DSP-ch6

DSP-ch6 - DSP EEE 407/591 by Andreas Spanias Ph.D Chapter 6...

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1 Copyright (c) Andreas Spanias Ch6-1 DSP EEE 407/591 by Andreas Spanias, Ph.D. Chapter 6 [email protected] http://www.eas.asu.edu/~spanias Copyright (c) Andreas Spanias Ch6-2 MULTIRATE SIGNAL PROCESSING QMF BANKS Chapter 6 Andreas Spanias [email protected]
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2 Copyright (c) Andreas Spanias Ch6-3 Sampling Rate Modifications are often used in many application areas. One popular applications has been oversampling - Σ A-to-D and D-to-A conversion. Other applications include sub-band coding of speech and audio MULTIRATE SIGNAL PROCESSING AND DSP APPLICATIONS Copyright (c) Andreas Spanias Ch6-4 DOWNSAMPLING x(n) x (n)=x(Mn) M . . . . x(n) 0 1234 0 1 2 D x (n)=x(2n) D 0 ... ... 2 pi -2 pi O 0 ... ... 2 pi -2 pi O 1/T 1/2T XX d 2 1 (2 ) / 0 () 1 j M jl M d l Xe M π Ω− = =
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3 Copyright (c) Andreas Spanias Ch6-5 J-DSP and downsampling Copyright (c) Andreas Spanias Ch6-6 UPSAMPLING x(n) x e (n)=x(n/M) M x u ( n ) =x ( n/2 ) n 0 …. …. 1234 x ( n ) n 0 12 …. …. 2 π 2 0 2 2 ( ) j e X ( ) j u e X 2 B 2 B 0 -B 2 B
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4 Copyright (c) Andreas Spanias Ch6-7 J-DSP and Upsampling Copyright (c) Andreas Spanias Ch6-8 UPSAMPLING AND RECONSTRUCTION x(n) M H(z) x e (n) x i (n) x u ( n ) =x ( n/2 ) n 0 …. …. 1234 x ( n ) n 0 12 …. …. 2 π 2 0 2 2 ( ) j e X ( ) j u e X 2 B 2 B 0 -B 2 B
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5 Copyright (c) Andreas Spanias Ch6-9 DOWNSAMPLING / UPSAMPLING RULES •To avoid aliasing when downsampling a signal by an integer factor M a signal must be bandlimited by a digital antialiasing filter with cut-off frequency π /M • If we are to upsample by a factor of M we use a digital reconstruction (interpolation) filter in order to eliminate imaging spectral components. Copyright (c) Andreas Spanias Ch6-10 Downsampling By Non-integer Factor (L/M) L LPF π / L M LPF π / M L M LPF min( π / M, π / L) or Example if we want to upsample by a factor 1.1 L=11 and M=10
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6 Copyright (c) Andreas Spanias Ch6-11 Practical Considerations in Downsampling Practical choices for passband and stopband edge frequencies and tolerances defined by application requirements, i.e., bandwidth of interest and tolerable noise within that bandwidth. Signal fidelity, not the only consideration; number of computations and memory required also considered. If the change in downsampling is large, the requirements on the anti- aliasing filter may require a numerically sensitive filter.
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This note was uploaded on 11/02/2009 for the course EEE DSP taught by Professor Ap during the Fall '09 term at ASU.

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DSP-ch6 - DSP EEE 407/591 by Andreas Spanias Ph.D Chapter 6...

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