FILTER BANKS

By

SANJANA PRASAD 1601RL01

PhD –Full Time Research scholar

PSG COLLEGE OF TECHNOLOGY

INTRODUCTION TO FILTER BANKS TYPES OF FILTER BANKS UNIFORM DFT FILTER BANK TWO CHANNEL FILTER BANK POLYPHASE TWO CHANNEL FILTER BANK SUMMARY REFERENCES

TOPICS

Array of BPF that seperates the input signal into multiple components, each one carrying a single sub-band of the original signal.

A Digital filter bank is a collection of filters having a common input or output.

2 types of filter banks Analysis filter bank Synthesis filter bank

INTRODUCTION

1-D AND 2-D FILTER BANKS

1-D FILTER BANK 2-D FILTER BANK

MULTIDIMENSIONAL ANALYSIS AND SYNTHESIS FILTER BANKS

DIRECTIONAL FILTER BANK•modulating the input signal and using diamond-shaped filters.•Advantages:•offers perfect reconstruction.•directional-selectivity and efficient structure.•use in 3-D to achieve the frequency sectioning.• Sparse image representation, medical imageing[ ignal and image processing

MULTI-DIMENSIONAL FILTER BANK

Decomposition performed by the filter bank is called analysis

Output of analysis - >subband signal The Analysis filter may be

non-overlapping, slightly overlapping substantially overlapping.APPLICATION OF ANALYSIS FILTER BANKS: Spectrum analysis. (split the input signal into R

different so – called subband signals)

ANALYSIS FILTER BANKS

Synthesis (i.e. recombining the outputs of multiple receivers) INVOLVES:  upsampling each one at a rate with the total bandwidth to

be created, translating each channel to its new center frequency, and

summing the streams of samples.

Interpolation filter +Upsampling -> Synthesis filter. The combination of several signal into a common output

signal is called a Synthesis filter bank. The reconstruction process is called synthesis, meaning

reconstitution of a complete signal resulting from the filtering process.

SYNTHESIS FILTER BANKS

Important characteristic of filter banks Bandwidth and spacing of the center

frequencies of the filters.FILTER BANKSUNIFORM FILTER BANKS same bandwidth and same sampling ratesNON UNIFORM FILTER BANKS Different bandwidth and different sampling

rates Uniform, maximal decimation filter banks are

often preferred .

OTHER FILTER BANK TYPES

TYPICAL FILTER BANK

DFT filter bank : If the rth band filter hr[n] is computed from the

“modulation” of a single prototype filter h[n] A DFT filter interpolation R = Number of bands

KApplications Of Filter Banks

Sub-band Adaptive Filtering Transmultiplexers Graphic Equalizer Signal Compression Vocoder

UNIFORM DFT FILTER BANK

R-CHANNEL FILTER BANK

An efficient implementation of the R channel filter bank can be generated using polyphasedecomposition of the filter and the input signal .

Because each of these bandpass filter is critically sampled, we use a decomposition with R polyphase signals according to

ANALYSIS DFT FILTER BANK FOR CHANNEL K

DFT ANALYSIS FILTER BANK

DFT SYNTHESIS FILTER BANK

If we now combine the analysis and synthesis filter banks, we can see that the DFT and IDFT annihilate each other, and perfect reconstruction occurs if the convolution of the included polyphase filter gives a unit sample function, i.e.,

In other words, the two polyphase functions must be inverse filters of each other, i.e.,

Where we allow a delay d in order to have casual (realizable) filters. These ideal conditions cannot be met exactly by two FIR filters.

 

TWO-CHANNEL FILTER BANKS

STRUCTURE OF A TWO-CHANNEL FILTER BANK

The construction rule is normally given by

For the synthesis use an expander (a sampling rate increase of 2), and then two separate reconstruction filters, and to reconstruct .

A perfectly reconstructed signal has the sample shape as the original, up to a phase (time) shift.

CONTD…

 

2-CHANNEL QMF BANK

BLOCK OF A 2-CHANNEL QMF BANK FREQUENCY RESPONSE

1. Run-length filter using short Winograd convolution algorithms

2. Fast convolution using FFT 3. Using advanced arithmetic concepts such

as distribute arithmetic, reduced adder graph, or residue number system

VARIOUS METHODS TO IMPLEMENT L/2 FILTERS

Constructs fast and efficient two-channel filter banks

The basic idea is the use of cross-terms (called lifting and dual lifting), as in a lattice filter, to construct a longer filter from short filter, while preserving the perfect reconstruction conditions

LIFTING

Thus we have discussed about Analysis and Synthesis filter banks,Uniform DFT and Non-uniform filter banks

Two channel filter banks /Polyphase two-channel filter bank.

Lifting approach has been listed out briefly.

Summary

Digital Signal Processing With Field Programmable Gate Arrays By Uwe Meyer Baese

https://en.wikipedia.org/wiki/Filter_bank

REFERENCES