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**Sampling Rate Conversion by a Rational Factor, I/D**

In Decimation and Interpolation, sampling rate conversion is achieved by Integer Factor When sampling rate conversion requires by non integer factor, we need to perform sampling rate conversion by rational factor I/D

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**Procedure: Perform Interpolation by a Factor I.**

Filter the output of interpolator using a Low Pass (Anti Imaging Filter) with the Bandwidth of /I. The output of Anti Imaging Filter is Passed through a another Low Pass Filter ( Anti Aliasing Filter) to limit the bandwidth of signal to /D. Finally Signal Band limited to /D is decimated by factor D.

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Block Diagram:

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The anti Imaging Filter and anti Aliasing Filter are operated at same sampling rate and hence can be replaced by simple lowpass filter with cut off frequency, Wc = min[/I, /D] It is Important to note that, in order to preserve the spectral characteristics of x(n), the interpolation has to be performed first and decimation is to performed next.

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Filter Bank In some applications like spectrum analysis, it is required to separate a signal into a set of sub band signals. There are some applications where this kind of sub bands signals have to be combined and represented as a single composite signal. For those applications digital filter banks are used.

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Types of Filter Bank In general, digital filter bank can be represented as a set of digital BandPass filters that can have either a common input or summated output. There are three types of Filter Bank: Analysis Filter Bank Synthesis Filter Bank Sub Band Coding Filter Bank

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**Analysis Filter Bank It consists of M no. of subfilters.**

The individual subfilter H(z) is Known as Analysis Filter

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Description: All the subfilter are equally spaced in frequency and each have the same bandwidth. The spectrum of the input signal will lie in the range 0 ≤ w ≤ The filter bank splits the signal into number of subband each having bandwidth of /m. The filter H0(z) is LowPass, H1(z) to Hm-2(z) are BandPass and Hm-1(z) is HighPass.

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Synthesis Filter Bank The M channel synthesis filter bank is a dual of M channel analysis filter bank.

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**Description: In this case, Um(z) is fed to an upsampler.**

The upsampling process produces the signal Um(zm). These signal are signal are applied to an filter Um(z) and Finally added to get X(z). The filter G0(z) to Gm-1(z) have same characteristics as the analysis filter H0(z) to Hm-1(z)

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**SubBand Coding Filter Bank**

If we combine the analysis filter with synthesis filter bank, as a result we will obtain a M channel subband coding filter bank.

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| Page 1 09.11.2012 Angelo Farina UNIPR | All Rights Reserved | Confidential Digital sound processing Convolution Digital Filters FFT.

| Page 1 09.11.2012 Angelo Farina UNIPR | All Rights Reserved | Confidential Digital sound processing Convolution Digital Filters FFT.

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