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Re: onedimensional and twodimensional convolution
 To: mathgroup at smc.vnet.net
 Subject: [mg69090] Re: onedimensional and twodimensional convolution
 From: "JensPeer Kuska" <kuska at informatik.unileipzig.de>
 Date: Wed, 30 Aug 2006 06:32:21 0400 (EDT)
 Organization: Uni Leipzig
 References: <ed0v1q$qe$1@smc.vnet.net>
 Sender: ownerwrimathgroup at wolfram.com
Hi,
and when you read future in your signal processing
book you
will find out, that discrete
convolutions/correlations
with real signals can be expressed in the
discrete Fourier domain in a simple way ...
Continue reading !
Regards
Jens
"bd satish" <bdsatish at gmail.com> schrieb im
Newsbeitrag news:ed0v1q$qe$1 at smc.vnet.net...

 Hi buddies ,

 Here is the definition of a 1dimensional
discretetime convolution
 (encountered in Signals & Systems ,etc) of two
functions x[n] and
 h[n] :

 y[n] = Sum[ x[k] * h[nk] , { k , Infiniy ,
Infinity }]

 The above command works when x[n] and y[n] are
functions in the strict
 sense (say , x[n] = Exp[2*pi*n/6] UnitStep[n]
and h[n] = Exp[4*Pi*n/7]
 UnitStep[n] )
 But in Signal processing , we often have lists :

 X= { 1,2,3,1,1 } , H = { 1,4,5,6} etc. where
the entries are the
 function's values at different values of n .
i.e.

 X = { x[0] , x[1] , x[2] , x[3] , x[4] } .
Similarly H = { h[0] , h[1]
 , h[2] , ... } (, say )

 Without using Sum ( and DiscreteDelta ) , is
there any way to directly (&
 quickly) find the convolution sum.
 I'm finding convolution of lists whose lengths
are typically 700 to 1000. So
 the code needs be really fast.

 The Mathematica command " ListConvolve " did
not help me. Anybody plz help
 me out !!

 Also , the 2dimensional convolution of
twovariable functions ,
 f[x,y] and h[x,y] is defined as :

 z[x,y] = Sum[ Sum[ f[m,n] * h[xm , yn] , { m
, Infinity, Infinity } ] ,
 { n , Infinity , Infinity } ]

 But in image processing , we often have nested
lists. In this case ,
 f[x,y] and h[x,y] are matrices :

 f = { { 1,2,3 } , { 4,5,6 } ,{7,8,9} } etc.
Similarly h . There are no
 restrictions on the dimensions of matrices f and
h .

 Mathgroup , plz help me in solving these 1D
and 2D convolutions !!


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