[Python] fftshift or convolve from NumPy module incorrect operation

I'm trying to show in Python equivalence of two signals multiplication in time domain to convolution of them in frequency domain.

Thanks to Baddioes in this post, it was shown that such equivalence can be shown by using fftshift function, but the example was done in Matlab. I expected to get absolutely the same result in Python, but it is not the same, the code is below:

f = 2e6
t = np.linspace(0,1,64)

x = np.sin(2*np.pi*f*t)
y = np.sin(2*np.pi*0.5*f*t)

# multiplication in time domain
signal_xy = x*y

# Fourier of multiplied signals and individual signal
FFT_xy = np.fft.fft(signal_xy)
FFT_x = np.fft.fft(x)
FFT_y = np.fft.fft(y)

# plot the result
plt.plot(abs(FFT_xy))
plt.plot(np.fft.fftshift(abs(np.convolve(np.fft.fftshift(FFT_x),np.fft.fftshift(FFT_y), 'same')))/len(FFT_x), linestyle='--')




I also tried to use fftshift and convolve from scipy module, but the result is absolutely the same.

Does fftshift and convolve functions work correctly in Python?

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