Ground Clutter Canceling with a Regression Filter

Transcription

1 1364 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 Ground Clutter Canceling with a Regression Filter SEBASTIÁN M. TORRES Cooerative Institute for Mesoscale Meteorological Studies, Norman, Oklahoma DUSAN S. ZRNIC NOAA/ERL/National Severe Storms Laboratory, Norman, Oklahoma (Manuscrit received 10 Setember 1998, in final form 4 January 1999) ABSTRACT This aer exlores ground clutter filtering with a class of cancelers that use regression. Regression filters erform this task in a simle manner, resulting in similar or better erformance than the fifth-order ellitic filter imlemented in the WSR-88D. Assuming a slowly varying clutter signal, a suitable rojection of the comosite signal is used to notch a band of frequencies at either side of zero Doler frequency. The comlexity of this rocedure is reduced by using a set of orthogonal olynomials. The frequency resonse of the resulting filter is related to the number of samles in each inut block and the maximum order of aroximating olynomials. Through simulations, it is demonstrated that the suression characteristic of this filter is better than that of ste-initialized infinite imulse resonse filters, whereby transients degrade the theoretical frequency resonse. The erformance of regression filters is tested with an actual weather signal, and their efficiency in ground clutter canceling is demonstrated. 1. Introduction Weather radar data are often contaminated with unwanted returns from the ground. Therefore, filtering techniques that attemt to ameliorate these signals are essential in nearly all Doler radar systems. If the clutter is not at least artially removed, it can mimic a meteorological signal and might roduce strongly biased estimates of the three fundamental hysical arameters (mean ower, mean Doler velocity, and sectrum width). In most cases, ground clutter signals have a narrow sectrum width (long correlation time) comared with weather signals, and their mean Doler velocity is zero. Thus, a high ercentage of this interfering signal can be reduced if the sectral comonents in a band centered at zero frequency (zero Doler velocity) are removed by a suitable high-ass filter. Ground clutter filters (GCFs) with shar narrow notches have been successfully designed and imlemented in the WSR-88D to oerate on ulse trains with uniformly saced ulses, that is, uniform ulse reetition time (PRT) (Heiss et al. 1990). In this aer we address the issue of ground clutter elimination with regression filters. Besides being easily Corresonding author address: Sebastian M. Torres, NSSL, 1313 Halley Circle, Norman, OK sebastian.torres@nssl.noaa.gov designed and imlemented, these filters can be directly extended to signals that are nonuniformly samled. First, some concets of clutter filtering are resented with articular emhasis on imlementation of such filters using regression. Once the design variables are described and analyzed, the regression filter erformance is assessed. This is accomlished by studying statistical roerties of sectral moments of simulated weather signals to which ground clutter is suerosed. Finally, a regression filter and a recursive filter designed for the Next Generation Weather Radar (NEXRAD) are alied to a time series of actual weather echoes and ground clutter collected by an oerational WSR-88D. 2. Regression ground clutter filter Ground clutter filters are high-ass filters that ideally remove frequency comonents at either side of zero Doler velocity and leave the rest of the sectrum almost intact. It is very imortant to recognize this roerty during the design hase because any changes in the magnitude resonse will directly bias the estimates of the three arameters of interest. On the other hand, it is relatively easy to rove that the hase characteristic of the filter is immaterial. To observe this, recall that ower, mean velocity, and sectrum width estimates deend on the estimated autocorrelation function of the filtered weather signal. It is well known that the ower sectral density (PSD) of the outut of a linear time American Meteorological Society

2 OCTOBER 1999 TORRES AND ZRNIC 1365 invariant filter S y () is related to the PSD of the inut S x () by the magnitude square of the frequency resonse of the filter, H() 2. That is, S y () S x () H() 2. (1) Moreover, the autocorrelation function is uniquely determined by the corresonding PSD through a Fourier transform air relation. Because the hase resonse of the filter is not involved in this transformations, it has no effect on the autocorrelation of the filter outut weather signal. Here we investigate suitability of regression filters for ground clutter suression and comare their erformance to the fifth-order ellitic infinite imulse resonse (IIR) ground clutter filters imlemented in the WSR-88D. Alication of regression filters to clutter suression in Doler ultrasonic blood flow meters was resented by Hoeks et al. (1991) and extended by Kadi and Louas (1995) and Tor (1997) in the context of a uniform PRT. Alication of the first-order regression GCF to wind rofiling radars was demonstrated by May and Strauch (1998). Classic digital filters can be divided into two classes: finite imulse resonse and infinite imulse resonse filters. For either class, filtering is achieved by suerosition of signal samles. Unlike these filters, regression filters utilize rojections of elements from the signal vector sace S onto the clutter signal subsace W of S. These rojections can be efficiently erformed if W is described by an orthogonal basis B. However, orthogonality alone is not sufficient to comletely secify this basis. To imrove the comutational efficiency of this filtering rocess, we can limit the functions in B to olynomials over a set of discrete oints on the real line. Orthogonal olynomials have received much attention in alications such as rational interolation, least squares olynomial aroximation, and smoothing of nonlinear functions. Egecioglu and Koc (1992) resented an efficient algorithm to generate such olynomials over an arbitrary set of oints {t m } {t 0, t 1,..., t M1 }. Regression filters aroximate their inut signals with olynomial functions in the time domain, and their design is not based on traditional tools such as the imulse or frequency resonses. The clutter signal varies slowly comared to the weather echo signal and consequently can be aroximated with a olynomial of a relatively low degree. This aroximation is usually erformed using least squares methods or the equivalent transformation, which rojects the inut signal samles V(t), t {t m } onto the subsace W sanned by a basis B consisting of 1 orthonormal olynomials. This set of olynomials is given by B {b 0 (t), b 1 (t), b 2 (t),..., b (t)}, where each b i (t) (0 i ) is a olynomial of ith degree; that is, b i (t) c 0i c 1i t c ii t i. Then, the rojection Vˆ (t) (i.e., the clutter signal) is obtained by constructing a linear combination of the elements of FIG. 1. Regression filter block diagram. Signals are rocessed in overlaing blocks of M f samles each. the basis B, that is, the imlication is that Vˆ (t) isinw and, therefore, m i i m i0 ˆV(t ) b (t ). (2) Accordingly, the residue V f (t m ) V(t m ) Vˆ (t m )is associated with the ortion of the inut signal that is not contained in the clutter subsace W [i.e., it is orthogonal to Vˆ (t)]. The i coefficients are comuted using the classical formula (Paoulis 1986, ) M1 m i m i m0 M1 i 2 b i(t m) m0 V(t )b (t ) (V, b ) i i 0,1,...,, (3) b 2 where V and b i are vectors of the samled inut signal and the b i (t) olynomials, resectively. Generalization in this analysis is not lost if each element of B is normalized such that b i 1, where b i 2 (b i, b i ). In addition, to simlify the notation define the basis matrix B and the coefficient vector A as b (t ) b (t ) b (t ) M1 0 b (t ) b (t ) b (t ) M1 1 B and A. 5 b (t 0) b (t 1) b (t M1) (4) Then, assuming a normalized base, Eqs. (2) and (3) can be rewritten as Vˆ B T A and A BV, resectively. Substitution of (3) into (2) roduces Vˆ B T BV. The residue or filtered signal V f can be exressed as V f V Vˆ (I B T B)V FV, (5) where I is the identity matrix and the regression filter matrix is defined by F I B T B. (6) The regression filter block diagram is shown in Fig. 1, and from Eq. (5) it is aarent that the filter is linear (matrix multilication is a linear transformation), timevarying, and resonds to the general inut outut equation of the form

3 1366 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 M1 y(t ) f (t, t )x(t ); l 0,...,M 1, (7) l l m m m0 where f(t l, t m ) are the entries of the matrix F defined in Eq. (6). The filter matrix F deends only on and M, so it can be recomuted for real-time alications and does not need to be recomuted if the notch width or samling scheme do not change. In any case, M need not be equal to the total number of samles M T in the inut signal used to estimate sectral moments. Imlementation of regression filters for the case M T M is discussed by Torres and Zrnic (1998). Hereafter, to avoid confusion we will use M f when referring to the length of the regression filter and M T to indicate the total number of samles in the time series. The frequency resonse H() of a linear shift-invariant system can be defined as the change in magnitude and hase of a comlex exonential signal e jt, which is assed through the system. More recisely, let x(t) and y(t) be the inut and outut of the filter whose imulse resonse is given by h(t). Let x(t) e jt, then the outut y(t) can be obtained by convolving x(t) with h(t), that is, y(t) h(t)*x(t) h(t)x(t t) h(t)e j(tt) [ ] t {t m} t {t m} jt jt jt h(t)e e H()e, t {t m} (8) in which H() describes the frequency resonse at. As reviously stated, the regression filter is time varying. However, the outut to a given signal of M f samles is always the same regardless of when this block of M f samles is encountered in the filtering rocess. We will exloit this fact by deriving an exression for the frequency resonse of the regression filter using Eq. (7) in an analogous fashion as Eq. (8) following the analysis by Tor (1997). That is, consider the regression filter whose inut is an exonential of the form e jt. The outut of this filter is Mf 1 [ ] y(t ) f (t, t )e jt m l l m m0 Mf 1 l m m l l m0 f (t, t ) ex[jt ] ex[jt ] ex[jt ]; l 1,...,M. f (9) Then, by noting the form of (9) we define H(, t ) F () ex[jt ], (10) l l l M 1 jt where F l () f f(t l, m m0 t m)e is the discrete Fourier transform (DFT) of f(t l, t m ) with fixed l. Finally, accounting for all the values of l in the M f samle segment Mf 1 l l0 1 H() F () ex[jt l]. (11) M f Using the results of Eq. (6), each entry in F is given by l m l m i l i m i0 f (t, t ) (t t ) b (t )b (t ), (12) where (t) is the usual discrete-time imulse sequence. The DFT of (12) is l l i l i i0 F () ex[jt ] b (t )B (), (13) where B i () is the DFT of b i (t). Then, 1 M f i0 [ Mf 1 ] l0 H() 1 B () b (t ) ex[jt ], (14) i i l l and finally the frequency resonse of the regression filter is given by 1 2 i M f i0 H() 1 B (). (15) Note that because H() is real, the hase resonse of this filter is constant and we only need to be concerned about its magnitude resonse. Also, as deicted in Fig. 1, H() consists of a direct ath, the 1 in Eq. (15), and a weighted ath given by the least squares fit rojection, which corresonds to the second term. The frequency resonse of the regression filter deends on the number of elements in B (i.e., the maximum degree of the olynomials used for aroximation) and on the number of samles M f in each rocessing block. High-frequency signals exhibit raid changes in time and hence they are better aroximated as increases. Therefore, by increasing, we allow high-frequency comonents to be subtracted from the inut signal, and this results in a broader notch width. On the other hand, for a fixed higher frequencies are eliminated if the filter window M f is shorter. That is, olynomials of a relatively low degree can still follow high-frequency comonents if the filter window is short. Consequently, the notch width of the regression filter increases when M f decreases. This deendence is illustrated in Figs. 2a and 2b for the uniform PRT scheme. From these lots, we can confirm that the notch bandwidth increases with and decreases as M f increases. The WSR-88D fifth-order ellitic GCF can be rogrammed for three different suression levels: low, medium, or high suression. These selections corresond to notch widths of 2.36 (1.18), 3.12 (1.56), and 5.06 ms 1 (2.53 m s 1 ), which do not change with the number of samles M T (Chrisman et al. 1995). The steady-state frequency resonses of the low, medium, and high suression fifth-order ellitic GCF for the WSR-88D are also lotted for comarison in Fig. 2

4 OCTOBER 1999 TORRES AND ZRNIC 1367 FIG. 2. Regression filter frequency resonse (solid lines) with (a) and (b) M f as arameters. The frequency resonses of the low (L), medium (M), and high (H) suression fifth-order ellitic filter used in the WSR-88D are also included (dashed lines) for comarison. Twoulse extension of the ste initialization rocess is used to imrove the resonse of the fifth-order ellitic filter, that is, suress the transient due to the ste inuts at the beginning of ulse bursts for velocity estimation. Bold lines corresond to the filters analyzed in section 4. (dashed lines). The general form of the transfer function of this filter is H (z) WSR-88D b0 bz 1 bz 2 bz 3 bz 4 bz 5, (16) az az az az az FIG. 3. Regression filter 3-dB notch width vs the number of samles and order of aroximating olynomials (solid lines). Notch widths of the WSR-88D filters are indicated with dashed lines. Note that the regression filter with 3 and the medium suression WSR-88D ground clutter filter have matched notch widths for M f 34. These two filters (bold lines) are comared in section 4. where the coefficient a i s and b i s are obtained from the classical design formulas for digital ellitic filters, as given in Parks and Burrus (1987). During scans at elevation angles larger than 1.5 the WSR-88D transmits an interlaced waveform whereby a batch of short PRTs is for Doler measurements. To achieve the indicated frequency resonse, the GCF uses a two-ulse extension of the ste initialization rocess, as described by Sirmans (1992). This rocess consists of setting the filter memories to steady state, assuming a DC clutter signal with amlitude equal to the first ulse in the batch. For this analysis, we adot the number of samles M T 34 in the inut signal. An increase in the number of samles causes a sharer notch, which tends to the theoretical steady-state resonse of (16). In the WSR-88D, the actual number of samles in a radial deends on the volume coverage attern (VCP) mode and can be from 33 to 111 samles. Therefore, the adoted M T 34 reresents a worst-case filter fitting scenario. Figure 3 shows how the filter s 3-dB notch width deends on the number of samles for both classes of GCFs. As a useful tool for further comarison, we find a direct equivalence between each suression level of the fifth-order ellitic filter and the order of aroximating olynomials in the regression filter. Observe, for instance, that for 3 and M f 34, the notch width of the regression filter matches that of the medium suression GCF in the WSR-88D. However, the regression filter achieves a sharer transition region. In section 4, we comare the two filters having this matching condition.

5 1368 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 FIG. 4. Clutter filtering rocess with a regression filter. (a) Sectrum of a weather signal contaminated with ground clutter. (b) Time-domain reresentation of the comosite signal. The dashed line is the third-order olynomial fit to this signal, that is, the estimated clutter. (c) Filtered signal in the time domain used to determine the three fundamental hysical arameters (mean ower, mean Doler velocity, and sectrum width). (d) Sectrum of the filtered signal. The regression filter has several attractive roerties comared to the GCF currently imlemented in the WSR-88D. While the latter is greatly influenced by the filter s transient resonse characteristics, the regression filter inherently avoids these transients (i.e., these filters do not cause transients). Moreover, regression filter s design methods diverge from the ones used with classical filters because their imlementation consists of a matrix multilication instead of a set of equations evaluated recursively at each time ste. Thus, regression filters are well suited for modern array rocessors. 3. Performance analysis of the regression filter In this section, we describe a series of simulations to establish the erformance of the regression filter and comare the results with the fifth-order ellitic GCF imlemented in the WSR-88D. The clutter signal is modeled as a narrowband Gaussian rocess with zero mean velocity. This clutter and white noise are added to a synthetic weather signal (Zrnic 1975). Then, the comosite signal is filtered to remove the ground clutter, and finally the first three moments of the weather Doler sectrum are estimated using the classical ulse air algorithm. This rocess is shown in Fig. 4. Two arameters of interest for these simulations are the signal-to-noise ratio (SNR) and the clutter-to-signal ratio (CSR), which are defined as SNR (db) 10 log 10 (S/N) and CSR (db) 10 log 10 (C/S), where S, C, and N are signal, clutter, and noise owers, resectively. The clutter filter suression ratio (CFSR), a measure of the filter s erformance, is defined by 1 CFSR (db) 10 log 10 ( G noise P out /P in ). (17) In this equation P in and P out are the owers measured at the inut and outut of the filter, resectively, and G noise is the noise gain of the filter defined by P out /P in when the inut to the filter is white noise. Note that G noise deends only on the frequency resonse of the filter, and for the regression filter can be comuted by using (15). The CFSR in the absence of weather signal of both the regression filter and the WSR-88D ellitic filter (described in section 2) is deicted in Fig. 5. Note that for the most common case of narrow clutter sectrum

6 OCTOBER 1999 TORRES AND ZRNIC 1369 FIG. 5. Clutter suression ratio vs the clutter signal sectrum width. Solid lines corresond to regression filters for different values of and dashed lines to the ellitic filters (low, medium, and high suression) imlemented in the WSR-88D. widths (i.e., c 0.5 m s 1 ), the suression ratio of the regression filter with 4 is at least 10 db better than the one achieved by the high-suression ellitic GCF. In general, the regression filter erforms better than the comarable ellitic filter, esecially if the sectrum width of the clutter is very narrow. The suression of weatherlike signals, by these filters, is lotted in Fig. 6, where the mean velocity changes from 0 to 25 m s 1 and the sectrum width is set at 4ms 1, which is the median found in severe storm observations (Doviak and Zrnic 1993). Over 1 db of suression is observed for signal mean velocities below m s 1, deending on the notch width of the filter. At that, erformances of regression filters are comarable to the ellitic filters of corresonding notch width. Similar results hold for weather signals with sectrum width of 1 m s 1 (tyical of stratiform rain) excet the 1-dB suression is for velocities below 3 5 ms 1. These curves (Fig. 6) indicate the ower estimation biases one can exect if the mean velocity of the weather signal is close to zero. However, when the mean velocity of the weather signal is well away from 0ms 1, neither filter biases the ower estimates. For a more realistic situation, a weather signal was combined with the ground clutter and the ratio P out /S was comuted for different CSRs. This analysis is shown in Fig. 7 for a CSR of 20 db. The clutter sectrum width is set at 0.28 m s 1, which is the same as the one used for testing the WSR-88D ground clutter filter erformance (Sirmans 1992). Measurements on the WSR- 88D in Norman, Oklahoma, indicate that the mean of clutter sectrum width is 0.25 m s 1 for a scan rate of 12 s 1 ; therefore, 0.28 m s 1 is in the worst-case category. Figure 7 confirms that the reflectivity estimates can have a significant negative bias if the mean Doler FIG. 6. Suression ratio for the weather signal vs its mean velocity. Here, 4ms 1 (median value in severe storms). Solid lines corresond to regression filters for different values of and dashed lines to the ellitic filters (low, medium, and high suression) imlemented in the WSR-88D. velocity of the weather signal is such that its sectrum overlas the one of the ground clutter. In addition, we observe a small ositive bias (WSR-88D low suression) if the mean Doler velocity dearts from the origin because the clutter signal is not fully removed by the ellitic filter. For the CSR of 40 db (not shown), we found that the ellitic GCF does not remove the clutter signal comletely, leaving an almost constant bias along the entire velocity range. Similar bias was resent for the second-order regression filter, but the fourth-order regression filter had no bias. Evidently, this FIG. 7. Suression ratio of regression and ellitic GCFs vs weather signal mean velocity for a CSR of 20 db. Solid lines corresond to regression filters for different values of and dashed lines to the ellitic filters (low, medium, and high suression) imlemented in the WSR-88D.

7 1370 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 FIG. 8. Pulse-air algorithm statistical erformance: bias and standard deviation of mean Doler velocity and sectrum width estimates (a) vs the weather signal mean velocity and (b) vs the weather signal sectrum width. Parameters for the simulation are indicated in the figure. Solid lines effect gets worse for larger CSR and wider clutter sectrum width, but it can be controlled by adjusting the ground clutter filter frequency resonse. As the ultimate goal is to accurately recover the three first sectral moments of the weather signal, the ulse air statistical erformance for different CSRs was comuted versus (i) the weather signal sectrum width and (ii) the weather signal mean velocity for both regression and ellitic WSR-88D filters. Consider first the case where the weather signal mean velocity is a arameter and the sectrum width is randomly selected from the interval (2, 6) m s 1 (Fig. 8a). Then, there are large ositive biases in both the mean velocity and the sectrum width estimates if the true mean velocity of the weather signal is less than aroximately 5 m s 1. This is due to overla of the weather sectra and clutter notch. A art of the sectrum close to zero velocity is eliminated by the filter; therefore, the nonfiltered comonents bias the velocity uward. Mean velocity bias for the regression filter is about 0.25 m s 1 larger than for the ellitic filter at 10ms 1. The standard deviations of the velocity estimates are comarable and very close to the erformance of the ulse-air algorithm in the absence of clutter. The bias and standard deviation of sectrum widths are smaller (at 8ms 1 ) for the regression filter. Next, we take the weather-signal sectrum width as a arameter and randomly select its mean velocity from the interval (25, 25) m s 1 (Fig. 8b). Notice that variations in the mean velocity bias and the standard deviation increase with the weather-signal sectrum width. This effect is consistent with the algorithm erformance and slightly more evident if there is contamination by the clutter signal. This is because the weather signal extends over a larger ortion of the sectrum and it is more likely to be adversely shaed by the ground clutter filter. The bias in and the standard deviations for the two filters are comarable. A slightly smaller bias and standard deviation are seen for the regression filter. Because the GCF does not remove the clutter signal comletely, for small sectrum widths, we observe a ositive bias in the sectrum width estimates, which increases with the CSR. From these figures, we conclude that influences of the regression filter and the corresonding ellitic filter on the statistical erformance of ulse-air estimators are comarable. 4. Alication of filters to the WSR-88D data Time series data (i.e., I and Q samles) have been collected from a WSR-88D in Memhis at the lowest elevation of 0.5, while the antenna was scanning at 12 s 1. Sixty-four samles of the in-hase comonent (Fig. 9a) reveal a slowly varying clutter signal and ossibly weak weather signal. The Doler sectrum (Fig. 9b) has a eak at zero, which is 75 db above the receiver noise level. This large sectral dynamic range has been routinely observed on both Memhis and Norman WSR- 88D and testifies to the very high quality of the system. The sectrum width of this ground clutter is 0.23 m s 1, the CSR is 33 db and the SNR is 26 db. Figure 10 shows the signals roduced by alication of the regression filter with 3 (solid lines) and the medium suression ellitic filter (dashed lines). The

8 OCTOBER 1999 TORRES AND ZRNIC 1371 FIG. 8.(Continued) corresond to the regression filters for 3 and dashed lines to the medium-suression ellitic filter imlemented in the WSR-88D. regression filter with M f 34 is alied to the 64 inut samles similar to a moving average filter. Note how the in-hase signal after regression filtering has no discernible slow varying comonent, whereas after filtering with the ellitic filter it does. This is also reflected in the sectral shaes at and close to zero velocity. The clutter sectrum has been suressed at least 40 db below the weather eak after alication of the regression filter (Fig. 10b, solid line) and it is slightly above the weather eak after alication of the ellitic filter (Fig. 10b, dashed line). Note that although the notch widths of the two filters are matched, it is the resonse in the transition region of the regression filter that makes it the better of the two. 5. Conclusions FIG. 9. Data collected with the WSR-88D in Memhis at an elevation of 0.5 and a range of 15 km. (a) In-hase comonent and (b) Doler sectrum of the time series to which the von Hann window has been alied. We have exlored the suitability of regression filters for ground clutter suression in Doler weather radars. First, a brief review of how to design these filters and determine the frequency resonse was resented. Parameters that control the frequency resonse are the number of samles to which regression is alied and the degree of the regression olynomial. The increase in the olynomial degree () broadens the filter s notch width because higher frequencies are subtracted from the signal. The notch width also broadens if the number of samles (M f ) decreases because then the regression olynomial better relicates high frequency comonents. Different families of aroximating olynomials only affect the comutational comlexity of the imlementation, which is considerably reduced if this set is orthonormal. Regression filters are easy to imlement and do not require initialization such as is needed in the Doler mode of data rocessing at higher than 1.5 in elevation on the WSR-88D. Preliminary studies and simulations indicate that the suression characteristics of regression filters meet or exceed those of ste-initialized IIR filters (with matched notch width), in which

9 1372 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 16 Frush, D. Ferraro, and J. VanAndel. This work was suorted by the Oerations Suort Facility of the National Weather Service. In addition, the helful comments of the reviewers and Dr. R. Strauch are gratefully acknowledged. FIG. 10. Time series data filtered with the medium-suression regression filter ( 3, solid line) and filtered with the medium suression WSR-88D ground clutter filter (dashed line). (a) In-hase filtered comonent and (b) Doler sectrum of the filtered signal (weighted with the von Hann window). transients degrade the theoretical frequency resonse. For 3 and M f 32, the regression filter aroximates the statistical erformance of the medium-suression fifth-order ellitic filter in the WSR-88D. Comarison of the two filters (with matched notch width) on an actual weather signal, collected by an oerational WSR-88D, indicates that the regression filter erforms better. This is due to the suerior shae of the regression filter s frequency resonse in the cutoff region. Acknowledgments. The authors areciate suggestions by R. J. Doviak, which have imroved the aer. The Memhis data were collected and sulied by C. REFERENCES Chrisman, J. N., D. M. Rinderknecht, and R. S. Hamilton, 1995: WSR-88D clutter suression and its imact on meteorological data interretation. Postrints, The First WSR-88D User s Conf., Norman, OK, WSR-88D Oerational Suort Facility and NEX- RAD Joint System Program Office, Doviak, R. J., and D. Zrnic, 1993: Doler Radar and Weather Observations. 2d ed. Academic Press, 562. Egecioglu, O., and C. Koc, 1992: A arallel algorithm for generating discrete orthogonal olynomials. Parallel Comuting, 18, Heiss, W., D. McGrew, and D. Sirmans, 1990: NEXRAD: Next Generation Weather Radar (WSR-88D). Microwave J., 33, Hoeks, A. P., J. J. van-de-vorst, A. Dabekaussen, P. J. Brands, and R. S. Reneman, 1991: An efficient algorithm to remove low frequency Doler signals in digital Doler systems. Ultrason. Imag., 13, Kadi, A. P., and T. Louas, 1995: On the erformance of regression and ste-initialized IIR clutter filters for color Doler systems in diagnostic medial ultrasound. IEEE Trans. Ultrason., Ferroelect., Freq. Control, 42, May, P. T., and R. G. Strauch, 1998: Reducing the effect of ground clutter on wind rofiler velocity measurements. J. Atmos. Oceanic Technol., 15, Paoulis, A., 1986: Signal Analysis. 3d ed. McGraw-Hill, 431. Parks, T. W., and C. S. Burrus, 1987: Digital Filter Design. John Wiley and Sons, 342. Sirmans, D., 1992: Clutter filtering in the WSR-88D. NWS/OSF Internal Re., 125. [Available from National Weather Service Oerational Suort Facility, 1200 Weistheimer Dr., Norman, OK ] Tor, H., 1997: Clutter rejection filters in color flow imaging: Atheoretical aroach. IEEE Trans. Ultrason., Ferroelect., Freq. Control, 44, Torres, S., and D. Zrnic, 1998: Ground clutter canceling with a regression filter. NSSL Interim Re. 35. [Available from Doler Radar and Remote Sensing Grou, National Severe Storms Laboratory, 1313 Halley Circle, Norman, OK ] Zrnic, D., 1975: Simulation of weatherlike Doler sectra and signals. J. Al. Meteor., 14,