gdpower

Purpose

Signal with a power-law group delay.

Synopsis

[x,gpd,f] = gdpower(N)
[x,gpd,f] = gdpower(N,k)
[x,gpd,f] = gdpower(N,k,c)

Description

gdpower generates a signal with a power-law group delay of the form

$$t_x(f) = t_0 + c\ f^{k-1}.$$

The output signal is of unit energy.

Name	Description	Default value
N	number of points in time (must be even)
k	degree of the power-law	0
c	rate-coefficient of the power-law group delay. c must be non-zero.	1
x	time row vector containing the signal samples
gpd	output vector containing the group delay samples, of length round(N/2)
f	frequency bins

Examples

Consider a hyperbolic group-delay law, and compute the Bertrand distribution of it :

         sig=gdpower(128); 
         tfrbert(sig,1:128,0.01,0.3,128,1);

We note that the perfect localization property of the Bertrand distribution on hyperbolic group-delay signals is checked in that case.

Plot the instantaneous frequency law on which the D-Flandrin distribution is perfectly concentrated :

         [sig,gpd,f]=gdpower(128,1/2); 
         plot(gpd,f); 
         tfrdfla(sig,1:128,.01,.3,218,1);

See Also

fmpower.

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