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,

book you
will find out, that discrete
convolutions/correlations
with real signals can be expressed in the
discrete Fourier domain in a simple way ...

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 !!
|
|

```

• Prev by Date: Re: Minor gripe re Table formatting
• Next by Date: RE: using FindRoot to find multiple answers in a domain?
• Previous by thread: Re: one-dimensional and two-dimensional convolution
• Next by thread: Re: high dpi expressions aren't allowed to be exported correctly - got a workaround?