Objective of the lab experiment:
The objective of this experiment is to demonstrate how the convolution is used to process signals entering a system.
1. Convolution in the time domain is equivalent to what mathematical operation in the frequency domain?
2. When we convolve the triangular 10 Hz input with the impulse response of the 50 Hz low-pass filter, why is it that the peaks of output become rounded and not a sharp point as in the input triangular function?
3. Why is it that we get no (or very little) output when we convolve the 60 Hz sinusoid with the impulse response of the filter?
4. When we apply the 10 Hz output, which is within the pass band of the filter, we see that we get nearly the same sinusoid in the output except for a time delay. How is the time delay a signal experiences as it passes through a system related to the phase characteristic of the system response?
The impulse response of the filter was recorded experimentally by applying an approximation of the impulse to the filter using the Tower board and storing the output using data acquisition equipment. We shall convolve this impulse response with the various inputs we apply to this filter to check whether we get an output that agrees with the output that was measured experimentally. In this effort, you can use, as your template, the MATLAB file Example_of_convolution.m.
As a first step, using the plot command of MATLAB, plot the impulse response (MATLAB memory variable IR) as a function of time. If you are not familiar with the plot command, run the MATLAB file Example_of_convolution.m located in Doc Sharing. You may also look up help for this command in the MATLAB help menu, where clear examples of how to use this command are given, and also read the MATLAB tutorial MATLAB_intro located in Doc Sharing.