090121Lecture07

090121Lecture07 - ECE 700 Digital Signal Processing Lecture...

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ECE 700 WI 2009 ECE 700 Digital Signal Processing Lecture 7 01/21/09 1
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ECE 700 WI 2009 Filterbanks Why filterbanks? Major applications Uniform modulated filterbanks DFT based implementation Two channel filterbanks Quadrature mirror filterbanks Conditions for no-aliasing Conditions for perfect reconstruction FIR PR filterbanks Generalizations M-channel filterbanks Iterated 2-channel filterbanks
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ECE 700 WI 2009 Why filterbanks? Analysis: Break up a signal into a number of (typically) non-overlapping frequency ranges Processing: Modify the signal in each frequency band to achieve desired properties Examples: Data compression in image, speech and audio processing Dynamic range compression in hearing aids Noise reduction Synthesis: Recombine signals from multiple frequency bands into a single signal
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ECE 700 WI 2009 Typical filterbank system • In most cases, because each of the subbands is narrow, the analysis stage will include decimation. • The synthesis stage will include expanders to recombine the decimated subbands. • For the purposes of this course, we will typically ignore the subband processing and only concentrate on analysis and synthesis filterbanks. Analysis stage Synthesis stage
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ECE 700 WI 2009 Filterbank example: MP3 audio coding MP3: MPEG 1 Audio layer 3 Psychoacoustic model: • Based on how humans hear • Loudness masking – a loud sound at a certain frequency masks soft sounds at nearby frequencies. • Allocate fewer bits to encoding masked sounds. Masking curve frequency magnitude
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ECE 700 WI 2009 Uniform modulated filterbank Analysis stage Synthesis stage • M-band critically-sampled, uniformly modulated filterbank • critically-sampled: Decimation factor = Number of subbands; no net increase in sample rate. • uniformly modulated: Center frequency equally spaced, identical H(z) in each branch. 2 , LPF BW . k k MM  
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ECE 700 WI 2009 k th branch of analysis filterbank 2 () 22 2 2 [ ] [ ] [ ] ( ( [ ] ) [ ]) ( ( [ ] [ ])) [ ] [ ] ( [ ] [ ]) [ ] [ ] j k n l M k l j kl j kn MM l j kn M k l j knM M k k k l k l v n h l x n l e h l e x n l e h l x n l e y n v nM h l x nM l e h l x nM l  
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ECE 700 WI 2009 More on the k th analysis branch • Look at the M -component polyphase decomposition of H k ( z ). 1 0 1 0 ( ) ( ), ( ) ( ) , so ( ) ( ) M lM k kl l m kl k m M mM l kk lm H z z H z H z h mM l z H z h mM l z       • Relate this back to the polyphase components of H ( z ). 22 () 2 2 2 1 1 1 0 0 0 ( ) ( ) ( ) . ( ) ( ) ( )( ) ( ) j k mN l j kl MM k M M M j kl j kl j kl mM l l M m l M M M M k l l l l m l m l h mM l h mM l e h mM l e H z p m e z e z p m z e z P z     
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ECE 700 WI 2009 Structure of the k th branch • After moving decimator and using Noble identity, This part is independent of branch k
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ECE 700 WI 2009 Uniform DFT analysis filterbank 2 1 0 [ ] [ ] M j kl M kl l y m v m e
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ECE 700 WI 2009 Uniform DFT Analysis and Synthesis Filterbanks
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090121Lecture07 - ECE 700 Digital Signal Processing Lecture...

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