Is there a way to find the impulse response of the given system without using a loop?

Is it possible to modify this code so that it would work without using any loop for the given system.

%y[n] = 1/3(x[n]-x[n-3])
y = zeros(1,21);
for i = 1:1:21 
    if i <= 3
        y(i) = x(i)*(1/3);
    else
        y(i) = (x(i)-x(i-3))*(1/3);
    end
end

Answer 1

[Ram Sreekar]

Hi Akash knrs,

It is possible to calculate y without using a loop. You can refer to the example code given below.

% Consider,
x = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21];

y = zeros(1,21);

y(1:3) = x(1:3) * (1/3);
y(4:end) = (x(4:end) - x(1:end-3)) * (1/3);

Hope this helps you resolve your query.

Answer 2

[Mahesh Chilla]

Hi Akash!

Assuming that the array "x" is the unit impulse. To solve this, you can create an array of "x" which is shifted by 3 units to the right.

The following code will solve this

n = 1:21 ; %defining an interval
x = (n==0) ; % unit impulse
x3 = (n==3) ; % unit impulse shifted by 3 units to the right
y = (x-x3)/3 ;

To learn more about the functions used in the code, refer the MATLAB's documentation.

• https://www.mathworks.com/help/signal/gs/impulse-step-and-ramp-functions.html

Hope this helps,

Thank you!!