Thread Subject: pwelch PSD estimator syntax, please someone?

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

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@gmail.com> wrote in message
news:1193355397.539932.8230@57g2000hsv.googlegroups.com...
> 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
>

 Hi ,
I am wondering if you could help me to estimate PSD from a
discrete series that represents measurements versus Depth.
after constructing PSD, i need to estimate Hurst Exponent
by plotting PSD versus frequency on a log-log plot and get
the slope.

The data looks like X(depth)= .1, .2,.......,
and X-axis values look like =0, .5, 1,......,100

your fast response is highly appreciated.

Ammal


Dutchice@gmail.com wrote in message
<1193355397.539932.8230@57g2000hsv.googlegroups.com>...
> 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
>