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.
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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