TimeMoments — Computes the time moments of a signal by smoothed pseudo Wigner-Ville distribution.
[T,IFreq,IAmp,IPow,IDisp,delay] = TimeMoments(signal,options)
A real vector of size N. the signal values
A struct with possible fields:
lowpass: an odd length vector of
real numbers. The coefficients of an fir lowpass
filter. The default value is computed by
wfir("lp",195,[0.01 0],"hm",[0,0])
timewindowlength: a real scalar
with positive integer odd value. The time smoothing window
length used in the smoothed pseudo Wigner-Ville
distribution. The default value is 77.
frequencywindowlength: a real
scalar with positive integer odd value. The
frequency smoothing window length used in the smoothed pseudo
Wigner-Ville distribution. The default value is 75.
frequencybins a real
scalar with positive integer power of 2 value. The number of frequency bins used in the smoothed pseudo
Wigner-Ville distribution. The default value is 128.
a real vector of size N+delay. The signal time instants.
a real vectorof size N+delay. The signal first moment in time (instantaneous frequency)
a real vectorof size N+delay. The signal instantaneous amplitude.
a real vector of size N+delay. The
signal time marginal (instantaneous power).
a real vector of size N+delay. The
signal second moment in time (instantaneous dispersion).
a real scalar with integer value. The delay (in sample) between the given signal and
the IFreq, Iamp ,
Idisp , Ipow
signals.
TimeMoments Computes the time moments of a
signal byusing smoothed pseudo Wigner-Ville distribution. The
input signal is extended by delay points
equal to the final value.
The output signals are delayed by delay
points so that IFreq(k) corresponds to
signal(k+delay).
// Create a frequency modulated signal
f0=11;Tmax=10;
freq_sampling=f0*55;
fw=0.3;
// time instants
t=0:1/freq_sampling:Tmax;N=size(t,'*');
// Frequency modulation (linear)
IFreq_ref=f0+linspace(-fw,fw,N);
// Amplitude modulation
n1=round(N/2);
A=[linspace(1,3,n1) linspace(3,2,N-n1)];; //variable amplitude (triangle
// Input signal
sig=A.*cos(2*%pi*IFreq_ref.*t);
[t1,IFreq,IAmp,IPow,IDisp,delay] = TimeMoments(sig);
//Take sampling frequency into account
IFreq=IFreq*freq_sampling;
//Draw results
clf;f.figure_name="SPWVD";
ds=delay/freq_sampling;
t1=(t1-1)/freq_sampling;
// Given signal
subplot(211);
plot(t+ds,sig,"m",t1,IAmp,"b");
a=gca();
a.grid(1:2)=color("gray");
ylabel("Signal&IAmp")
legend(["signal","Amplitude"],"in_lower_left");
// Instantaneous frequency
subplot(212);
dsig=diff(sig);
k=find((dsig(1:$-1)>0)&(dsig(2:$).*dsig(1:$-1)<0));
p=t(k(2:$))-t(k(1:$-1));
IFe=1 ./p;
plot(t1,IFreq,'b',t+ds,IFreq_ref,'r',t(k(1:$-1)+1),IFe,'g');
a=gca();a.data_bounds(:,2)=[10;13];
ylabel("IF (Hz)")
a.grid(1:2)=color("gray");
legend(["SPWVD","Real","Estimated"],"in_upper_left");