filter2

# Filter2 - Fourier Transform Analytic geometry gives a coordinate system for describing geometric objects Fourier transform gives a coordinate

This preview shows pages 1–10. Sign up to view the full content.

Fourier Transform Analytic geometry gives a coordinate system for describing geometric objects. Fourier transform gives a coordinate system for functions.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Decomposition of the image function The image can be decomposed into a weighted sum of sinusoids and cosinuoids of different frequency. Fourier transform gives us the weights
Basis P=(x,y) means P = x(1,0)+y(0,1) Similarly: + + + + = ) 2 sin( ) 2 cos( ) sin( ) cos( ) ( 2 2 1 2 2 1 1 1 θ a a a a f

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
cosc a sin sin cos ) sin( : such that , , 2 1 2 1 2 1 = = + = + 5 2200 c a a a c a a c θ
Orthonormal Basis ||(1,0)||=||(0,1)||=1 (1,0).(0,1)=0 Similarly we use normal basis elements eg: While, eg: = π θ 2 0 2 cos ) cos( ) cos( ) cos( d = 2 0 0 sin cos d

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2D Example

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
i )e A( ϖ t i e t ω i t e t i sin cos + = Sinusoids and cosinuoids are Why are we interested in a decomposition of the signal into harmonic components? Thus we can understand what the system (e.g filter) does to the different components (frequencies) of the signal (image)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 01/13/2012 for the course CMSC 426 taught by Professor Staff during the Winter '08 term at Maryland.

### Page1 / 18

Filter2 - Fourier Transform Analytic geometry gives a coordinate system for describing geometric objects Fourier transform gives a coordinate

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online