Create a function on MATLAB that extracts the main lobe of the magnitude spectrum of a window given the

window type and its length. The function should return the samples corresponding to the main lobe in decibels

$($dB$).$ The input arguments of the function are the window type and the length of window. You may expect as

input the window type to be rectangular, Hamming, and Blackman$-$Harris.

Tip: log$10(0)$ is not well defined, so it$$s a common practice to add a small value such as $1020$ to the magnitude

spectrum before computing it in dB$.$

$2.$ Measure the SNR in the reconstructed signal using the STFT model

Create a function that computes the SNR of a signal using the short$-$time Fourier model $($STFT$).$ Use the timedomain energy definition to calculate the SNR$.$ The input arguments to the function are a wav. file name including

the path, window type, window length, FFT size, and hop size. The function should return the SNR over the entire

length of the input $($SNR$1)$ and the SNR for the segment of signals left after discarding M samples from both the

start and the end, where M is the STFT window length.

Test case: you may run your code using the piano.wav file with $$blackman$$ window, window length $=513,$ FFT

size $=2048$ and hop size $=128.$

$3.$ Computing band$-$wise energy envelopes of a signal

Create a function that computes band$-$wise energy envelopes of a given audio signal using STFT in decibels.

For this task, consider two frequency bands: low and high. The low frequency band is the set of all frequencies

between $0$ and $3000$ Hz and the high frequency band is the set of all frequencies between $3000$ and $10000$ Hz$.$ At

$3$

a given frame, the value of the energy envelope of a band is computed as the sum of squared values of all

frequency coefficient in that band. The input arguments to the function are a wav. file name including the path,

window type, window length, FFT size, and hop size. The function should return a matrix with two columns,

where the first column is the energy envelope of the low frequency band and the second is that of the second

frequency band.

Test case: you may run your code using the piano.wav file with $$blackman$$ window, window length $=513,$ FFT

size $=1024$ and hop size $=128.$

$4.$ Computing an onset detection function

Create a function that computes a simple onset detection function $($ODF$)$ using STFT$.$ Compute two ODFs

for two frequency bands: the set of all frequencies between $0$ and $3000$ Hz and the set of all frequencies between

$3000$ and $10000$ Hz$.$ A brief description of the onset detection function is provided in this document. Set

ODF$(0)=0$ to make the length of the ODF the same as the energy envelope. Remember to apply a half wave

rectification on the ODF. The input arguments to the function are a wav. file name including the path, window

type, window length, FFT size, and hop size. The function should return a matrix with two columns, where the

first column is the ODF computed on the low frequency band and the second column is the ODF computed on

the high frequency band.

Test case: you may run your code using the piano.wav file with $$blackman$$ window, window length $=513,$ FFT

size $=1024$ and hop size $=128.$