Strange FFT spectrum from a near perfect sinusoid

Question

I have retrieved some signal in my Abaqus simulation for verification purpose. The true signal shall be a perfect sinusoid at 300kHz and I performed fft on the sampled signal using scipy.fftpack.fft.

But I got a strange spectrum as shown below (sorry that I am too lazy to scale the x-axis of the spectrum to the correct frequency). In the same figure, I sliced the signal into pieces and plotted in the time domain. I also repeated the same process for a pure sine wave. This totally surprises me. As indicated below in the code, sampling frequency is 16.66x of the frequency of the signal. At the moment, I think it is due to the very little error in the sampling period. In theory, Abaqus shall sample it in a regular time interval. As you can see, there is some little error so that the dots in my signal appear to be thicker than the perfect signal. But does such a small error give a striking difference in the frequency spectrum? Otherwise, why is the frequency spectrum like that?

FYI1: This is the magnified fft spectrum of my signal:

FYI2: This is the python code that was used to produce the above figures

def myfft(x, k, label):
    plt.plot(np.abs(fft(x))[0:k], label = label)
    plt.legend()

plt.subplot(4,1,1)
for i in range(149800//200):
    plt.plot(mysignal[200*i:200*(i+1)], 'bo')
plt.subplot(4,1,2)
myfft(mysignal,150000//2, 'fft of my signal')
plt.subplot(4,1,3)
[Fs,f, sample] =  [5e6,300000, 150000]
x = np.arange(sample)
y = np.sin(2 * np.pi * f * x / Fs)
for i in range(149800//200):
    plt.plot(y[200*i:200*(i+1)], 'bo')
plt.subplot(4,1,4)
myfft(y,150000//2, 'fft of a perfect signal')
plt.subplots_adjust(top = 2, right = 2)

FYI3: Here is my signal in .npy and .txt format. The signal is pretty long. It has 150001 points. The .txt one is the raw file from Abaqus. The .npy format is what I used to produce the above plot - (1) the time vector is removed and (2) the data is in half precision and normalized.

Your FFT result appears almost sinusoidal in the frequency domain. This generally implies some impulse-like-thing in the time domain. Your plots of the time domain don't show that impulse - but I think your time-domain plots skip the very end of the waveform. Maybe there's something going on there? — Eric Backus

Mouse On Mars Mouse On Mars · Accepted Answer · 2019-03-17T15:08:18

Any standard FFT algorithm you use operates on the assumption that the signal you provide is uniformly sampled. Uniform in this context means equally spaced in time. Your signal is clearly not uniformly sampled, therefore the FFT does not "see" a perfect sine but a distorted version. As a consequence you see all these additional spectral components the FFT computes to map your distorted signal to the frequency domain. You have two options now. Resample your signal i.e. it is uniformly sampled and use your off the shelf FFT or take a non-uniform FFT to get your spectrum. Here is one library you could use to calculate your non-uniform FFT.

Strange FFT spectrum from a near perfect sinusoid

1 Answers