Re: pwelch PSD estimator syntax, please someone?

Hi Mario,



In general, if you use 8 segments to estimate the spectrum in a 1024 sample
data series without overlap, each segment's length is



P = 1024/8 = 128.



However, when you allow Welch's method to calculate the spectrum using
overlapped data segments, each segment can be longer. Essentially, with an
overlap of 50%, there will be 9 ½-length segments to divide the entire
series. Therefore, the length of each data segment, P, becomes



P = 1024/(9*0.5) = 227.



This also leads to the fact that the number of overlap points, M, is given
by 113 instead of 64.



So, as you observed, pwelch(x,[],[],[],4) is actually the same as
pwelch(x,227,113,25,4).



Hope this helps,



Honglei



<Dutchice@xxxxxxxxx> wrote in message
news:1193355397.539932.8230@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hi all!

I sometimes feel MATLAB Help documentation really comes examples
short! :(

My question is the following;
I know that the pwelch estimator syntax for a discrete time series
vector x is as follows:
[Pxx,f] = pwelch(x,window,noverlap,nfft,fs)
and that when written as:
[Pxx,f] = pwelch(x,[],[],[],fs)
MATLAB will let for:
window: hamming(P)
noverlap: M
nfft: N
fs: Fs
where the defaults are:
P: number of samples needed to cut the record sample length into 8
segments
M: number of samples overlapping between two adjacent segments in
order to overlap 50%
N: 256
fs: 1 (sampling rate in hertz)

For my case, vector x has the following characteristics:
Sample record lenght: 1024 samples
sampling rate: 4 Hz
Sample input type: Real-valued

So this means that with the following syntax:
[Pxx,f] = pwelch(x,[],[],[],4)
MATLAB should compute:
P = 1024/8 = 128
M = 128*0.5 = 64
N = 256
fs = 4

Now would someone be able to explain please, how come when plotting as
follows;
[Pxx1,f1] = pwelch(x,[],[],[],4)
[Pxx2,f2] = pwelch(x,hamming(128),64,256,4)
loglog(f1,Pxx1,'b',f2,Pxx2,'r')

or also;

pwelch(x,[],[],[],4)
figure
pwelch(x,hamming(128),64,256,4)

the two plots JUST don't fall on each other neatly as if there was
only one plot!? :|
Very very curiously enough they do match perfect, one on other when;

[Pxx1,f1] = pwelch(x,[],[],[],4)
[Pxx2,f2] = pwelch(x,hamming(227),113,256,4)
loglog(f1,Pxx1,'b',f2,Pxx2,'r')

Can someone please explain why? (scaling of the two Pxx1 & Pxx2 to
match the variance of x didn't and shouldn't either make any
difference)
Download link for vector x is here:
http://rapidshare.com/files/65194703/OceanWaveData.dat.html

Cheers,

Mario



.

Relevant Pages

  • Re: determining if two line segments overlap
    ... >that if the line segments touch, then, either the two line segments are ... > on the same ray or they share a common end point. ... >segments lie on the same ray, absmay not be exactly zero due ... Also, if the overlap is very, very ...
    (sci.math.num-analysis)
  • Re: determining if two line segments overlap
    ... > that if the line segments touch, then, either the two line segments are ... > on the same ray or they share a common end point. ... > segments lie on the same ray, absmay not be exactly zero due ... Also, if the overlap is very, very ...
    (sci.math.num-analysis)
  • RE: Any way to automate set intersection discovery?
    ... what data are you using to determine the overlap? ... would then generate a series of queries that append data to that table, ... to tbl_n to get the records that fall in segments ... a single command or query that would give me tables for each section, ...
    (microsoft.public.access.queries)
  • determining if two line segments overlap
    ... What is the best way to determine if two line segments overlap in the ... on the same ray or they share a common end point. ... segments lie on the same ray, absmay not be exactly zero due ...
    (sci.math.num-analysis)
  • Re: DRM - Solution to Flat Fading
    ... >> segments: ... > dramatic re-planning of the Band II spectrum. ... "a bit of a nightmare" means that although it might be difficult, ...
    (alt.radio.digital)