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Design of Interpolation/ Decimation Filters

IP.com Disclosure Number: IPCOM000122394D
Original Publication Date: 1991-Dec-01
Included in the Prior Art Database: 2005-Apr-04
Document File: 2 page(s) / 78K

Publishing Venue

IBM

Related People

Galand, C: AUTHOR [+3]

Abstract

Sampling rate conversion by an arbitrary ratio requires to up-sample the input signal at a common multiple of the input and output sampling rates. Even if the filter implementation does not require the actual up-sampling of the signal, the filter design does. Then, the filter order required for proper filter characteristics may be far too high to be synthesized by usual filter design algorithms that may break down or fail to converge. A multi-step design technique can be used to avoid these problems. The technique is illustrated in a particular case that requires only two steps, but can easily be extended.

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Design of Interpolation/ Decimation Filters

      Sampling rate conversion by an arbitrary ratio requires
to up-sample the input signal at a common multiple of the input and
output sampling rates. Even if the filter implementation does not
require the actual up-sampling of the signal, the filter design does.
Then, the filter order required for proper filter characteristics may
be far too high to be synthesized by usual filter design algorithms
that may break down or fail to converge. A multi-step design
technique can be used to avoid these problems. The technique is
illustrated in a particular case that requires only two steps, but
can easily be extended.

      The signal processing operations required to get a signal
sampled at 20 kHz from an input signal sampled at 44 kHz include an
up-sampling at 220 kHz, a low-pass filtering with filter F to remove
the signal components above 10 kHz, and then a down-sampling at 20
kHz. The figure shows, in the frequency domain, the specifications of
the filter F to be synthesized. In our design example, we considered
the following filter characteristics:
           Sampling frequency (kHz)           220
           Cutoff frequency (kHz)               8
           Pivot frequency(kHz)                 9
           Out-of-band rejection (dB)         -60
           In-band ripple(dB)                   0.5

      As said, synthesizing a filter with such characteristics is not
feasible using the classical design tools. Instead, one can consider
that the filter F is the product of two (or more) filters. Each of
these filters is short enough to be easily designed by the tools. In
the Z transform domain:
(1)       F(Z) = F1(Z5).F2(Z)

      The figure shows the frequency characteristics of filters F1
and F2 .

      F1 is the basic low-pass filter at the input sampl...