How does "pwelch" function assign frequency bins?

I’m giving a timeseries vector with 14600 data points as an input to the “pwelch” function and getting 2049 data points as an output. I’m not sure how to assign these output points to specific frequencies, I need more info on how the averaging/binning works with this function?

Answer 1

[MathWorks Support Team]

Welch's overlapped segment averaging method reduces the variance in the periodogram by averaging PSD estimates based on segments.

In your case, the signal is 14,600 elements long, so the signal is divided into segments of length 3244 and use the default overlap of 50% or 1622 samples.

In this case the 8 segments have start and end times as follows:

Start points End points

1 3244

1623 4866

3245 6488

4867 8110

6489 9732

8111 11354

9733 12976

11355 14598

Since the segment length is 3244, the help states about the default NFFT value or number of frequency bins:

"If NFFT is specified as empty, NFFT is set to either 256 or the next power of two greater than the length of each section of X, whichever is larger." In this case the next power of two greater than 3244 is 4096.

So, the resulting PSD estimate is obtained by averaging the PSD estimates of the given eight 3244-point segments padded to 4096 points.

The actual frequencies are available as an output from pwelch(). " >> [pxx,w] = pwelch(ts)" returns the normalized frequency vector, w.

They are spaced as (2*pi)/4096 if your do not specify a sampling frequency -- radians/sample. or Fs/4096 if a sampling frequency is specified.

If the signal is real-valued, then by default we only return the non-negative frequencies, so then you will obtain only 2049 points for the PSD estimate and the frequencies, but the frequency resolution (spacing between DFT bins) is as I described.