ambifunb

Purpose

Narrow-band ambiguity function.

Synopsis

[naf,tau,xi] = ambifunb(x)
[naf,tau,xi] = ambifunb(x,tau)
[naf,tau,xi] = ambifunb(x,tau,N)
[naf,tau,xi] = ambifunb(x,tau,N,trace)

Description

ambifunb computes the narrow-band ambiguity function of a signal, or the cross-ambiguity function between two signals. Its definition is given by

$$A_x(\xi,\tau)=\int_{-\infty}^{+\infty} x(s+\tau/2)\ x^*(s-\tau/2)\ e^{-j2\pi \xi s}\ ds.$$

Name	Description	Default value
x	signal if auto-AF, or [x1,x2] if cross-AF (length(x)=Nx)
tau	vector of lag values	(-Nx/2:Nx/2)
N	number of frequency bins	Nx
trace	if non-zero, the progression of the algorithm is shown	0
naf	doppler-lag representation, with the doppler bins stored in the rows and the time-lags stored in the columns
xi	vector of doppler values

This representation is computed such as its 2D Fourier transform equals the Wigner-Ville distribution. When called without output arguments, ambifunb displays the squared modulus of the ambiguity function by means of contour.

The ambiguity function is a measure of the time-frequency correlation of a signal $x$, i.e. the degree of similarity between $x$ and its translated versions in the time-frequency plane.

Examples

Consider a BPSK signal (see anabpsk) of 256 points, with a keying period of 8 points, and analyze it with the narrow-band ambiguity function:

         sig=anabpsk(256,8);
         ambifunb(sig);

The resulting function presents a high thin peak at the origin of the ambiguity plane, with small sidelobes around. This means that the inter-correlation between this signal and a time/frequency-shifted version of it is nearly zero (the ambiguity in the estimation of its arrival time and mean-frequency is very small).

Here is an other example that checks the correspondance between the WVD and the narrow-band ambiguity function by means of a 2D Fourier transform:

         N=128; sig=fmlin(N); amb=ambifunb(sig);
         amb=amb([N/2+1:N 1:N/2],:);
         ambi=ifft(amb).';
         tdr=zeros(N); 		% Time-delay representation
         tdr(1:N/2,:)=ambi(N/2:N-1,:);
         tdr(N:-1:N/2+2,:)=ambi(N/2-1:-1:1,:);
         wvd1=real(fft(tdr));

         wvd2=tfrwv(sig);
         diff=max(max(abs(wvd1-wvd2)))
         diff = 
                1.5632e-13

See Also

ambifuwb.

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