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MathGroup Archive 2006

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Re: one-dimensional and two-dimensional convolution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69090] Re: one-dimensional and two-dimensional convolution
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 30 Aug 2006 06:32:21 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <ed0v1q$qe$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup 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 1-dimensional 
discrete-time convolution
| (encountered in Signals & Systems ,etc)  of two 
functions x[n] and
| h[n] :
|
| y[n] = Sum[ x[k] * h[n-k] , { 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 2-dimensional convolution of 
two-variable functions ,
| f[x,y] and h[x,y]  is defined as :
|
| z[x,y] = Sum[ Sum[ f[m,n]  * h[x-m , y-n] , { 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 1-D 
and 2-D convolutions !!
|
| 



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