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# Convolution.slides.p - Convolution and Filtering The Convolution Theorem Convolution and Filtering The Convolution Theorem CS 450 Introduction to

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Convolution and Filtering: The Convolution Theorem Convolution and Filtering: The Convolution Theorem CS 450: Introduction to Digital Signal and Image Processing Bryan Morse BYU Computer Science

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Convolution and Filtering: The Convolution Theorem Introduction Linear Systems and Responses Time/Spatial Frequency Input f F Output g G Impulse Response h Transfer Function H Relationship g = f * h G = FH Is there a relationship?
Convolution and Filtering: The Convolution Theorem Convolution Theorem The Convolution Theorem Let F , G , and H denote the Fourier Transforms of signals f , g , and h respectively. g = f * h g = fh implies implies G = FH G = F * H Convolution in one domain is multiplication in the other and vice versa.

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Convolution and Filtering: The Convolution Theorem Convolution Theorem The Convolution Theorem Thus, F ( f ( t ) * g ( t )) = F ( f ( t )) F ( g ( t )) Likewise, F ( f ( t ) g ( t )) = F ( f ( t )) * F ( g ( t ))
Convolution and Filtering: The Convolution Theorem Convolution Theorem Filtering: Frequency-Domain vs. Spatial (Convolution)

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Convolution Theorem Linear Systems and Responses Time/Spatial Frequency Input f F Output g G Impulse Response h Transfer Function H Relationship
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## This note was uploaded on 03/02/2012 for the course C S 450 taught by Professor Morse,b during the Winter '08 term at BYU.

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Convolution.slides.p - Convolution and Filtering The Convolution Theorem Convolution and Filtering The Convolution Theorem CS 450 Introduction to

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