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instfreq

Instantaneous frequency estimation

Calling Sequence

[FNORMHAT,T] = instfreq(X)
[FNORMHAT,T] = instfreq(X, T)
[FNORMHAT,T] = instfreq(X, T, L)
[FNORMHAT,T] = instfreq(X, T, L, TRACE)

Parameters

X :

a complex vector of size N: the analytic signal to be analyzed.

T :

a vector with integer elements in [L, N-L]: the Time instants (default : 2:length(X)-1).

L :

An integer >=1:

If L=1 (the default value) computes the (normalized) instantaneous frequency of the signal 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.

TRACE :

A boolean (or a real scalar) if true (or nonzero),the progression of the algorithm is shown (default : %f).

FNORMHAT :

a column vector with same size as T: the (normalized) instantaneous frequency.

T :

a row vector: the time instants.

Description

instfreq computes 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.

Examples

[x,iflaw] = fmsin(70,0.05,0.35,25); 
[instf,t] = instfreq(x); 
clf; plot(t',instf,t',iflaw(2:$-1))
xlabel(_("Time"))
ylabel(_("Frequency"))
legend(_("Theoritical"),_("Estimated"))

See also

Authors


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