EE 322/522 Linear Systems II
Computer Project 2: Convolution and Simulation of Linear Systems
Due Date: May 5, 2009
1. Use convolution sum to find the response of an LTI system. Let the input signal be given by:
( ) 2*( ( -0.05)- ( - 0.64)),x t u t u t
where,
( ) ut
denotes a unit step function. The Impulse Response of the LTI system is given by,
-4
( ) e ( ( ) - ( - 0.8)),
t
h t u t u t
(an FIR filter)
Both the input signal and the impulse response are to be sampled with a sampling interval of
T=0.01s.
(a) INPUT GENERATION:
The input is sampled from t = 0 and exactly 64 samples are collected. Hand-calculate the number
of zeros at the beginning of the input and the number of ones. Then use the MATLAB commands
"ones" and "zeros" to create the input sequence, x(n). Note that, N1 = 64.
Examples:
>> v1 = zeros(1,4); % Creates a row vector with 4 zeros, i.e., v1 = [0 0 0 0]
>> v2 = ones(1,5); % Creates a row vector with 5 ones. i.e., v2 = [1 1 1 1 1]
>> v3 = [v1 v2]; % Concatenates v1 and v2 to form a larger row vector v3.
% In this case, v3 = [0 0 0 0 1 1 1 1 1].
>> v3 = [zeros(1,4) ones(1,5)] ; % Is equivalent to the previous three commands.
>> length(v3); % Will return the length of the vector v3.
% In this case, the result is 9.
- The nth member of an array can be addressed by, x(n). For example, if x is formed as,
>> x = [-1 3 -5 4 2 4];
then, x(1) =-1, x(2)=3, and so on. The
m
th through
n
th members of a sequence can be
addressed by x(m:n). In the above example, x(1:3) = [-1 3 -5] and x(4:6) = [4 2 4].
