Lect2a - 0 0 50 50 100 100 150 150 200 200 250 0 50 100 150...

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1 Wavelet Based Methods in Image Wavelet Based Methods in Image Processing Processing Lecture 2.a Lecture 2.a - - Fourier Transform Fourier Transform Applied Mathematics Seminar S. Allen Broughton 0 50 100 150 200 250 300 350 0 0 0
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2 Lecture 2.a Lecture 2.a signal samples and time domain model wave forms and frequency domain signal analysis & synthesis Discrete Fourier transform - DFT extension to 2D convolution theorem restoration
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3 Signal Samples and Signal Samples and Time Domain Time Domain X = [X(0),. ..,X(N-1)] vector of length N X(i) = f(i/N) : sample analog signal f X(i+N) = X(i) : periodic extension (mod N ) time domain {0,1/N,. ..,(N-1)/N} or {0,1,. ..,N-1}
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4 Model Wave Forms Model Wave Forms model wave forms frequency domain Maple script - waveform.mws En i k n N k () e x p ( ( ) ) =⋅ 2 π kN = 01 ,...,
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5 Signal Analysis & Synthesis Signal Analysis & Synthesis - - 1 1 energy of a signal (* = conjugate transpose) analysis of a signal - “energy content at a frequency” ~ () e x p ( ( ) ) * Xr E X EX Xn i k n N kk n N =⋅ = =− =
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This note was uploaded on 05/28/2010 for the course EE EE564 taught by Professor Runyiyu during the Spring '10 term at Eastern Mediterranean University.

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Lect2a - 0 0 50 50 100 100 150 150 200 200 250 0 50 100 150...

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