)
x(n)=2*cos(0.5*pi*n).u(n);
% ~ (check indexes im not sure ..)
y(n)=x(n(3:1000))+x(n(2:999))+x((1:998))

[Jens Kritian Poulsen]

There are errors in the solution shown by Michael Scheinfeild, e.g. last line and it doesn't calculate the impulse response.

The solution by John D'Errico is okay (albeit a bit short)

The problem by itself is so simple you don't really need Matlab ([1 1 1] is the impulse response).

Answer 2

[John D'Errico]

Use filter, or conv. WTP?

Compute the vector x, then get y from x.

y = conv(x,[1 1 1]);

and if x was [0 0 1 0 0], then what would y be from the above call to conv?

Answer 3

[MathWorks Support Team]

To compute a 3 tap FIR filter impulse response, use “fft” with the corresponding coefficients. In this case,

>> fft([1 1 1])

Depending on the frequency resolution that you need, you will also have to specify the length of the transformation.

Answer 4

[K Karthika]

A2+B2+2AB=(A+B)2