In this problem, you will be given audio signals with noise $($Noisy$.$wav and Noisy$2.$wav$).$ Your goal is to design and apply nulling filters $($a$.$k$.$a$.,$ notch or bandstop filters$)$ to remove the noise.

$($a$)$ For Noisy.wav, use the DTFT function to calculate the DTFT of the audio file. Plot its frequency$-$domain magnitude. Note: your magnitude plot should have at least $10000$ points to properly identify the noise $($it may take a minute or so to compute$).$

$($b$)$ For Noisy.wav, identify the frequency that is contaminated with noise $($Note: you can use "Tools $$ Data Tips" to identify the values of specific points in the plot$).$ Answer in your comments: List this frequency in normalized angular frequency and continuous$-$time cyclic frequency.

$($c$)$ Consider the following nulling FIR filter:

$y[n]=x[n]-2cos(widehat(w{)}_0)x[n-1]+x[n-2],$

This filter can remove the normalized frequency specified by widehat$(w{)}_0.$ For Noisy.wav, design this filter to remove the frequency that you identified in $($b$).$ Use subplot and the DTFT function to plot the magnitude response and phase response of the filter.

$($d$)$ Apply $($i$.$e$.,$ convolve$)$ the nulling filter to the noisy audio data. Use the DTFT function to plot the magnitude response of the filtered audio data. Answer in your comments: What are the differences between the original audio and the output of the nulling filter?

$($e$)$ Listen to the output of the nulling filter. Turn in a $.$wav file of this audio output along with your PDF$.$

$($f$)$ For Noisy$2.$wav, there are multiple contaminated frequencies. Use a similar approach and adapt your strategy $($based on what you previously learned$)$ to remove every frequency and identify the underlying audio. Turn in a $.$wav file of this audio output with your PDF$.$

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