Reference no: EM131724802

Lab - IIR Filters

Theory:

IIR filters are digital filters with infinite impulse responses, and hence are called infinite impulse response filters. Unlike FIR filters, IIR filters have a feedback mechanism or recursive part. Because of their infinite impulse response, IIR filters can be matched to analog filters which also have an infinite impulse response. Typically, IIR filters can meet a given specification with a much lower filter order than corresponding FIR filters, thus making them more efficient and requiring less calculations.

Prelab Assignment:

Lab:
1. A digital resonator is to be designed with ω₀ = Π/4 that has two zeros at z = 0.
a. Compute and plot the frequency response of this resonator for r = 0.8, 0.9 and 0.99.
b. For each case in part 1, determine the 3 dB bandwidth and the resonant frequency ω_r from your magnitude plots.
c. Check if your results in part 2 are in agreement with the theoretical results.

2. A digital resonator is to be designed with ω₀ = Π/4 that has two zeros at z = 1 and z = -1.
a. Compute and plot the frequency response of this resonator for r = 0.8, 0.9, and 0.99.
b. For each case in part 1 determine the 3 dB bandwidth and the resonant frequency ω_r from your magnitude plots.

3. We want to design a digital resonator with the following requirements: a 3 dB bandwidth of 0.05 rad, a resonant frequency of 0.375 cycles/sam, and zeros at z = 1 and z = -1. Using trial and error approach, determine the difference equation of the resonator.

4. A notch filter is to be designed with a null at the frequency ω₀ = Π/2.
a. Compute and plot the frequency response of this notch filter for r = 0.7, 0.9 and 0.99.
b. For each case in part 1, determine the 3 dB bandwidth from your magnitude plots.
c. By trial-and-error approach, determine the value of r if we want the 3 dB bandwidth to be 0.04 radians at the null frequency ω₀ = Π/2.

5. Repeat 4 for a null of ω₀ = Π/6.

6. A speech signal with bandwidth of 4 kHz is samples at 8 kHz. The signal is corrupted by sinusoids with frequencies 1kHz, 2kHz and 3kHz.
a. Design an IIR filter using notch filter components that eliminates these sinusoidal signals.
b. Choose the gain of the filter so that the maximum gain is equal to 1, and plot the log-magnitude response of your filter.

c. Load the handel sound file in MATLAB and add the preceding three sinusoidal signals to create a corrupted sound signal. Now filter the corrupted sound signal using your filter and comment on its performance.