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Browse Prior Art Database

Quantization Effects in Digital Filters

IP.com Disclosure Number: IPCOM000076890D
Original Publication Date: 1972-May-01
Included in the Prior Art Database: 2005-Feb-24
Document File: 2 page(s) / 46K

Publishing Venue

IBM

Related People

Besseyre, JA: AUTHOR

Abstract

This is a method for estimating the output signal-to-noise ratio (S/N) of a first-order digital filter used as an analog-to-digital converter, as a function of the number of bits n used to encode each analog signal sample, having a spectrum S(f) in the presence of white Gaussian input noise.

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Quantization Effects in Digital Filters

This is a method for estimating the output signal-to-noise ratio (S/N) of a first-order digital filter used as an analog-to-digital converter, as a function of the number of bits n used to encode each analog signal sample, having a spectrum S(f) in the presence of white Gaussian input noise.

A first-order digital filter has a Z transform transfer function H(Z) of H(Z) = 1 over 1-alpha Z/-1/; where alpha is the pole location of the filter and a normalized amplitude response absolute H(jw) absolute/2/ of absolute H(jw) absolute/2/ = (1- alpha)/2/ over 1+alpha/2/-2 alpha cos wt.

If phi is defined as the level of noise for a pulse-code modulation (PCM) encoding function, then phi is related to the number of bits n by phi = 2-n. Consequently, as n varies then phi will also vary. It should be recalled that A. N. Kolmogorov in 1956, (IEEE Trans. Information Theory, Vol. 12, pages 102-108) derived the rate R in bits/second for encoding information and the noise N as a function of encoding error or noise phi. These are parametrically related as:

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The integrals are evaluated by numerical integration of S(f) and log S(f) over phi/2/. The integration for determining R(phi) should be performed only over the region where S(f) > phi/2/. It should also be noted that the signal S can be measured as

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As previously suggested, when one digitally encodes an analog sample, then one introduces a level of noise which...