ifmt

Purpose

Inverse fast Mellin transform.

Synopsis

x = ifmt(mellin,beta)
x = ifmt(mellin,beta,M)

Description

ifmt computes the inverse fast Mellin transform of mellin.
Warning : the inverse of the Mellin transform is correct only if the Mellin transform has been computed from fmin to 0.5 Hz, and if the original signal is analytic.

Name	Description	Default value
mellin	Mellin transform to be inverted. mellin must have been obtained from fmt with frequency running from fmin to 0.5 Hz
beta	Mellin variable issued from fmt
M	number of points of the inverse Mellin transform	length(mellin)
x	inverse Mellin transform with M points in time

Example

To check the perfect reconstruction property of the inverse Mellin transform, we consider an analytic signal, compute its fast Mellin transform with an upper frequency bound of 0.5, and apply on the output vector the ifmt algorithm:

         sig=atoms(128,[64,0.25,32,1]); clf;
         [mellin,beta]=fmt(sig,0.08,0.5,128); 
         x=ifmt(mellin,beta,128); plot(abs(x-sig));

We can observe the almost perfect equality between x and sig.

See Also

fmt, fft, ifft.

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