Transcription of ECE 431 Digital Signal Processing Lecture Notes
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ECE 431 Digital Signal Processing Lecture Notes
ECE 431 Digital Signal ProcessingLecture NotesProf. Dan CobbContents1 Introduction22 Review of the DT Fourier De nition and Properties .. Periodic Convolution .. Fourier Series .. 93 Time and Frequency Domain Analysis .. Aliasing .. The Nyquist Theorem .. Anti-Aliasing Filters .. Downsampling .. Upsampling .. Change of Sampling Frequency .. 204 CT Signal Hybrid Systems .. Ideal Signal Reconstruction .. The Zero-Order Hold .. A/D and D/A Converters .. Digital Filters .. 335 The Discrete Fourier De nition and Properties .. Circular Operations .. Fast Fourier Transform Algorithms .. Zero-Padding .. 416 Applications of the Spectral Analysis .. Linear Convolution .. Windowing .. 4517 The CT Laplace Transform.
Since X ej and Y ej both have period 2ˇ;the linear (i.e. ordinary) convolution blows up (except in trivial cases): Z1 1 X 1 ej( 2 X 2 ej d = X1 i=1 Z ˇ(i+1) 2ˇi X 1 ej( X 2 ej d = X1 i=1
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