Problem $5[20$ pts$.]$: Three audio files $($named "Audio$1.$m$4$a$",$ "Audio$2.$m$4$a$",$ and "Audio$3.$m$4$a$")$ have been provided for this problem. There are two files, each containing a single note$/$key played on the piano. The third file has two notes. Play $($and listen$)$ the audio file to understand what is being analyzed. All audio data provided in the files are sampled at $48$ KHz $.$

$($a$)$ Calculate and plot the spectrum of the audio signal$/$data in each file. Determine the dominant frequency of key$/$note $($if possible, guess the note, for those who know to read sheet music$).$ Use appropriate spectral estimation techniques$/$windows as needed and document them in your response. Show both the spectra and the time domain plots. $(10$ points$)$

Note: You may use the MATLAB command "audioread" to load the file into the workspace. There may be minor noise contamination. In addition, you'll notice, as with any real instrument, the sound may contain harmonic components. However, most of the signal power should be concentrated at the frequencies of the keys being played. Make sure you pick up original note and not the harmonics.

$($b$)$ Plot Time Dependent Fourier Transform for the file that has two piano notes$/$keys and demonstrate that the shift in frequency with time corresponding to the notes$/$keys$.$ Based on TDFT$,$ show if the keys were played simultaneously or in time sequence. $(10$ points$)$