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.TH "idmt" 2 " June 6th 1997" "Fractales Group" "Scilab Function"
.so ../sci.an
.SH NAME
idmt - Inverse Discrete Mellin transform
.sp
Author: Paulo Goncalves
.sp
Computes the Inverse Fast Fourier-Mellin transform of a signal.
.sp
.sp
.SH Usage
\f(CR[\fPx,t\f(CR]\fP = idmt(mellin,beta,\f(CR[\fPM\f(CR]\fP)
.SH Input parameters
.RS
.TP
o
\fBmellin\fP : complex vector \f(CR[\fP1,N\f(CR]\fP
Fourier-Mellin transform to be inverted. For a correct inversion of the Fourier-Mellin
transform, the direct Fourier-Mellin transform \fImellin\fP must have been computed from \fIfmin\fP
to \fB0.5 cycles per sec\fP.
.TP
o
\fBbeta\fP : real vector \f(CR[\fP1,N\f(CR]\fP
Variable of the Mellin transform \fImellin\fP.
.TP
o
\fBM\fP : positive integer.
Number of time samples to be recovered from \fImellin\fP.
.RE
.SH Output parameters
.RS
.TP
o
\fBx\fP : complex vector \f(CR[\fP1,M\f(CR]\fP
Inverse Fourier-Mellin transform of \fImellin\fP.
.TP
o
\fBt\fP : time variable of the Inverse Fourier-Mellin transform \fIx\fP.
.RE
.SH Description
The Inverse Fourier-Mellin transform can be viewed as an Inverse Fast
Fourier Transform which result is assumed geometrically sampled. To
recover the initial time signal, a Discrete Inverse Fourier Transform
is applied to this geometrically Fourier representation.
\fBImportant\fP The Inverse Fourier-Mellin transform is correct only if
the direct Fourier-Mellin transform has been computed from \fIfmin\fP
to \fB0.5 cycles per sec.\fP
.SH See also:
dmt, dilate
.SH Example:
\fI Signal synthesis \fP
.sp
.ft CR
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x = morlet(0.1,32) ;
plot(x)
.fi
.ec
.ft P
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\fI Computation of the Mellin transform\fP
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.ft CR
.nf
[mellin,beta] = dmt(x,0.01,0.5,128) ;
plot(beta,abs(mellin))
.fi
.ec
.ft P
.sp
\fI Computation of the Inverse Mellin transform\fP
.sp
.ft CR
.nf
[y,t] = idmt(mellin,beta,65) ;
plot(t,abs(x-y))
.fi
.ec
.ft P
.sp
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