Calculate several samples of t
Calculate several samples of the unit impulse and impulseresponses of y(n) = -0.75 y(n–1) + x(n) – 0.3 x(n–1) – 0.4x(n-2).
Re-write the equation in standard formand then indicate the name of eachcoefficient (a1, etc.). Use the filter() function inMATLAB to check your results to 1 and 2.
Answer:
Code:
N =10; % number of samples
%% unit impulse
x_1 = 0; % x(-1)
x0 = 1;
for n = 1:N-1
x(n) = 0;
end
d = 1;
% in MATLAB index zero won’t exist
% d is for adjusting MATLAB index
% so in below line y(0+d) is true value of y(0)
y(0+d) = 1; % Initial condition assumption
%% impulse response
y(1+d) = -0.75*y(0+d)+ x(1) – 0.3*x0 – 0.4*x_1;
y(2+d) = -0.75*y(1+d)+ x(2) – 0.3*x(1) – 0.4*x0;
for n=3:N-1
y(n+d)= -0.75*y(n-1+d) + x(n) – 0.3*x(n-1) – 0.4*x(n-2);
end
y
%% Filter
b = [ 1 -0.3 -0.4]; %
a = [1 0.75]; %
X = [1, zeros(1,N-1)];
Y = filter(b,a,X)
% subplot(2,1,1)
% plot([0:N-1],y)
% title(‘equation response’)
% subplot(2,1,2)
% plot([0:N-1],Y)
% title(‘filter output’)
Output:
Response from equation
Responsefrom filter()
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