lectmr1 - Multirate Filtering Resampling Filters Polyphase...

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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 1 Multirate Filtering, Resampling Filters, Polyphase Filters or how to make efficient FIR filters
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 2 THE NOBLE IDENTITY 1 Efficient Implementation of Resampling filters H(z M ) M:1 H(z) M:1 Rule 1: Filtering with M-unit delays followed by a M:1 downsampling is equivalent to M:1 downsampling followed by filtering with 1 unit delays.
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 3 THE NOBLE IDENTITY 2 Efficient Implementation of Resampling filters H(z M ) 1:M 1:M H(z) Rule 2: 1:M upsampling followed by filtering with M-unit delays is equivalent to filtering with 1 unit delays followed by 1:M upsampling. It is always more efficient to apply the filter at the lower sample rate
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 4 Downsampling • Sometimes called decimation. This is poor nomenclature since decimation refers to removing 1 in 10. • It is useful to think of the downsampling operation as the output of a commutator. M:1
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 5 Downsampling x(n) x D (n) 0 1 2 . M-1 x(n) M:1 Commutator If x(n) has samples indexed from 0 to N-1, then x D (n) has samples indexed from 0 to (N/M)-1 . x D (n)
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 6 Upsampling • Sometimes called interpolation although it is not interpolation in the conventional sense; it is just putting zeros between samples. If we wish to perform interpolation in the conventional sense, we must pass the DSP interpolated data through a low pass filter (anti-imaging or interpolation filter). • In DSP, interpolation is also called zero-packing. 1:L
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 7 Upsampling x(n) x I (n) 1:L 0 1 2 . L-1 x(n) Commutator If x(n) has samples indexed from 0 to N-1 , then x I (n) has samples indexed from 0 to LN-1 . 1:L x I (n)
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 8 Digital Receiver Options Frequency Shift Low Pass Filter Sample Frequency Shift Low Pass Filter Sample Resample Frequency Shift Low Pass Filter/Freq Shift Sample Resample Frequency Shift Low Pass Filter Sample Resample
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 9 2 3 1 4 frequency shift low pass filter sample Fs -Fs Frequency Shift Low Pass Filter Sample
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 10 X Analog Low Pass Filter e j t − ω 0 s(t) 1 2 3 4 X s(t) 1 2 3 4 X r(n) x(n) y(n) cos sin ω ω 0 0 t t Fs Fs Fs Receiver Structure Which can be implemented by Analog Low Pass Filter Analog Low Pass Filter
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20-Mar-2006 ELEC4600/7602 Signal and Image Processing II Brian Lovell 11 Comments • Need to have – two perfectly matched analog mixers
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This note was uploaded on 12/06/2011 for the course ELEC 4600 taught by Professor Mehrtashharandi during the One '09 term at Queensland.

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lectmr1 - Multirate Filtering Resampling Filters Polyphase...

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