DESIGNING A UNIFORM FILTER BANK

USING MULTIRATE CONCEPT

Submitted by

Md. Redwan Islam(1006066)

Md. Rayhan Khan (1006067)

Nurani saoda (1006176)

Rakib Hasan (1006180)

Umme Fatema (1006194)

Farhan Shams (0806152)

Digital Filter Bank•A digital Filter Bank is a set of digital bandpass filters either a common input or summed output.•The figure shows an M-band analysis filter bank with Hk(z) as the analysis filter and Hk(z) decomposes the input signal into M-subband signals.

Figure 01: Digital Filter Bank

Analysis filter bank Synthesis filter bank

Uniform Filter BankThe uniform filter bank is composed of M filters which are uniformly shifted versions of the basic prototype filter.According to the definetion a uniform filter bank,

Hk(ejw) = Ho(ej(w-2 k/M)π ) ; 0≤ k ≤ (M-1)Where Ho(ejw) is the basic prototype filter.

Figure 02: Unifomly Shifted Filter Bank

Uniform Filter Bank using Multirate Concept

Polyphase Implementation of Uniform Filter BankM-band polyphase decomposition of Hk(z),

Figure 03: Polyphase implementation of a uniform DFT analysis filter bank

For k= 0,1,2…. M-1,

Figure 04: Uniform DFT analysis filter bank

Outputs of frequency response of some of the

filters of M band Analysis Filter Bank with M=20

FFT of an input comprising of sinusoids with

different magnitudes

APPLICATION

Few major applications of uniform digital filter bank are: Digital Audio Systems Sub-band Coding of Speech and Image

Signals Analog Voice Privacy Systems

CONCLUSION The prototype filter was chosen to be FIR filter for

the ease of calculation and polyphase decomposition.

Commutation operation was implemented by reshaping the prototype impulse response which also formed the banks.

All the outputs, e.g. magnitude response of the impulse response of the filters, magnitude response of the input and output of each bank and reconstruction observed in frequency domain, since, only frequency domain gives the perfect visualization of the signal.