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Topic: Introduction to Convolution

Software used : Matlab

Course : Signal and Systems Lab

1.

a) Make the flowchart or pseudo code for convolution.

b) Implement convolution in MATLAB.

   Hint: Make a function using the format: functionresult = myconv (a,b)

           Where a and b are input matrix and result is convolutionanswer.

c) Compare it with conv command.

2. Let input signal x be [1, 3, –2, 4, -1] and the system h be[-2, 3, 4, –3, 6]. Find the output of the system y using the convcommand.

3. Now suppose we add another system j = [3, –1, 2, 4, 1] inseries with the above system. Now find the overall response andoutput y of the above system using the conv command. Hint: Thesystems h and j should be convolved first and then the resultantshould be convolved with x to get the overall response.

4. Again suppose now j is attached in parallel to h. Now findthe impulse response y for the system.

5. Now suppose the two systems h and j are again in series and athird system k = [2, 3, 4, 5, 6] has also been attached with themin parallel. Find the impulse response of the overall system andhence the output y. Hint: You will have to make sure that the sizeof the system k be made equal to the resultant of the size of thesystem obtained by convolving the systems h and k that are attachedin series.

Up until now we have supposed that all signals starting point issame say 0. Now suppose the system h starting point is –2, that ofsystem j is 0 and that of system k is 3. Now handle this situationcarefully and get the overall impulse response of the system andhence the output y. Also please draw stem plot of each of systemincluding the input x, systems, h, j, k, the overall response andfinally the output y.

6. Write a program without using conv command and for loop toconvolve two arbitrary length signals. (Hint: Use toeplitzcommand)