Question: Filtering a Pulse from Noise Filter the signals pnd_ l and pnd_2 with both the IIR and FIR filters. Since the noise occupies a different frequency band from the signal, either filter should remove the noise and make it easy to fi nd the pulse.

a. Plot the output signals for the IIR filter, and from these plots estimate, as best you can, the time de lay of the pulse in each of the two received signals. Explain your time-delay measurements in terms of the group de lay curves plotted in Exercises 1 and 2.

b. Repeat part (a) with the FIR filter.

c. Describe any differences in pulse shape that you observe. Ex plain how the constant group delay of the FIR filter and nonuniform group delay of the IIR filter determine the quality of the output signal. Which filter, FIR or !IR, performs better for this application?

Exercises 1: Group Delay of the IIR Filter

a. Generate and plot the first 150 points of the impulse response of the IIR filter.

b. Compute and plot its frequency response magnitude and its group delay.

c. Plot the signals xl and x2 and the air Fourier transforms. Use these plots and the plots of the magnitude and group delay from part (b) to estimate the output you will get from running each sequence through the !IR system.

d. Verify your estimate in part (c) by explicitly computing the outputs due to xl and x2 using filter.

Exercises 2: Group Delay of the FIR Filter

a. Plot the impulse response of the FIR filter. Then generate and plot its frequency response magnitude and group delay. How could you have anticipated from the impulse response that the group delay would be constant?

b. For the signals xl and x2, what output would you expect to get from processing each sequence with the FIR system. Verify your prediction by explicitly computing the outputs due to xl and x2 using conv or filter.