Main: Main Lab Page

Part 2: Discrete Time Convolution

The program has a similar layout as the continuous-time program. To define your own signal, click and drag the dot of the sample you would like to change."

Signal 1:	Signal 2:
Rectangular Triangular Delta Exponential Sinc Non Causal Causal	Rectangular Triangular Delta Exponential Sinc Non Causal Causal

Start					Stop/Clear

Problem 1:

Perform convolutions of the following 3 pairs of signals using the above program.

• (a) Convolve a non causal rectangular signal and a non causal sinc signal. (Take the screenshot and label the graph as graph4)

• (b) Convolve the following two signals. (Take the screenshot and label the graph as graph5)
  

  

• (c) Convolve the following two signals. (Take the screenshot and label the graph as graph6)
  

  

Problem 2:

In part 1, problem 1 of this lab you found the impulse response of a system. Now, we want you to sample that impulse response and the given input signal. Use these sampled signals to perform a discrete time convolution. You can use the program above and set samples which are smaller than 0.1 to zero. Since the program only allows you to enter samples up to n=5, neglect any samples for n>5.

Is the waveform which results from the discrete-time convolution the same as (or similar to) what would be obtained by sampling the result of the continuous-time convolution of the analog signals? Does the sampling rate make a difference? (make comparison in terms of both the shape and sample values)

For sampling rate, use

• (a) 1 s (save the graph of the discrete convolution and label it as graph7)
• (b) 250 ms (save the graph of discrete convolution and label it as graph8)

  Hint: Calculate sample values on paper and then drag the samples to set them to desired values.
  For 1s sampling rate, samples will be taken at 0s,1s,2s,... . For 250ms sampling rate, samples will be taken at 0s, 0.25s, 0.5s,... .