fmt

Purpose

Fast Mellin Transform.

Synopsis

[mellin,beta] = fmt(x)
[mellin,beta] = fmt(x,fmin,fmax)
[mellin,beta] = fmt(x,fmin,fmax,N)

Description

fmt computes the Fast Mellin Transform of signal x.

Name	Description	Default value
x	signal in time
fmin, fmax	respectively lower and upper frequency bounds of the analyzed signal. These parameters fix the equivalent frequency bandwidth (expressed in Hz). When unspecified, you have to enter them at the command line from the plot of the spectrum. fmin and fmax must be between 0 and 0.5
N	number of analyzed voices. N must be even	auto1
mellin	the N-points Mellin transform of signal x
beta	the N-points Mellin variable

The Mellin transform is invariant in modulus to dilations, and decomposes the signal on a basis of hyperbolic signals. This transform can be defined as:

$$M_x(\beta)=\int_0^{+\infty} x(\nu)\ \nu^{j2\pi \beta-1}\ d\nu$$

where $x(\nu)$ is the Fourier transform of the analytic signal corresponding to $x(t)$. The $\beta$-parameter can be interpreted as a hyperbolic modulation rate, and has no dimension; it is called the Mellin's scale.

In the discrete case, the Mellin transform can be calculated rapidly using a fast Fourier transform (fft). The fast Mellin transform is used, for example, in the computation of the affine time-frequency distributions.

¹ This value, determined from fmin and fmax, is the next-power-of-two of the minimum value checking the non-overlapping condition in the fast Mellin transform.

Example

         sig=altes(128,0.05,0.45); 
         [mellin,beta]=fmt(sig,0.05,0.5,128);
         plot(beta,real(mellin));

See Also

ifmt, fft, ifft.

References

[1] J. Bertrand, P. Bertrand, J-P. Ovarlez ``Discrete Mellin Transform for Signal Analysis'' Proc IEEE-ICASSP, Albuquerque, NM USA, 1990.

[2] J-P. Ovarlez, J. Bertrand, P. Bertrand ``Computation of Affine Time-Frequency Representations Using the Fast Mellin Transform'' Proc IEEE-ICASSP, San Fransisco, CA USA, 1992.

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