Learning about Power Spectral Density

Question

I am sorry to ask a basic question. I am new in signal processing and want to know about the difference between PSD and fft.

I have a audio signal. Which I convert into PSD by using pwelch in matlab. But, when I plot this signal, I want to see the frequency (hz) in x axis and energy (db) in y axis.

But, it doesn't show like this way.

Can anybody explain me the relationship between PSD and FFT and also please let me know, how to plot these two things.

Thanks

Answer 1

To put things simply (for the first pass), the FFT is an algorithm that implements the Discrete Fourier Transform (DFT). The DFT takes N points of the input signal and performs a fourier transform. Power spectrum of the signal is got after you plot the square of the magnitude of the FFT output.

So, the DFT takes N points as input and spits out N points as the output. If you think of the signal as a frame of N samples, the DFT finds statistics using only one frame (N points).

However, the pwelch method is an average statistic over multiple frames. The signal can be a very long signal of length (say L) where its length is many times greater than N. The pwelch method starts off by calculating the DFT of the first N samples, then moves ahead to look at the next N samples and so on until all the "frames" have been looked at. So, what you are left with is the DFTs of every frame of sample size N of the signal of length N. Say, N is 256 points and the L is 44100 points.

Therefore, pwelch takes L points (L > N) and spits out N points for each "frame" of length N of a signal of length L.

There are more details involving windowing and whether you want consecutive frames to have some samples that overlap with each other and so on.

I hope this helps as a first pass explanation.