#### Double check that Discrete Fourier Transform plot is right

I’m trying to transform a file containing a soundwave. I just want to make sure that my transform looks right because it doesn’t look right to me. I unfortunately don’t know how to provide the files I’m using but I will link the problem and plots I’ve made.

Code for Part B:

``````FT1=rfft(sax)
``````
``````FT2=rfft(clar)
``````
``````tsax=np.linspace(0,len(FT1)/44100,len(FT1))
``````
``````tclar=np.linspace(0,len(FT2)/44100,len(FT2))
``````
``````plt.plot(tsax,real(FT1))
``````
``````plt.xlabel('time (s)')
``````
``````plt.title('Saxophone Soundwave Discrete Fourier Transform')
``````
``````plt.figure()
``````
``````plt.plot(tclar,real(FT2))
``````
``````plt.xlabel('time (s)')
``````
``````plt.title('Clarinet Soundwave Discrete Fourier Transform')
``````
``````plt.show()
``````

Code for Part A & C:

plt.figure(figsize=(12, 12))

FT1=rfft(sax)

FT2=rfft(clar)

N=len(FT1)

tsax=np.linspace(0,len(FT1)/44100,len(FT1))

tclar=np.linspace(0,len(FT2)/44100,len(FT2))

tau=tsax[1]

freq=array([k/(2*N*tau) for k in range(N)])

tsax=np.linspace(0,len(sax)/44100,len(sax))

tclar=np.linspace(0,len(clar)/44100,len(clar))

plt.subplot(221)

plt.plot(tsax, sax)

plt.xlabel(‘time (s)’)

plt.title(‘Saxophone Soundwave’)

plt.subplot(223)

plt.plot(tclar, clar)

plt.xlabel(‘time (s)’)

plt.title(‘Clarinet Soundwave’)

plt.subplot(222)

plt.plot(freq/1000, abs(real(FT1)))

plt.xlabel(‘Frequency (kHz)’)

plt.title(‘Saxophone Soundwave Discrete Fourier Transform Coefficients vs Frequency’)

plt.subplot(224)

plt.plot(freq/1000, abs(real(FT2)))

plt.xlabel(‘Frequency (kHz)’)

plt.title(‘Clarinet Soundwave Discrete Fourier Transform Coefficients vs Frequency’)

plt.show()

I was expecting the FFT plot to be more spread out rather than it being so concentrated in such a small region for the Fourier Transformation. I made sure I used the right functions and that it did what it was suppose to do which seems like it did. I made sure my time step tau was right and I think it is. The sample rate is 44100Hz so tau should be 1/44100 or the first nonzero point in the time array. The code looks right yet the plot feels wrong.

Hopefully someone is able to confirm or deny my plots.

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