Browse Prior Art Database

PRE-INTERPOLATION FILTERS FOR UPSAMPLING

IP.com Disclosure Number: IPCOM000008625D
Original Publication Date: 1998-Mar-01
Included in the Prior Art Database: 2002-Jun-27
Document File: 4 page(s) / 165K

Publishing Venue

Motorola

Related People

George Jianwei Miao: AUTHOR [+3]

Abstract

Multirate signal processing is out of the unique advantages of discrete-time signal processing in the domain of signal processing. The area of multirate signal processing is very broad. It includes basic topics such as decimation system and interpolation system, and more involved topics such as perfect reconstruction filter banks and wavelets. If higher sampling rates are required to display digital wave- form for D/A convertor, then an interpolation sys- tem can be used. However. a fundamental idea in the area of multirate signal processing is that one should always perform computations at the lowest possible sampling rate. In our case, we are only considering the interpolation system. Therefore, other multirate signal processing approaches are omitted herein.

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MOTOROLA Technical Developments

PRE-INTERPOLATION FILTERS FOR UPSAMPLING

by George Jianwei Miao, Jeremy Ho and Dan Brookshire

BACKGROUND OF THE PROBLEM

  Multirate signal processing is out of the unique advantages of discrete-time signal processing in the domain of signal processing. The area of multirate signal processing is very broad. It includes basic topics such as decimation system and interpolation system, and more involved topics such as perfect reconstruction filter banks and wavelets. If higher sampling rates are required to display digital wave- form for D/A convertor, then an interpolation sys- tem can be used. However. a fundamental idea in the area of multirate signal processing is that one should always perform computations at the lowest possible sampling rate. In our case, we are only considering the interpolation system. Therefore, other multirate signal processing approaches are omitted herein.

  An interpolation filter is a digital filter that follows a sampling expander, that is, an interpolation system is accomplished by first upsampling a digital signal, then filtering the upsampled signal as shown in Figure I. Classically, the system on the left is called a sampling expander. The interpolation filter on the right is lowpass with cutoff frequency T/M. The

purpose of interpolation filter is to suppress all the image spectrums. Thus, it retains only the shaded portion of the compressed spectrum. On the other hand, in the time domain, xJn] is a convolution of x,[n] with the impulse response h[n]. The effect is that the zero-valued samples introduced by the sampling expander are filled with "interpolated" values. However, a direct implementation of inter- polation system is inefficient because at most 50% of the input samples at filter h[n] are nonzero. In other words, we mean that only 50% of the multi- pliers h[n] have nonzero input at any point in time. Therefore, the remaining multipliers are resting. Moreover, those multipliers which are not resting are expected to complete their job in half of the time because the output of the delay elements will change by that time. As can be seen, the disadvan- tages of such a system are that the interpolation filter is operated at upsampling rate increased by M, and it has a resting-time. In order to overcome above the problems, we have proposed an approach based on reversing the order of the upsampling expander and the interpolation filter (along with symmetric coefficients of the halfband lowpass filter).

Lowpass

+M

* Filter H(z) w

xl4 xe[nl xdnl

Fig. 1 General discrete-time system for upsampling rate by M

141 Murch 1998

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MOTOROLA Technical Developments

PROPOSED SOLUTIONS and b: = 1. Therefore, Ho(z) = z'.

  This paper provides a method of interpolation system to perform all computations at the "lowest rate permissible within the given context," and reduces the speed requirements on the digital s...