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

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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

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.

Block Diagram:

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.

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.

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

Analysis Filter Bank It consists of M no. of subfilters.
The individual subfilter H(z) is Known as Analysis Filter

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.

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

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)

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.