Print ISBN 0-471-98626-7 Electronic ISBN 0-470-84183-4 Chapter 4 Examples discrete-time Fourier transform of a periodic signal with period N the above
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WALSH BASIS IMAGES FOR N=4 Where white is +0 25 and black is -0-25 9 • Consider Walsh transform of the letter 'O' To calculate each transform
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(iv) The mean vectors for slant transform matrix S are not sequentially ordered for n ≥ 3 8 Define discrete cosine transform The 1-D discrete cosine transform is
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Print ISBN 0-471-98626-7 Electronic ISBN 0-470-84183-4 Chapter 4 Examples discrete-time Fourier transform of a periodic signal with period N the above
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Digital Image Processing Prof zhengkai Liu Dr Rong Zhang 4 The One- Dimensional Discrete Fourier Transform and its Inverse 2 1 N j ux π - - ∑ 0 1 1 u
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1-D Walsh Transform ( ) 2 0 1 10 )( )( 2 ,1 ,,0 ),( xbx b x n u x N N xxf n n - = = - = them represent to bits need We and for tion representa binary
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N must be a power of 2 (2, 4, 8, 16, 32, ) Although in Matlab it is possible to define the 12 ∙2k point or the 20 ∙2k point Walsh transform, the inverse
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Separable transforms • Walsh • Hadamard • Haar • Discrete Sine • DCT • Slant For example, N=4 we have The harr function can be defined as For N=8
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The Fourier transform becomes an N by N unitary matrix F relationships N/2 0 Wo W3 W2 Wi and for N 4, F = ~o ~2 ~ O ~2) where ~ nk ~nkmod N DN/2 1 ~
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