ambifuwb

Purpose

Wide-band ambiguity function.

Synopsis

[waf,tau,theta] = ambifuwb(x)
[waf,tau,theta] = ambifuwb(x,fmin,fmax)
[waf,tau,theta] = ambifuwb(x,fmin,fmax,N)
[waf,tau,theta] = ambifuwb(x,fmin,fmax,N,trace)

Description

ambifuwb calculates the asymetric wide-band ambiguity function, defined as

$$\begin{eqnarray*} \Xi_x(a,\tau) = \frac{1}{\sqrt{a}}\ \int_{-\infty}^{+\infty} x... ...\infty}^{+\infty} X(\nu)\ X^*(a\nu)\ e^{j2\pi a \tau\nu}\ d\nu. \end{eqnarray*}$$

Name	Description	Default value
x	signal (in time) to be analyzed (the analytic associated signal is considered), of length Nx
fmin, fmax	respectively lower and upper frequency bounds of the analyzed signal. When specified, these parameters fix the equivalent frequency bandwidth (both are expressed in Hz)	0, 0.5
N	number of Mellin points. This number is needed when fmin and fmax are forced	Nx
trace	if non-zero, the progression of the algorithm is shown	0
waf	matrix containing the coefficients of the ambiguity function. X-coordinate corresponds to the dual variable of scale parameter ; Y-coordinate corresponds to time delay, dual variable of frequency.
tau	X-coordinate corresponding to time delay
theta	Y-coordinate corresponding to the $\log(a)$ variable, where $a$ is the scale

When called without output arguments, ambifuwb displays the squared modulus of the ambiguity function by means of contour.

Example

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

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

The result, to be compared with the one obtained with the narrow-band ambiguity function, presents a thin high peak at the origin of the ambiguity plane, but with more important sidelobes than with the narrow-band ambiguity function. It means that the narrow-band assumption is not very well adapted to this signal, and that the ambiguity in the estimation of its arrival time and mean frequency is not so small.

See Also

ambifunb.

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