white noise has flat power spectral density

Question

I am trying to prove that the white noise has constant power spectral density using matlab but the amplitude of the spectrum looks like random amplitude.

can anyone tell me why?

here is my code.

noise = randn(1,10000);
fft_noise=fft(noise);
plot(abs(fft_noise(1:5000)))

thanks.

Answer 1

您需要平均一堆（大量定律）的白噪声FFT才能接近平均功率谱密度。

Answer 2

If you take the FFT of an independent set of random variables from the same distribution, then you'll get an independent set of random variables from the same distribution since the inverse Fourier transform is (more or less) the same as the Fourier transform. The point is that the expected value for each frequency is the same.

Answer 3

you need to multiple the fft by the complex conjugate of the fft to show a flat PSD. ie change

fft_noise=fft(noise);

to

fft_noise=fft(noise).*conj(fft(noise));