periodogram for 200 Hz sample rate returns 129 array length

why periodogram for 200 Hz sample rate, for 1 second, returns an array lenght of 129, if called without parameters. why it's not 100

signal = linspace(0,3000,200)'; %this is 1 second of my signal (200 because that's the sample rate)
[x,y] = periodogram(signal,[],[],200);
x

x = 129×1

1.0e+06 * 2.2500 1.1035 0.2091 0.0750 0.0438 0.0316 0.0222 0.0152 0.0112 0.0093

Answer 1

[Paul]

Hi sam,

signal = linspace(0,3000,200)'; %this is 1 second of my signal (200 because that's the sample rate)
[x,y] = periodogram(signal,[],[],200);
numel(signal)

ans = 200

Because signal is only 200 elements and nfft is set for default, nfft will be (according to periodogram)

nfft = max(256,2^nextpow2(length(signal)))

nfft = 256

The default for "freqrange" is 'onesided', in which case with nfft = 256, x will have length nfft/2 + 1 = 129 (also on periodogram)

[sam]

interesting, so basically what i can do to get 100 is to change my nfft

signal = linspace(0,3000,200)'; %this is 1 second of my signal (200 because that's the sample rate)
[x,y] = periodogram(signal,[],199,200);
numel(x)

ans = 100

the idea is I prefer to end up with 100 Hz and not 129 bins when displaying my spectrogram and other graphical representations.

[Paul]

I don't know what you mean by "100 Hz and not 129 bins," as in I don't know how you're relating Hz and bins. In the original code, the periodogram was computed as

signal = linspace(0,3000,200)'; %this is 1 second of my signal (200 because that's the sample rate)
[x,y] = periodogram(signal,[],[],200);

The resulting frequency vector y has

numel(y)

ans = 129

129 bins and the final frequency in y is

y(end)

ans = 100

100 Hz, which is what happens when nfft is even and freqrange is onesided. With nfft even, numel(y) will always be odd when freqrange is onesided.

In the new code

[x,y] = periodogram(signal,[],199,200);

the frequency vector has 100 bins

numel(y)

ans = 100

but the final frequency point is just short of 100 Hz

y(end)

ans = 99.4975

which is what happens when nfft is odd and freqrange is onesided.

[sam]

I beleive I need to do more reading on nfft, I wanted to end up with a frquency vector of 100 bins only not 129, that's why I thought using 199.

the part that confuses me is if changing the nfft might affect my periodogram results. I guess this is beyond the scope of this post and MATLAB itself.

thank you.

Sam