Design of Hign Speed Bandpass Filter

7/29/2019 Design of Hign Speed Bandpass Filter

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DESIGN OF HIGH-SPEED DIGITAL BANDPASS FILTERSWITHOUT MULTIPLIERSMichael A . Soderstrand *Electrical and Computer Engineering DepartmentUniversity of CaliforniaDavis, CA 95616Phone: (916) 752-2669

AbstractUsing a special case of the frequency-sampling design ap-proach with N =6, t is possible to design FIR band-passfilters without the need for multipliers. The technique ishighly modular and thus lends itself to VLSI implementa-tion and since it uses only adders and registers (delays), i tcan be implemented with a very high sampling frequency(eg: 100 MHz). The basic band-pass fi lters are limited tocenter frequencies at multiples of n/3, and thus are some-what restrictive. However, by applying amulti-rate tech-nique and adding an additional low-sampling-rate filter, itis possible to place center frequencies at any multiple ofn/18. Further stages can refine the center frequency toany multiple of 2*/(6" ) where n is the number of stages.The low-sampling rate fil ters may be time multiplexed, butthey do create undesirable image spectrums unless theyare centered at one of the original n / 3 multiples. Adjust-ment of the sampling frequency can place these band-passfi lters at any desired center frequency. A n alternative tovarying the sampling frequency is to make use of a com-plex multiplier in the reduced-sample-rate filter. This isconveniently realized using GQRNS arithmetic.

1 IntroductionIn the reception of broad-band signals such as spread-spectrum BPSK communications systems, it is often nec-essary to eliminate narrow-band interference from suchthings as "push-to-talk" transmissions [l , 2,3].This prob-lem is analogous to the problem of detecting narrow-bandsignals or sinusoidal signals in the presence of broad-bandsignals and noise. One simple technique to accomplish thisdetection is the use of a bank of bandpass filters tuned tovarious frequencies in the band of interest. Detection ofexcessive power in one of these band-pass fi lters comparedto the others would indicate the presence of anarrow-bandinterferer. With this knowledge, a notch fil ter of appro-priate design could be used to eliminate the interference.

'Th s wor k was supported in part by a grant from the UnitedStatesAir Force through the Naval Postgraduate School, Monterey,CA.

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Figure 1: Basic B and-Pass Fil ter

Usually, the band-pass fi lter itself can be used to form thenotch filter using a signal cancelling approach.In the case of a very broad-band spread-spectrumsignal, high sampling rates are required to accommodatethe necessary band-width. These high sampli ng rates pre-clude the use of multipl iers in the band-pass fi lters. In thispaper we shall demonstrate how four equally spaced band-pass filters can be placed between DC and the Nyquistfrequency wi thout the need of multipli ers. These fi ltersonly provide lOdb attenuation compared to the other fre-quencies, but are well suited to the problem stated in theprevious paragraph. If more attenuation is needed, then aprocess of decimation by six, low-pass filtering of the dec-imated signal, and zero-padded up-sampling followed by asecond stage of band- pass filtering can yield aminimumof 20db attenuation and amuch narrower band-pass filter.Using a similar technique, band-pass filters at multiplesof 2n/(6" ) can be generated for n-stage systems, but thefiltering must be done with complex filter coefficients in

order to prevent images due to the down-sampling. Thiscan be accomplished through Quadratic Residue NumberSysiem ( QRNS) arithmetic using only one integer multi-plier per band-pass stage at the reduced-sample rate.553

0-7803-0593-0/92$3.001992IEEE


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2 Basic Band-Pass FilterFigure 1shows the basic bank of four fi lters. T he fi lterlabeled BPo is actually a low-pass fi lter (ie: band-passfilter centered at DC). Similarly the filter labeled BP3 isactually a high-pass filter (ie: band-pass fi lter centered atthe Nyquist frequency). Because these fi lters are locatedat center frequencies that are multiples of a/3, they donot require any multipliers for their reali zation. Figure 2gives the output spectrum for the four filters of Figure 1.Because this structure is modular and uses no multipliers,the hardware can be constructed very easily in VLSI andcan be built with only adders and registers, thus allowingvery high sampling rates.3 Narrow-Band Band-Pass FilterOur first modification to Figure 1 s to down-sample theoutput BPi of each of our four fi lters by decimating by six.The decimated signal is then passed through a band-passfilter with exactly the same characteristics as filter BPo.We then up-sample by six inserting zeros inbetween thesamples of the output of the reduced-sampling-rate filterBPo. Finally, we use an interpolating filter that is iden-tical to BPi to yield the final band-pass filter. Figure 3shows the structure and Figure 4 gives the output spec-trum for the four filters of Figure 3. (NOT E: The outputspectrum for these fi lters was generated by passing WhiteGaussian Noise through the entire filter system and mea-suring the output spectrum. This results in the somewhatrough appearance of the spectrum. The actual spectrumis quite smooth.)4 Other Band-Pass FiltersIf we were to replace the reduced-sample-rate low-pass fil-ter BPo of Figure3with B reduced-sample-rate band-passfilter such as BP1 or BP2 or the high-pass filter BP3,wewould generate band-pass filters at multiples of */18 be-tween DC and the Nyquist frequency. Unfortunately, eachof these band-pass filters would be accompanied by an im-age filter creating a pair of band-pass fi lters. Figure 5shows the result of these image fi lters. One method ofeliminating these image filters is to use reduced-sample-rate fi lters with complex coefficients. A t first this mayseem to be impossible while maintaining the high sam-pling frequency through-put for the fi lter. However, theuse of QRNS arithmetic can realize these filters with onesimple integer multiplier per band-pass filter [4]. This willallows us to realize single band-pass fi lters at any multipleof n/(6") or an n-stage system.

5 ConclusionsThe four filters of Figure 1can be used effectively to moni-tor the energy content of the four frequency bands between

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Figure2: Transfer Function Magnitudes for the four Band-Pass Fi lters of Figure 1

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- - I - -Figure 3: Narrow-Band Notch Filters

DC and the Nyquist frequency. F igure 3can realize nar-rower filters at these same frequencies. Finally, Figure 5can realize filters at sixteen frequency bands between DCand the Nyquist frequency. T hese band-pass fi lters can allbe realized in V LSI with extremely high sampli ng rates.References[l]M.A. Soderstrand, H.H. Loomis, and K.V . Rangarao,

Improved Real-Time Adaptive Detection, Enhance-ment, or Elimination of M ultiple Sinusoids, I E E EMidwest Symp. on C ircuits and Systems, Monterey,CA, May 1991.[2] M.A. Soderstrand, H.H. Loomis, and K.V . Rangarao,Elimination of Narrow-Band I nterference in BPSK -Modulated Signal Reception, I E E E I ntemationalSymp. on C ir cui ts and Systems, Singapore, J une, 1991.[3] K .V. Rangarao, Adaptive Digital Notch Fil tering, M.S.Thesis, Naval Postgraduate School, Monterey, CA ,September 1991.[4] M.A. Soderstrand and R. Miller, A Moving RecursiveCNT T Implemented in GQR NS A rithmetic, I E E E

I ntemational Symposium on Ci rcui ts and Systems,Portland, OR, May 1989.Figure4: Transfer Function Magnitudes for the four Band-Pass Filters of Figure 3

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Name: BP l / B P l tsub6ram I Nam: B P l m t arb6" I

Figure5 : Transfer Function M agnitudes for the four Band-Pass Fi lters with Spectrum Images due to Down-Sampling

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Design of Hign Speed Bandpass Filter