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8.3.6.2 FIR Filter Section

The second section of the digital filter is a multistage, FIR low-pass filter. Partially filtered data from the sinc filter are input to the FIR filter. The FIR filter determines the final frequency and phase response of the data. Figure 8-14 shows that the FIR filter consists of four stages.

Figure 8-14 FIR Filter

The first two FIR stages are half-band filters with decimation = 2 for each stage. The third and fourth FIR stages determine the final frequency and phase response. Decimation is 4 and 2, for FIR stages three and four. The overall decimation ratio of the FIR filter is 32. Unique coefficient sets in stage 3 and 4 determine linear and minimum phase filter response. The phase response is selected by the PHASE bit of the CONFIG0 register. Table 8-4 lists the combined decimation ratio of the sinc and FIR filter stages and the corresponding FIR filter data rate.

Table 8-4 FIR Filter Data Rate

DR[2:0] BITS	COMBINED DECIMATION RATIO	DATA RATE (SPS)
DR[2:0] BITS	COMBINED DECIMATION RATIO	HIGH- AND MID-POWER MODES	LOW-POWER MODE
000	8192	250	125
001	4096	500	250
010	2048	1000	500
011	1024	2000	1000
100	512	4000	2000

Table 8-5 lists the FIR filter coefficients and the data scaling for the linear and minimum phase coefficients.

Table 8-5 FIR Filter Coefficients

COEFFICIENT	STAGE 1	STAGE 2	STAGE 3		STAGE 4
	SCALE = 1/512	SCALE = 1/8388608	SCALE = 1/134217728		SCALE = 1/134217728
	LINEAR PHASE	LINEAR PHASE	LINEAR PHASE	MINIMUM PHASE	LINEAR PHASE	MINIMUM PHASE
b₀	3	–10944	0	819	–132	11767
b₁	0	0	0	8211	–432	133882
b₂	–25	103807	–73	44880	–75	769961
b₃	0	0	–874	174712	2481	2940447
b₄	150	–507903	–4648	536821	6692	8262605
b₅	256	0	–16147	1372637	7419	17902757
b₆	150	2512192	–41280	3012996	–266	30428735
b₇	0	4194304	–80934	5788605	–10663	40215494
b₈	–25	2512192	–120064	9852286	–8280	39260213
b₉	0	0	–118690	14957445	10620	23325925
b₁₀	3	–507903	–18203	20301435	22008	–1757787
b₁₁		0	224751	24569234	348	–21028126
b₁₂		103807	580196	26260385	–34123	–21293602
b₁₃		0	893263	24247577	–25549	–3886901
b₁₄		–10944	891396	18356231	33460	14396783
b₁₅			293598	9668991	61387	16314388
b₁₆			–987253	327749	–7546	1518875
b₁₇			–2635779	–7171917	–94192	–12979500
b₁₈			–3860322	–10926627	–50629	–11506007
b₁₉			–3572512	–10379094	101135	2769794
b₂₀			–822573	–6505618	134826	12195551
b₂₁			4669054	–1333678	–56626	6103823
b₂₂			12153698	2972773	–220104	–6709466
b₂₃			19911100	5006366	–56082	–9882714
b₂₄			25779390	4566808	263758	–353347
b₂₅			27966862	2505652	231231	8629331
b₂₆			25779390	126331	–215231	5597927
b₂₇			19911100	–1496514	–430178	–4389168
b₂₈			12153698	–1933830	34715	–7594158
b₂₉			4669054	–1410695	580424	–428064
b₃₀			–822573	–502731	283878	6566217
b₃₁			–3572512	245330	–588382	4024593
b₃₂			–3860322	565174	–693209	–3679749
b₃₃			–2635779	492084	366118	–5572954
b₃₄			–987253	231656	1084786	332589
b₃₅			293598	–9196	132893	5136333
b₃₆			891396	–125456	–1300087	2351253
b₃₇			893263	–122207	–878642	–3357202
b₃₈			580196	–61813	1162189	–3767666
b₃₉			224751	–4445	1741565	1087392
b₄₀			–18203	22484	–522533	3847821
b₄₁			–118690	22245	–2490395	919792
b₄₂			–120064	10775	–688945	–2918303
b₄₃			–80934	940	2811738	–2193542
b₄₄			–41280	–2953	2425494	1493873
b₄₅			–16147	–2599	–2338095	2595051
b₄₆			–4648	–1052	–4511116	–79991
b₄₇			–874	–43	641555	–2260106
b₄₈			–73	214	6661730	–963855
b₄₉			0	132	2950811	1482337
b₅₀			0	33	–8538057	1480417
b₅₁			0	0	–10537298	–586408
b₅₂					9818477	–1497356
b₅₃					41426374	–168417
b₅₄					56835776	1166800
b₅₅					41426374	644405
b₅₆					9818477	–675082
b₅₇					–10537298	–806095
b₅₈					–8538057	211391
b₅₉					2950811	740896
b₆₀					6661730	141976
b₆₁					641555	–527673
b₆₂					–4511116	–327618
b₆₃					–2338095	278227
b₆₄					2425494	363809
b₆₅					2811738	–70646
b₆₆					–688945	–304819
b₆₇					–2490395	–63159
b₆₈					–522533	205798
b₆₉					1741565	124363
b₇₀					1162189	–107173
b₇₁					–878642	–131357
b₇₂					–1300087	31104
b₇₃					132893	107182
b₇₄					1084786	15644
b₇₅					366118	–71728
b₇₆					–693209	–36319
b₇₇					–588382	38331
b₇₈					283878	38783
b₇₉					580424	–13557
b₈₀					34715	–31453
b₈₁					–430178	–1230
b₈₂					–215231	20983
b₈₃					231231	7729
b₈₄					263758	–11463
b₈₅					–56082	–8791
b₈₆					–220104	4659
b₈₇					–56626	7126
b₈₈					134826	–732
b₈₉					101135	–4687
b₉₀					–50629	–976
b₉₁					–94192	2551
b₉₂					–7546	1339
b₉₃					61387	–1103
b₉₄					33460	–1085
b₉₅					–25549	314
b₉₆					–34123	681
b₉₇					348	16
b₉₈					22008	–349
b₉₉					10620	–96
b₁₀₀					–8280	144
b₁₀₁					–10663	78
b₁₀₂					–266	–46
b₁₀₃					7419	–42
b₁₀₄					6692	9
b₁₀₅					2481	16
b₁₀₆					–75	0
b₁₀₇					–432	–4
b₁₀₈					–132	0
b₁₀₉					0	0

Figure 8-15 shows the FIR pass-band frequency response to 0.375 × f_DATA with ±0.003-dB pass-band ripple. Figure 8-16 shows the pass-band, transition-band, and stop-band performance from 0 Hz to f_DATA. The filter is designed for –135-dB stop-band attenuation at the Nyquist frequency.

Figure 8-15 FIR Filter Pass-Band Response

Figure 8-16 FIR Filter Transition Band Response

As with many sampled systems, the filter response repeats at multiples of the modulator sample rate (f_MOD). The filter response repeats at frequencies = N × f_MOD ± f₀, where N = 1, 2, and so on, and f₀ = filter pass-band). These frequencies, if not filtered and are otherwise present in the signal, fold back (or alias) into the pass-band causing errors. A low-pass input filter reduces the aliasing error. For a band-limited signal typical of many geophones, a single-pole filter at the PGA output is sufficient to suppress the aliasing frequencies.