Question about fft

[m3atwad]

Hello,

New poster here. I apologize if this is a dumb question, but I'm trying to find some confirmation (or falsification) regarding my loose understanding of what is happening with the scipy fft funciton. I've pasted my code in here because I can't figure out how to attach my .py file.

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import numpy as np import matplotlib.pyplot as plt from scipy.fftpack import fft, ifft, fftshift   f = 10.0 overSampRate = 30.0 fs = overSampRate * f phase = 1/3.0*np.pi nCyl = 5.0 NFFT = 1024     def sine_wave(f,overSampRate,phase,nCyl):     """     Generate sine wave signal with the following parameters     Parameters:         f : frequency of sine wave in Hertz         overSampRate : oversampling rate (integer)         phase : desired phase shift in radians         nCyl : number of cycles of sine wave to generate     Returns:         (t,g) : time base (t) and the signal g(t) as tuple     Example:         f=10; overSampRate=30;         phase = 1/3*np.pi;nCyl = 5;         (t,g) = sine_wave(f,overSampRate,phase,nCyl)     """     fs = overSampRate*f # sampling frequency     t = np.arange(0,nCyl*1/f-1/fs,1/fs) # time base     g = np.sin(2*np.pi*f*t+phase) # replace with cos if a cosine wave is desired     return (t,g) # return time base and signal g(t) as tuple         # # Plot time domain signal # (t,x) = sine_wave(f,overSampRate,phase,nCyl) #function call fig1, ax1 = plt.subplots(nrows=1, ncols=1) #plt.plot(t,x) # plot using pyplot library from matplotlib package ax1.plot(t, x) ax1.set_title('Sine wave f='+str(f)+' Hz') # plot title ax1.set_xlabel('Time (s)') # x-axis label ax1.set_ylabel('Amplitude') # y-axis label   # # Calc freq domain # X = fft(x)   # not shifted around 0Hz/rad X = X / (len(X)*1.0) X = X * 2.0 nVals = np.arange(start=0, stop=len(X))#*fs/(NFFT*1.0)    # need to cast divisor (NFFT) to float #nVals = np.arange(start=0, stop=NFFT)#*fs/(NFFT*1.0)    # need to cast divisor (NFFT) to float     # plot fft fig2, ax2 = plt.subplots(nrows=1, ncols=1) ax2.plot(nVals, np.abs(X))      # take abs() to convert to complex to real num ax2.set_title('Double Sided FFT - with FFTShift') ax2.set_xlabel('Sample points (N-point DFT)') ax2.set_ylabel('DFT Values')   plt.show()      # display the figure

In this code I basically make a sine wave and plug it into the fft function on line #50.

My questions are the following:
1. Is it correct to divide the result by N (number of samples in waveform) and then multiply by 2?
2. If #1 is correct, does the multiply by 2 come in because of the result of the fft always being half the expected magnitude due to the mathemeatics of the DFT?
3. If I do the following for the FFT calculation my output magnitude gets attenuated greatly.
-Change FFT calc on line 50 to this

1	X = fft(x, NFFT)   # not shifted around 0Hz/rad

Now that the NFFT parameter is passed the resulting magnitude is much smaller? What is going on here and why would someone pass this parameter to the FFT function?

Any help is greatly appreciated!