Lecture 10_winter_2012

Lecture 10_winter_2012 - Digital Speech Processing Lecture...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Digital Speech Processing— Lecture 10 Short-Time Fourier Analysis Methods - Filter Bank Design
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Review of STFT 1 123 0 2 1 ˆˆ ˆ ˆ ˆ ˆ ˆ ˆ .( ) [ ] [ ] ˆ function of (looks like a time sequence) ˆ function of (looks like a transform) ˆ ˆ ( ) defined for , , ,. ..; . Interpretations of ( ) ˆ . f i x ωω ω ωπ =−∞ =− =≤ ± ± jj m n m j n j n Xe x m w n m e n n n ˆ ˆ ˆ ed, variable; ( ) DTFT [ ] [ ] DFT View OLA implementation ˆ ˆ 2. variable, fixed; ( ) [ ] [ ] Linear Filtering view filter bank implementation FBS i == ⇒⇒ j n n n x m w n m nn X e x n e w n mplementation
Background image of page 2
3 Review of STFT 3 2 2 ˆ ˆ . Sampling Rates in Time and Frequency ˆ recover [ ] from ( ) 1. time: ( ) has bandwidth of Hertz samples/sec rate Hamming Window: (Hz) sample ω =⇒ j n j S xn X e We B B F B L exactly 4 at (Hz) or every L/4 samples 2. frequency: [ ] is time limited to samples need at least frequency samples to avoid time aliasing S F L wn L L
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Review of STFT with OLA method can recover ( ) using lower sampling rates in either time or frequency, e.g., can sample every samples (and divide by window), or can use fewer than frequency sam ± xn L L exactly ples (filter bank channels); but these methods are highly subject to aliasing errors with any modifications to STFT can use windows (LPF) that are longer than samples and still recover with ± L frequency channels; e.g., ideal LPF is infinite in time duration, but with zeros spaced samples apart where / is the BW of the ideal LPF <⇒ S NL N FN
Background image of page 4
5 Review of STFT H 0 (e j ω ) H 1 (e j ω ) H N-1 (e j ω ) + X(e j ω ) Y(e j ω ) 1 0 1 0 1 0 [] () [][] [ ] [ ][ ] [ ] . . . need to design digital filters that match criteria for exact reconstr ω ωω δ = = =−∞ = == = =− = + + % % % k jn k N jj k k N k k r r hn wne He H e hn h n n wnpn pn N n rN N wrN n rN w wN uction of [ ] and which still work with modifications to STFT xn
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Tree-Decimated Filter Banks 6
Background image of page 6
Tree-Decimated Filter Banks • can sample STFT in time and frequency using lowpass filter (window) which is moved in jumps of R<L samples if L N where: L is the window length, R is the window shift, and N is the number of frequency channels • for a given channel at ω = ω k , the sampling rate of the STFT need only be twice the bandwidth of the window Fourier transform – down-sample STFT estimates by a factor of R at the transmitter – up-sample back to original sampling rate at the receiver – final output formed by convolution of the up-sampled STFT with an appropriate lowpass filter, f [ n ] 7
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Filter Bank Channels 8 Fully decimated and interpolated filter bank channels; (a) analysis with bandpass filter, down- shifting frequency and down-sampling; (b) synthesis with up-sampler followed by lowpass interpolation filter and frequency up-shift; (c) analysis with frequency down-shift followed by lowpass filter followed by down-sampling; (d) synthesis with up-sampling followed by frequency up-shift followed by bandpass filter.
Background image of page 8
Full Implementation of Analysis-Synthesis System 9 Full implementation of STFT analysis/synthesis system with channel decimation by a factor of R , and channel interpolation by the same factor R (including a box for short-time modifications.
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/29/2011 for the course ECE 259 taught by Professor Rabiner,l during the Fall '08 term at UCSB.

Page1 / 57

Lecture 10_winter_2012 - Digital Speech Processing Lecture...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online