0.5 Lab 5a - digital filter design (part 1)  (Page 3/5)

Put all three plots on the same figure using the subplot command.

In the next experiment, we will use the filter $H_f\left(z\right)$ to remove an undesirable sinusoidal interference from a speech signal.To run the experiment, first download the audio signal nspeech1.mat , and the M-file DTFT.m Load nspeech1.mat into Matlab using the command load nspeech1 . This will load the signal nspeech1 into the workspace. Play nspeech1 using the sound command, and then plot 101 samples of the signal for the time indices (100:200).

We will next use the DTFT command to compute samples of the DTFT of the audio signal.The DTFT command has the syntax

[X,w]=DTFT(x,M)

where x is a signal which is assumed to start at time $n=0$ , and $M$ specifies the number of output points of the DTFT. The command [X,w]=DTFT(x,0) will generate a DTFT that is the same duration as the input; if thisis not sufficient, it may be increased by specifying M . The outputs of the function are a vector X containing the samples of the DTFT, and a vector w containing the corresponding frequencies of these samples.

Compute the magnitude of the DTFT of 1001 samples of the audio signal for the time indices (100:1100).Plot the magnitude of the DTFT samples versus frequency for $\left|\omega \right|<\pi$ . Notice that there are two large peaks corresponding to the sinusoidalinterference signal. Use the Matlab max command to determine the exact frequency of the peaks.This will be the value of $\theta$ that we will use for filtering with $H_f\left(z\right)$ .

Write a Matlab function FIRfilter(x) that implements the filter $H_f\left(z\right)$ with the measured value of $\theta$ and outputs the filtered signal (Hint: Use convolution).Apply the new function FIRfilter to the nspeech1 vector to attenuate the sinusoidal interference.Listen to the filtered signal to hear the effects of the filter. Plot 101 samples of the signal for the time indices (100:200),and plot the magnitude of the DTFT of 1001 samples of the filtered signal for the time indices (100:1100).

Inlab report

• The time domain plot of 101 samples.
• The plot of the magnitude of the DTFT for 1001 samples.

Design of a simple iir filter

Download the file pcm.mat for the following section.

While zeros attenuate a filtered signal, poles amplify signals that are near their frequency.In this section, we will illustrate how poles can be used to separatea narrow-band signal from adjacent noise. Such filters are commonly used to separate modulatedsignals from background noise in applications such as radio-frequency demodulation.