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Approximation Technique for Correlation Computations of Companded Signals

IP.com Disclosure Number: IPCOM000059804D
Original Publication Date: 1986-Jan-01
Included in the Prior Art Database: 2005-Mar-08
Document File: 4 page(s) / 44K

Publishing Venue

IBM

Related People

Jones, GD: AUTHOR

Abstract

This disclosure describes a technique that utilizes the logarithmic properties of digitized signals that have been companded in pulse code modulation (PCM) form. The logarithmic properties are utilized to compute correlation values for signals without requiring the use of a multiplier. Simple shifting and adding steps can be performed instead. The approximation permits calculation of the complex correlation functions to be performed on simple microprocessors not having multipliers. The general use of logarithmic relations for replacing multiplication by addition is well known. The logarithmic properties of companded digitized PCM signals is not so apparent.

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Approximation Technique for Correlation Computations of Companded Signals

This disclosure describes a technique that utilizes the logarithmic properties of digitized signals that have been companded in pulse code modulation (PCM) form. The logarithmic properties are utilized to compute correlation values for signals without requiring the use of a multiplier. Simple shifting and adding steps can be performed instead. The approximation permits calculation of the complex correlation functions to be performed on simple microprocessors not having multipliers. The general use of logarithmic relations for replacing multiplication by addition is well known. The logarithmic properties of companded digitized PCM signals is not so apparent. However, the logarithmic properties of such companded signals can be utilized to perform an approximation to the correlation calculations without using multiplication, as will appear. This disclosure describes a technique for approximating the correlation calculations that significantly reduces the processing load required and avoids altogether the requirement for a multiplier.

There are numerous applications that involve the processing of signals which require calculation of correlation functions. The calculation of auto correlation and auto covariance are required in the case of speech coding and the calculations of cross correlation or cross covariance between two signals is required in the case of modem equalizers and echo cancellers. Equations 1 and 2 set out below represent the fundamental functions involved in auto correlation or auto covariance and in cross correlation and cross covariance calculations. Auto-correlation/covariance

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Cross-correlation/covariance

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where A(i) are samples of the signal a(t) B(i) are samples of the signal b(t) N is the block size over which the correlation is to be computed k is the displacement for which the correlation is computed i is the index In addition, most algorithms utilizing the correlation functions utilize normalized correlation coefficients which requires that the functions shown in Equations 1 and 2 be divided by the sum of their squares over the processing block of data, as shown by Equation 3.

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Companded PCM coding is often subjected to correlation calculations. Linear PCM codes are preferred and companded PCM coding is the most prevalent method for analog-to-digital (A/D) conversion employed in the telecommunications systems currently in use. The coders utilized in such

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applications have been reduced to single-chip implementations by several vendors and represent the most economical method of A/D conversion for voice band signals. Companding reduces the number of bits necessary for describing the sample of an analog signal over a specified dynamic range and signal-to- noise ratio. The two prevalent methods of companding employed are the mu-law in North America and the a-law in E...