instfreq

Purpose

Instantaneous frequency estimation.

Synopsis

[fnormhat,t] = instfreq(x)
[fnormhat,t] = instfreq(x,t)
[fnormhat,t] = instfreq(x,t,l)
[fnormhat,t] = instfreq(x,t,l,trace)

Description

instfreq computes the estimation of the instantaneous frequency of the analytic signal x at time instant(s) t, using the trapezoidal integration rule. The result fnormhat lies between 0.0 and 0.5.

Name	Description	Default value
x	analytic signal to be analyzed
t	time instants	(2:length(x)-1)
l	if l=1, computes the estimation of the (normalized) instantaneous frequency of x, defined as angle(x(t+1)*conj(x(t-1)) ; if l>1, computes a Maximum Likelihood estimation of the instantaneous frequency of the deterministic part of the signal blurried in a white gaussian noise. l must be an integer	1
trace	if nonzero, the progression of the algorithm is shown	0
fnormhat	output (normalized) instantaneous frequency

Examples

Consider a linear frequency modulation and estimate its instantaneous frequency law with instfreq:

         [x,ifl]=fmlin(70,0.05,0.35,25); 
         [instf,t]=instfreq(x); 
         plotifl(t,[ifl(t) instf]);

Now consider a noisy sinusoidal frequency modulation with a signal to noise ratio of 10 dB:

         N=64; SNR=10.0; L=4; t=L+1:N-L; 
         x=fmsin(N,0.05,0.35,40);
         sig=sigmerge(x,hilbert(randn(N,1)),SNR);
         plotifl(t,[instfreq(sig,t,L),instfreq(x,t)]);

See Also

ifestar2, kaytth, sgrpdlay.

Reference

[1] I. Vincent, F. Auger, C. Doncarli ``A Comparative Study Between Two Instantaneous Frequency Estimators'', Proc Eusipco-94, Vol. 3, pp. 1429-1432, 1994.

[2] P. Djuric, S. Kay ``Parameter Estimation of Chirp Signals'' IEEE Trans. on Acoust. Speech and Sig. Proc., Vol. 38, No. 12, 1990.

[3] S.M. Tretter ``A Fast and Accurate Frequency Estimator'', IEEE Trans. on ASSP, Vol. 37, No. 12, pp. 1987-1990, 1989.

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