ECE425 Matlab report

I’m studying for my Programming class and need an explanation.

I attached an instruction about this problem, and the file of code will be sent through email to you, because I could not upload here. Thank you so much.

1. The problem

This project involves designing and implementing a narrow double notch filter to remove two undesired tones from an audio signal while leaving most of the signal untouched. In particular, we have a band-limited audio signal sampled sampling period of T=1/8192 seconds. This is a speech clip with a bandwidth of that of a phone signal. The digital signal can be found in the data file x.mat. The original analog signal is corrupted by the tones created by a phone when pressing the number 1. The tones created originally had continuous-time frequencies of f1=697 Hz and f2=1209 Hz. You can listen to the file in MATLAB after loading it (using >>load x.mat), using the command >>sound(x,Fs).

You are going to process the sampled signal to remove the tones while keeping as much of the signal intact as possible. A discrete double notch filter with two pairs of finite poles and two pairs of finite zeros must be designed to surgically eliminate these undesired tones from the signal (using the pole-zero placement filter design method).

Once you know where you want your poles and zeros, specify H(z) and derive your system difference equation from H(z). Implement the system and processing the data in the file x.mat. Use the filter() command or put the difference equation for the system in a loop. Convince yourself the system is performing correctly by listening to the output signal.

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