152 IEEE SIGNAL PROCESSING LETTERS, VOL. 10, NO. 5, MAY 2003

Modified CIC Filter for Sample Rate Conversion inSoftware Radio Systems

Wajih A. Abu-Al-Saud, Student Member, IEEE,and Gordon L. Stüber, Fellow, IEEE

Abstract—Cascaded-integrator-comb (CIC) filters performsample rate conversion (SRC) efficiently using only additions/sub-tractions. However, the limited number of tuning parameters maymake conventional CIC filters unsuitable for SRC in softwareradio (SWR) systems. A simple modification to the CIC filter thatenhances its SRC performance at the expense of requiring a fewextra computations per output sample is proposed. Simulationresults show that the modified CIC filter outperforms the conven-tional CIC filter for the purpose of SRC in SWR systems.

Index Terms—Cascaded-integrator-comb (CIC) filters, samplerate conversion (SRC), software radio systems.

I. INTRODUCTION

A MONG the methods described in the literature for samplerate conversion (SRC) [1]–[3], only a few have the

computational efficiency that is required for software radio(SWR) systems. Cascaded-integrator-comb (CIC) filters [4],[5] perform SRC efficiently by using only additions/subtrac-tions, which makes them attractive for SWR applications.However, conventional CIC filters may be unsuitable for SWR,especially for SRC factors that are close to unity, because theyhave a limited number of tuning parameters, and they exhibit apassband droop.

Fig. 1 shows a CIC filter of order that performs SRCby a rational factor of [4], where and are the numberof comb-integrator stages in the interpolation and decimationsections, respectively. For fixed , the performance of CICfilters can be altered by changing the filter order that controlsthe image attenuation and/or the delay of the comb stagesthat controls the filter bandwidth.

II. CONVENTIONAL CIC FILTER

The transfer function of the CIC filter for SRC by a factoris obtained by reflecting the low sample rate combs across

the upsampler and downsampler to the intermediate high samplerate (IHSR) section. This results in a transfer function with re-spect to the IHSR given by

(1)

Manuscript received February 5, 2002; revised September 4, 2002. Theassociate editor coordinating the review of this manuscript and approving it forpublication was Dr. Xi Zhang.

The authors are with the School of Electrical and Computer Engineering,Georgia Institute of Technology, GCATT, Atlanta, GA 30332-0490 USA(e-mail: stuber@ece.gatech.edu).

Digital Object Identifier 10.1109/LSP.2003.810023

Fig. 1. Conventional CIC filter of orderN +N for SRC byR=L.

where is the interpolation factor; is the decimation factor;is the order of the CIC filter ( ); and is the

delay of each comb stage. The power response of the CICfilter is

(2)

where is normalized with respect to the IHSR. Equation (2)shows that the CIC filter is a lowpass filter with zeros occurringat multiples of and . The distribution ofzeros, over which there is limited control, is uneven, resultingin a low attenuation at some image frequencies. The effect ofthe uneven distribution of zeros over the undesired images be-comes more significant with input signals that have wide dy-namic ranges because insufficiently attenuated parts of the im-ages may alias over low-power parts of the desired basebandsignal.

III. M ODIFIED CIC FILTER

The construction of CIC filters makes their frequencyresponse unsuitable for specific SWR applications. An SWRsystem must be capable of processing narrowband channelizedsignals at wideband reception. Due to variations in the propa-gation environment, the wideband input signal to an SWR hasa very high dynamic range. For example, in accordance withGSM 5.05, a GSM receiver should be capable of withstandinga blocking signal that is 85 dB above the desired signal (whenthe two signals are from 0.8–1.6 MHz apart) [6]. Dependingon the location of the high-power narrowband channels in thewideband signal, the attenuation of their images may be in-sufficient. To achieve better performance, we suggest an SWRreceiver that locates the high-power channels and accordingly

1070-9908/03$17.00 © 2003 IEEE

ABU-AL-SAUD AND STÜBER: MODIFIED CIC FILTER FOR SAMPLE RATE CONVERSION 153

Fig. 2. Modified CIC filter of orderN for SRC byR=L.

sets the zeros of the CIC filter close to their images to providethem with higher attenuation.

The CIC filter is modified by spreading the delays in the CICfilter comb stages. While the delays of the combs in the con-ventional CIC filter are equal to or delay units at theIHSR, the delays are either distributed evenly to provide a moreuniform image attenuation, or they are set around specific valuesto provide additional suppression to particularly strong imagecomponents. The modified CIC filter has transfer function

(3)

and power response

(4)

where is a set of comb delays in delay unitsof the IHSR section that provide the power response of theCIC filter with zeros at multiples of the normalized frequen-cies . Fig. 2 shows the modi-fied CIC filter of order . For the best performance, the de-lays are experimentally set to values in therange to depending on thepower spectrum of the input signal such that the modified CICfilter provides the most uniform image attenuation.

Fig. 3 illustrates the power response of fourth-order conven-tional and modified CIC filters for SRC by 9/10. The zerosof the conventional CIC filter are located at multiples of

and , while the delays of the modified CIC filter are16, 14, 12, and 10, which produce zeros at multiples of

and . For a signal occupying 3/4 of thedigital band, the conventional and modified CIC filters provideSNR of 15 and 50 dB, respectively, where the SNR is defined asthe power ratio after lowpass filtering of the lowest power levelin the desired signal to the highest power level in the images.

The complexities of the conventional and modified CICfilters of order can be compared in terms of theirmemory requirements and number of additions (or subtractions)

Fig. 3. Power response of fourth-order conventional (N = N = 2) andmodified (N = 4) CIC filters for SRC byR=L = 9=10.

Fig. 4. Input signal to conventional and modified CIC filters containing33 frequency multiplexed channels (f is normalized with respect to theintermediate high sample rate).

per output sample (APOS). While the conventional CIC filterrequires memory elements, the modifiedCIC filter requiresmemory elements on average. The integrators of theconventional and modified CIC filters require the same numberof APOS. Since the integrators operate in the IHSR section,every integrator requires additions per input sample (APIS).Therefore, the integrator stages require a total numberof APOS. The interpolation and decimationcombs of the conventional CIC filter require APIS (APOS) and APOS, respectively. When expanded in treestructure, the transfer function of the modified CIC filter combsection has a maximum of 2 branches and operates ona signal that has zero samples between consecutivesamples of the input signal. This results in every branch re-quiring one addition/subtraction everysamples of the IHSRsignal and the comb stages requiring a maximum of 2APIS or 2 APOS. Therefore, the conventional andmodified CIC filters require and amaximum of APOS, respectively.For values of close to unity, the modified CIC filterrequires approximately 3/2 the number of memory elementsand performs a maximum of moreAPOS than the conventional CIC filter. The extra number ofAPOS is small for SRC factors close to unity and practical filter

154 IEEE SIGNAL PROCESSING LETTERS, VOL. 10, NO. 5, MAY 2003

Fig. 5. Filtered signals before downsampling of (a) conventional CIC filterhaving SNR of�13 dB and (b) modified CIC having SNR of+28 dB.

orders when compared to the total number of computations thatthe conventional CIC filter requires.

IV. SIMULATION RESULTS

In this example, the signal shown in Fig. 4 is processed by afourth-order CIC filter to perform SRC by a factor of 9/10. Theinput signal, chosen to illustrate the benefits of the modified CICfilter, occupies 0.83 of the available digital band and contains31 equal power frequency multiplexed channels and two 25-dBhigher power channels. Fig. 5(a) shows that the conventionalCIC filter fails to attenuate the high-power images resulting invisible aliasing and an SNR of13 dB. Fig. 5(b) shows that themodified CIC filter provides an SNR of 28 dB. Fig. 6 showsthe output signals of both filters where the output of the con-ventional CIC filter [Fig. 6(a)] contains visible aliasing whilethe modified CIC filter [Fig. 6(b)] does not. A second-order in-finite impulse resonse (IIR) filter (requiring two multiplicationsper output sample) is used to correct for the passband droopin the output signals of both CIC filters. Fig. 6 shows that alllow-power channels have approximately equal power, i.e., thereis little passband droop.

V. CONCLUSION

The modified CIC filter provides higher SNRs and betterimage attenuation than the conventional CIC filter by adjusting

Fig. 6. Output signals of (a) conventional CIC showing visible aliasing and(b) modified CIC filter (f is normalized with respect to the intermediate highsample rate). Both filters are followed by second-order IIR filter to correct forthe passband droop of both filters.

the zeros of the filter to target high-power image components.SWR systems can take advantage of this flexibility when thewideband input contains narrowband channels with a high dy-namic range. An SWR receiver can measure the power of dif-ferent channels and correspondingly adjust the delays of the CICfilter to minimize aliasing caused by high-power narrowbandchannels. The modified CIC filter gains this improved perfor-mance over the conventional CIC filter at the expense of a smallincrease in the number of computations.

REFERENCES

[1] R. E. Crochiere and L. R. Rabiner,Multirate Digital Signal Pro-cessing. Englewood Cliffs, NJ: Prentice-Hall, 1983.

[2] T. A. Ramstad, “Digital methods for conversion between arbitrary sam-pling frequencies,”IEEE Trans. Acoust., Speech, Signal Processing, vol.ASSP-32, pp. 577–591, June 1984.

[3] R. E. Crochiere and L. R. Rabiner, “Interpolation and decimation of dig-ital signals—A tutorial review,”Proc. IEEE, vol. 69, pp. 300–331, Mar.1981.

[4] E. B. Hogenauer, “An economical class of digital filters for decimationand interpolation,”IEEE Trans. Acoust., Speech, Signal Processing, vol.ASSP-29, pp. 155–162, Apr. 1981.

[5] L. Wasserman and A. N. Willson Jr., “A variable-rate filtering systemfor digital communications,” inProc. ICASSP, 1999, pp. 1497–1500.

[6] ETSI, “Radio transmission and reception,” Eur. Telecommun. Standard-ization Inst., Sophia-Antipolis, France, GSM 5.05, 1986.