Appendix H. Frequency Sampling Filter Design Tables

In Section 7.1 we described the so-called Type-IV frequency sampling filter (FSF). The tables in this appendix provide a list of optimum transition coefficient values for the Case I (see Figure 7-25) Type-IV lowpass FSFs of various passband bandwidths, over a range of values of N. Table H-1 provides the H(k) single transition coefficient and two transition coefficients for even values of N. Table H-2 provides the H(k) three transition coefficients for even N. Table H-3 provides the H(k) single transition coefficient and two transition coefficients for odd values of N, while Table H-4 provides the H(k) three transition coefficients for odd N.

The passband bandwidth in these tables, signified by the BW parameter, is the number of FSF sections having unity-valued H(k) gain factors. For example, an N = 32 lowpass FSF using six passband sections and a single transition region coefficient (T1) would have the H(k) gain values shown in Figure H-1(a). In this case, the T1 coefficient would be found in Table H-1 for N = 32 at a bandwidth BW = 6. An N = 23 lowpass FSF with five passband sections and two transition region coefficients (T1 and T2) would have the H(k) gain values shown in Figure H-1(b). In this case, the T1 and T2 coefficients are found in Table H-2 for N = 23 at a bandwidth BW = 5. An additional parameter in the tables is the maximum stopband sidelobe attenuation levels (Atten).

Figure H-1. Transition coefficient examples: (a) one coefficient for N = 32 and BW = 6; (b) two coefficients for N = 23 and BW = 5.

 

 

 

 

 

Table H-1. Lowpass Type-IV FSF for Even N (One and Two Coefficients)

BW	Atten	T1	BW	Atten	T1	T2
	N = 16				N = 16
1	–44.9	0.41924081	1	–76.5	0.56626687	0.07922718
2	–45.8	0.38969818	2	–77.2	0.55487263	0.08012238
3	–47.3	0.36942214	3	–81.2	0.53095099	0.07087993
4	–49.6	0.34918551	4	–87.7	0.49927622	0.05813368
	N = 24				N = 24
1	–44	0.42452816	1	–73.6	0.57734042	0.08641861
2	–44.1	0.40042889	2	–72.5	0.57708274	0.09305238
3	–44.9	0.38622106	3	–72.9	0.56983709	0.09177956
4	–45.7	0.37556064	4	–73.8	0.55958351	0.08770698
5	–46.5	0.36663149	5	–75.6	0.54689579	0.08202772
	N = 32				N = 32
1	–43.6	0.42638815	1	–72.6	0.58109341	0.08892320
2	–43.6	0.40407598	2	–71	0.58466392	0.09771906
3	–44	0.39197681	3	–70.8	0.58101218	0.09823378
4	–44.5	0.38377786	5	–71.6	0.57002693	0.09442029
6	–45.5	0.37172559	7	–73.2	0.55593774	0.0879846
7	–45.8	0.38912443	9	–76.2	0.53661082	0.07884406
8	–46.6	0.36087271	13	–106	0.43242657	0.03643965
	N = 48				N = 48
1	–43.4	0.42772741	1	–72	0.58385966	0.09079945
2	–43.2	0.40654471	2	–70	0.58999731	0.10107095
3	–43.5	0.39569517	3	–69.5	0.58898579	0.1030238
4	–43.8	0.38879556	5	–69.6	0.58356869	0.10204926
6	–44.4	0.37994174	7	–70	0.57749269	0.09959325
8	–44.9	0.37394938	9	–70.6	0.57143299	0.09683486
10	–45.3	0.3690437
	N = 64				N = 64
1	–43.3	0.42815077	1	–71.8	0.58480329	0.09144087
2	–43.1	0.40742967	2	–69.7	0.59178518	0.10221701
3	–43.4	0.39690507	3	–69.2	0.59168291	0.10467406
4	–43.6	0.39043339	4	–68.9	0.5899207	0.10496398
5	–43.9	0.38583162	5	–68.9	0.58788109	0.10457886
6	–44.1	0.38244173	9	–69.4	0.58010661	0.10157302
10	–44.7	0.37382147	13	–70.2	0.57272483	0.09810828
14	–45.3	0.36813961	17	–71.1	0.56417336	0.09386963
	N = 96				N = 96
1	–43.2	0.42856954	1	–71.6	0.585424	0.09185794
2	–43	0.40790815	2	–69.5	0.59305878	0.10302346
3	–43.3	0.3977603	3	–68.8	0.59332978	0.10571202
4	–43.5	0.39154291	4	–68.4	0.59202942	0.10623854
5	–43.7	0.38719365	5	–68.3	0.59062246	0.10623287
6	–43.9	0.38409245	9	–68.5	0.58514671	0.10445521
10	–44.4	0.37686993	13	–68.9	0.58087019	0.10253761
14	–44.7	0.37270333	17	–69.3	0.57751103	0.10097157
18	–45	0.36984146	21	–65.3	0.59419612	0.11180709
	N = 128				N = 128
1	–43.2	0.42864273	1	–71.6	0.58574352	0.09208128
2	–43	0.40823844	2	–69.4	0.59357535	0.10335703
3	–43.2	0.39811024	3	–68.6	0.59383385	0.10601544
4	–43.4	0.39188378	4	–68.3	0.59279342	0.10671242
5	–43.7	0.38774353	6	–68.1	0.59024028	0.10655014
7	–44	0.38236389	9	–68.2	0.5868017	0.10542034
10	–44.3	0.37771128	17	–68.7	0.58071332	0.10271656
18	–44.8	0.3717883	25	–69.2	0.57652818	0.1006787
26	–45.1	0.36862161	33	–69.8	0.57265344	0.09871098
	N = 192				N = 192
1	–43.2	0.42881027	1	–71.5	0.58589507	0.09218797
2	–43	0.40831822	2	–69.4	0.59383365	0.1035231
3	–43.2	0.39830476	3	–68.6	0.59433749	0.10635017
4	–43.4	0.39219024	4	–68.2	0.5933049	0.10702144
5	–43.6	0.38797095	6	–67.9	0.59098287	0.10700026
7	–43.9	0.3828125	9	–68	0.58790082	0.10604544
10	–44.2	0.37845008	17	–68.4	0.58295021	0.10399738
18	–44.7	0.37302517	25	–68.7	0.57978921	0.10242432
26	–44.9	0.37049755	33	–69	0.57773363	0.10143253
34	–45	0.36908526	41	–69.2	0.57597277	0.10055134
42	–45.2	0.36764286	49	–69.5	0.57407637	0.09954949
	N = 224				N = 224
1	–43.2	0.42874481	1	–71.5	0.58591935	0.09220841
2	–43	0.40836093	2	–69.4	0.593894	0.10355622
3	–43.2	0.39831237	3	–68.5	0.59435536	0.10634325
4	–43.4	0.3921651	4	–68.1	0.59354863	0.10719315
5	–43.6	0.38807204	6	–67.9	0.59106856	0.1070268
7	–43.9	0.38281226	9	–67.9	0.58816185	0.10619806
10	–44.2	0.37847605	10	–67.9	0.58726527	0.10582934
11	–44.3	0.37742038	17	–68.3	0.58317185	0.10407347
18	–44.6	0.37324982	33	–68.8	0.57860121	0.10189345
34	–45	0.36946431	49	–69.2	0.5757377	0.10043439
50	–45.2	0.36753866	57	–69.4	0.57440527	0.09975201
	N = 256				N = 256
1	–43.2	0.42874481	1	–71.5	0.58599793	0.09225917
2	–43	0.40844072	2	–69.4	0.59395199	0.10360852
3	–43.2	0.39839019	3	–68.5	0.59445009	0.10641045
4	–43.4	0.39231838	4	–68.1	0.59358715	0.10721801
5	–43.6	0.38814788	6	–67.9	0.59121865	0.10712227
7	–43.9	0.38296192	9	–67.9	0.58824601	0.10622746
10	–44.2	0.37855003	10	–67.9	0.58727091	0.10580213
11	–44.3	0.37756795	17	–68.2	0.58347729	0.10424412
18	–44.6	0.3733958	33	–68.7	0.57913354	0.1021842
34	–44.9	0.36982575	49	–69	0.57667852	0.10093887
50	–45.1	0.36804233	57	–69.2	0.57568486	0.10043603
58	–45.2	0.3673716	65	–69.3	0.57469205	0.09993526

 

 

 

Table H-2. Lowpass Type-IV FSF for Odd N (One and Two Coefficients)

BW	Atten	T1	BW	Atten	T1	T2
	N = 15				N = 15
1	–45.1	0.41802444	1	–77.3	0.56378193	0.07767395
2	–46.2	0.38716426	2	–78.9	0.54831544	0.07646082
3	–48	0.36461603	3	–83.4	0.52139051	0.06627593
4	–51.4	0.34005655	4	–96.3	0.47732772	0.0487037
	N = 23				N = 23
1	–44	0.42412451	1	–73.8	0.57648809	0.08585489
2	–44.3	0.3995718	2	–72.7	0.57569102	0.09221862
3	–45.1	0.38497937	3	–73.2	0.56732401	0.09032595
4	–46	0.37367551	4	–74.6	0.55575797	0.08563268
5	–46.8	0.36445788	5	–76.5	0.54245814	0.07981527
	N = 33				N = 33
1	–43.6	0.42659097	1	–72.6	0.58141103	0.08913503
2	–43.5	0.40433257	2	–70.9	0.58529197	0.09811292
3	–44	0.39239983	3	–70.7	0.58187597	0.09874619
4	–44.4	0.3843389	5	–71.3	0.57154421	0.09525674
6	–45.3	0.37272147	7	–72.9	0.55826179	0.08918146
8	–46.4	0.36256798	9	–75.3	0.54128598	0.08116809
	N = 47				N = 47
1	–43.4	0.42768264	1	–72	0.58376507	0.09073592
2	–43.2	0.40649692	2	–70.1	0.58975381	0.1009182
3	–43.5	0.39553589	3	–69.6	0.5886934	0.10284475
4	–43.8	0.38859729	5	–69.6	0.58311582	0.10178496
6	–44.4	0.37968179	7	–70.1	0.57687412	0.09925266
8	–44.9	0.37362421	9	–70.7	0.57045477	0.0963056
10	–45.4	0.36853968	11	–71.6	0.56319305	0.09280396
	N = 65				N = 65
1	–43.3	0.4281872	1	–71.7	0.58480896	0.09144011
	–43.1	0.40743541	2	–69.7	0.59188395	0.10227409
3	–43.4	0.39694541	3	–69.1	0.59158717	0.10459977
4	–43.6	0.39043991	4	–68.9	0.59001405	0.10501496
5	–43.9	0.3859325	5	–68.8	0.58797401	0.10462176
6	–44.1	0.38249194	9	–69.4	0.58031079	0.10167681
10	–44.7	0.37399454	13	–70.1	0.57312044	0.09830111
14	–45.2	0.36841874	17	–71	0.56506463	0.0943328
18	–45.8	0.36324429	21	–72.5	0.55369626	0.08867447
	N = 95				N = 95
1	–43.2	0.42852251	1	–71.6	0.58559589	0.09199196
2	–43	0.40799464	2	–69.5	0.59306419	0.10302347
3	–43.3	0.39772511	3	–68.8	0.59323668	0.10563966
4	–43.5	0.39143867	4	–68.5	0.59207559	0.10628422
5	–43.7	0.38722579	5	–68.3	0.5905046	0.10614086
6	–43.9	0.38400287	9	–68.5	0.58506537	0.10440925
10	–44.4	0.3766755	13	–68.9	0.58094477	0.10262083
14	–44.8	0.37268027	17	–69.3	0.57725045	0.10081244
18	–45	0.369842	21	–69.8	0.57370707	0.09903691
	N = 125				N = 125
1	–43.2	0.42857276	1	–71.5	0.5856764	0.0920373
2	–43	0.40819419	2	–69.5	0.59346193	0.10328234
3	–43.2	0.39806479	3	–68.7	0.59389103	0.1060686
4	–43.5	0.39191493	5	–68.1	0.59144981	0.1067222
6	–43.8	0.38458541	7	–68.1	0.58887274	0.10611287
8	–44.1	0.38046599	9	–68.2	0.58670301	0.10535739
10	–44.3	0.37761366	17	–68.7	0.5805297	0.10262003
18	–44.8	0.37166577	25	–69.3	0.57610034	0.10041636
26	–45.1	0.36836415	33	–69.9	0.57206269	0.0984002
	N = 191				N = 191
1	–43.2	0.42865655	1	–71.5	0.5859143	0.09220684
2	–43	0.40839373	2	–69.4	0.5937664	0.10346999
3	–43.2	0.39822053	3	–68.5	0.59423193	0.1062604
4	–43.4	0.39214502	5	–68	0.59213475	0.1071269
6	–43.8	0.38503751	7	–67.9	0.589875	0.10671096
8	–44	0.38095089	9	–68	0.58788996	0.10603382
10	–44.2	0.37828083	17	–68.4	0.58282022	0.10390276
18	–44.7	0.37305805	25	–68.7	0.57971044	0.10236319
26	–44.9	0.37048161	33	–69	0.57760031	0.10133385
34	–45	0.36904678	41	–69.2	0.57578133	0.10042123
42	–45.1	0.3676021	49	–69.5	0.57404729	0.09954845
	N = 223				N = 223
1	–43.2	0.42874481	1	–71.5	0.58589267	0.0921919
2	–43	0.40836093	2	–69.4	0.59379277	0.10347913
3	–43.2	0.39835128	3	–68.5	0.59435536	0.10634325
4	–43.4	0.3921651	4	–68.1	0.59354863	0.10719315
5	–43.6	0.38807204	6	–67.9	0.59114264	0.10708575
7	–43.9	0.38288709	9	–67.9	0.58797899	0.10606475
10	–44.2	0.37851304	10	–67.9	0.58726527	0.10582934
11	–44.3	0.37742038	17	–68.3	0.58329541	0.10416575
18	–44.6	0.37324982	33	–68.8	0.57849661	0.10182631
34	–45	0.36946431	49	–69.2	0.57568307	0.10040604
50	–45.2	0.3674667	57	–69.4	0.5744086	0.09975962
	N = 255				N = 255
1	–43.2	0.42874481	1	–71.5	0.58590294	0.09218854
2	–43	0.40836093	2	–69.3	0.59392035	0.10356223
3	–43.2	0.39831237	3	–68.5	0.59440493	0.10637653
4	–43.4	0.39224174	4	–68.1	0.59363182	0.10725379
5	–43.6	0.38814788	6	–67.9	0.59121586	0.10712951
7	–43.9	0.38296192	9	–67.9	0.58822523	0.10621751
10	–44.2	0.37855003	10	–67.9	0.58747402	0.10596604
11	–44.3	0.37756795	17	–68.2	0.58351595	0.10427857
18	–44.6	0.3733958	33	–68.7	0.57906429	0.10213183
34	–44.9	0.36982575	49	–69	0.57660259	0.10088411
50	–45.1	0.36804233	57	–69.2	0.57562728	0.10040259
58	–45.2	0.3673716	65	–69.4	0.57461162	0.09987875

 

 

 

Table H-3. Lowpass Type-IV FSF for Even N (Three Coefficients)

BW	Atten	T1	T2	T3
		N = 16
1	–112.6	0.64272445	0.15442399	0.00880089
2	–95.9	0.70487291	0.22419597	0.01947599
3	–100.7	0.70063089	0.21872748	0.01757096
4	–115.9	0.68531929	0.19831357	0.01270197
		N = 24
1	–103.8	0.6599002	0.17315143	0.01189889
2	–101.8	0.67718249	0.19461557	0.01429673
3	–95.5	0.69609682	0.21773826	0.01860944
4	–104.1	0.66830223	0.18959572	0.01339907
		N = 32
1	–99.6	0.6642114	0.17798254	0.01278046
2	–98.5	0.68804961	0.20639825	0.01646338
4	–87.4	0.73378289	0.26142233	0.02762054
6	–100.5	0.67913658	0.20169658	0.01554611
8	–105.3	0.65936975	0.18380663	0.01270743
		N = 48
1	–93.8	0.68361144	0.2010237	0.01735969
2	–96	0.69534463	0.21480253	0.01812435
4	–87.2	0.73314865	0.26098449	0.02762804
6	–86.4	0.73802064	0.26732823	0.02900775
8	–95	0.69703503	0.2211425	0.01909109
10	–90	0.71746809	0.24474881	0.02420421
		N = 64
1	–96.6	0.67620503	0.19208214	0.01551621
2	–94.9	0.69693984	0.21653685	0.01842226
3	–89.7	0.72079468	0.24569738	0.02432222
4	–92.3	0.7068141	0.22927121	0.02042893
8	–91.4	0.70957119	0.23498487	0.02215407
12	–93.8	0.7026052	0.22772953	0.02059288
16	–85.3	0.74439511	0.27543213	0.03085705
		N = 96
1	–98.5	0.6720933	0.18712559	0.01449609
2	–92.9	0.70471821	0.22591053	0.02048075
3	–93	0.70905096	0.23165702	0.02121954
4	–88.7	0.72625477	0.25269331	0.02574193
8	–90.8	0.71369108	0.23929089	0.02281527
12	–90.8	0.71110318	0.23715671	0.02248568
16	–85.2	0.74356072	0.27478153	0.03080406
20	–85.8	0.74022029	0.27104418	0.02999046
		N = 128
1	–98.3	0.67221636	0.18725564	0.01451885
2	–94.4	0.70015724	0.22042278	0.01929075
3	–92.6	0.70981704	0.23257905	0.02143209
5	–90.6	0.71933148	0.24480839	0.02391897
8	–89.8	0.72190475	0.24869701	0.02481883
16	–88.5	0.72569265	0.25405918	0.02615712
24	–87.4	0.7301942	0.25964746	0.02748522
		N = 192
1	–98.1	0.67216994	0.1871603	0.01447431
2	–94.3	0.70064573	0.22097713	0.01939796
3	–92.6	0.71046628	0.23329177	0.02156244
5	–90.6	0.71933299	0.24477507	0.0238993
8	–89.8	0.72185688	0.24857861	0.02477626
16	–88.5	0.72617255	0.2545026	0.02622728
24	–87.7	0.72957884	0.25880678	0.02726692
32	–90.9	0.71321929	0.24041037	0.02328586
40	–91.2	0.71133926	0.23853571	0.02293979
48	–91.4	0.70862489	0.2357226	0.0224067
		N = 224
1	–98.2	0.67256687	0.18767169	0.01459779
2	–94.2	0.70077254	0.22112728	0.01942992
3	–90.4	0.7026477	0.22304697	0.01885735
5	–91.1	0.71677647	0.24176238	0.0232377
8	–89.9	0.72168089	0.24837531	0.02473386
9	–89.8	0.71675825	0.24253218	0.02331464
16	–90.3	0.71805244	0.24514888	0.0241623
32	–90.6	0.71429115	0.24150812	0.0234885
48	–91.1	0.71133746	0.23857357	0.02295657
		N = 256
1	–95.7	0.67780153	0.19398356	0.01590119
2	–94	0.70138048	0.22187281	0.01959708
3	–90.3	0.70235664	0.22265441	0.01875372
5	–91	0.71654134	0.24139758	0.02311255
8	–89.9	0.72167623	0.24835995	0.02472548
9	–89.7	0.71676546	0.24249377	0.02328724
16	–90.2	0.71841628	0.24555225	0.02424786
32	–90.5	0.71523646	0.24257287	0.02372755
48	–90.8	0.71282545	0.2402303	0.02331467
56	–90.7	0.71353605	0.24104134	0.02347778

 

 

 

Table H-4. Lowpass Type-IV FSF for Odd N (Three Coefficients)

BW	Atten	T1	T2	T3
		N = 15
1	–99.1	0.67276446	0.18765467	0.01448603
2	–109	0.65109591	0.16879848	0.01032845
3	–103	0.64743501	0.16597437	0.00887322
4	–129.8	0.58430569	0.11830427	0.0041067
		N = 23
1	–98.6	0.67021235	0.18516808	0.01420518
2	–96.9	0.6596023	0.17408826	0.00996838
3	–95.3	0.64635467	0.16260027	0.0077623
4	–86.1	0.60390729	0.12509768	0.00296913
		N = 33
1	–98.4	0.67150869	0.18654613	0.01442309
2	–97.9	0.68975409	0.20844142	0.01686088
4	–93.8	0.70392025	0.22717012	0.02035858
6	–92.1	0.70836197	0.23374423	0.02185812
8	–92.9	0.70271751	0.22868478	0.02098636
		N = 47
1	–99.7	0.66933083	0.18386234	0.01384901
2	–94.7	0.69037782	0.20845236	0.01654889
4	–94.4	0.70435781	0.22714301	0.02019897
6	–94.5	0.70200706	0.22582668	0.01999782
8	–95.4	0.69662478	0.22082819	0.01907788
10	–97	0.69029654	0.21493063	0.01807728
12	–88.8	0.64107819	0.16254219	0.0076571
		N = 65
1	–98.8	0.67071168	0.18547676	0.01416929
2	–94.8	0.69743725	0.21725	0.01864255
3	–93.6	0.70659336	0.22882367	0.02062804
4	–93	0.70962871	0.23307976	0.02141978
8	–92.6	0.70884359	0.23403175	0.02173011
12	–88.7	0.72402053	0.25220517	0.02579854
16	–89.9	0.71679306	0.24461807	0.02427071
		N = 95
1	–98.6	0.67204252	0.18706788	0.0144861
2	–94.5	0.69934889	0.21945399	0.01908355
3	–93	0.70879388	0.23134381	0.02114855
4	–92.2	0.71277193	0.23666779	0.0221755
8	–89.2	0.72434568	0.25160197	0.02547937
12	–88.8	0.72479877	0.25277864	0.02583655
16	–90.1	0.71754976	0.24492389	0.02419794
20	–92.6	0.70606236	0.23250776	0.02165584
		N = 125
1	–98.3	0.67220923	0.18724753	0.01451708
2	–94.4	0.7001615	0.22041952	0.01928486
4	–90.8	0.71816438	0.24299337	0.02355056
6	–90.5	0.71950797	0.24538851	0.02405304
8	–90.5	0.71546288	0.2410237	0.02303409
16	–89.5	0.72139717	0.24910324	0.02505485
24	–89.9	0.71817491	0.24597097	0.02448715
32	–88.9	0.72170356	0.25030101	0.02550214
		N = 191
1	–98.1	0.67223344	0.1872747	0.01452257
2	–94.3	0.70075621	0.22112031	0.01943466
4	–90.5	0.7196321	0.24471727	0.02393159
6	–90.9	0.71816017	0.24379217	0.02370239
8	–90.4	0.71833134	0.24451461	0.02390559
16	–90.4	0.71734228	0.244362	0.02399541
24	–90.1	0.71838476	0.24599127	0.02444213
32	–89	0.72239379	0.25075541	0.02551853
40	–89.7	0.7188511	0.24690437	0.0247143
48	–91.6	0.70888027	0.23598149	0.02243978
		N = 223
1	–98.2	0.67257273	0.18768014	0.01460038
2	–94.2	0.70072996	0.22108243	0.01942305
3	–90.4	0.70262204	0.22302806	0.0188601
5	–91	0.71641456	0.24126979	0.02309323
8	–89.9	0.72166528	0.24835901	0.02473006
9	–89.8	0.71674758	0.24252389	0.02331481
16	–90.3	0.7179882	0.24507651	0.02414698
32	–90.6	0.71403002	0.24119297	0.02341017
48	–91.2	0.71143573	0.2386827	0.02297579
56	–90.7	0.71338506	0.24097504	0.02348867
		N = 255
1	–97.6	0.67176623	0.18670931	0.01441482
2	–94.2	0.70070534	0.22105163	0.01941457
3	–90.3	0.70233551	0.22263226	0.01874791
5	–91	0.71654995	0.24140965	0.02311617
8	–89.9	0.72164196	0.24831241	0.02471143
9	–89.7	0.71673449	0.2424607	0.02328277
16	–90.1	0.71885073	0.24604614	0.02435372
32	–89.6	0.71549778	0.24342724	0.02411907
48	–90.9	0.71268842	0.23999548	0.02323405
56	–90.7	0.71349454	0.240994	0.02346651
64	–91.3	0.71035623	0.23761455	0.02277658

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Chapter One. Discrete Sequences and Systems

• Chapter One. Discrete Sequences and Systems
• DISCRETE SEQUENCES AND THEIR NOTATION
• SIGNAL AMPLITUDE, MAGNITUDE, POWER
• SIGNAL PROCESSING OPERATIONAL SYMBOLS
• INTRODUCTION TO DISCRETE LINEAR TIME-INVARIANT SYSTEMS
• DISCRETE LINEAR SYSTEMS
• TIME-INVARIANT SYSTEMS
• THE COMMUTATIVE PROPERTY OF LINEAR TIME-INVARIANT SYSTEMS
• ANALYZING LINEAR TIME-INVARIANT SYSTEMS
• REFERENCES

Chapter Two. Periodic Sampling

• Chapter Two. Periodic Sampling
• ALIASING: SIGNAL AMBIGUITY IN THE FREQUENCY DOMAIN
• SAMPLING LOW-PASS SIGNALS
• SAMPLING BANDPASS SIGNALS
• SPECTRAL INVERSION IN BANDPASS SAMPLING
• REFERENCES

Chapter Three. The Discrete Fourier Transform

• Chapter Three. The Discrete Fourier Transform
• UNDERSTANDING THE DFT EQUATION
• DFT SYMMETRY
• DFT LINEARITY
• DFT MAGNITUDES
• DFT FREQUENCY AXIS
• DFT SHIFTING THEOREM
• INVERSE DFT
• DFT LEAKAGE
• WINDOWS
• DFT SCALLOPING LOSS
• DFT RESOLUTION, ZERO PADDING, AND FREQUENCY-DOMAIN SAMPLING
• DFT PROCESSING GAIN
• THE DFT OF RECTANGULAR FUNCTIONS
• THE DFT FREQUENCY RESPONSE TO A COMPLEX INPUT
• THE DFT FREQUENCY RESPONSE TO A REAL COSINE INPUT
• THE DFT SINGLE-BIN FREQUENCY RESPONSE TO A REAL COSINE INPUT
• INTERPRETING THE DFT
• REFERENCES

Chapter Four. The Fast Fourier Transform

• Chapter Four. The Fast Fourier Transform
• RELATIONSHIP OF THE FFT TO THE DFT
• HINTS ON USING FFTS IN PRACTICE
• FFT SOFTWARE PROGRAMS
• DERIVATION OF THE RADIX-2 FFT ALGORITHM
• FFT INPUT/OUTPUT DATA INDEX BIT REVERSAL
• RADIX-2 FFT BUTTERFLY STRUCTURES
• REFERENCES

Chapter Five. Finite Impulse Response Filters

• Chapter Five. Finite Impulse Response Filters
• AN INTRODUCTION TO FINITE IMPULSE RESPONSE (FIR) FILTERS
• CONVOLUTION IN FIR FILTERS
• LOW-PASS FIR FILTER DESIGN
• BANDPASS FIR FILTER DESIGN
• HIGHPASS FIR FILTER DESIGN
• REMEZ EXCHANGE FIR FILTER DESIGN METHOD
• HALF-BAND FIR FILTERS
• PHASE RESPONSE OF FIR FILTERS
• A GENERIC DESCRIPTION OF DISCRETE CONVOLUTION
• REFERENCES

Chapter Six. Infinite Impulse Response Filters

• Chapter Six. Infinite Impulse Response Filters
• AN INTRODUCTION TO INFINITE IMPULSE RESPONSE FILTERS
• THE LAPLACE TRANSFORM
• THE Z-TRANSFORM
• IMPULSE INVARIANCE IIR FILTER DESIGN METHOD
• BILINEAR TRANSFORM IIR FILTER DESIGN METHOD
• OPTIMIZED IIR FILTER DESIGN METHOD
• PITFALLS IN BUILDING IIR FILTERS
• IMPROVING IIR FILTERS WITH CASCADED STRUCTURES
• A BRIEF COMPARISON OF IIR AND FIR FILTERS
• REFERENCES

Chapter Seven. Specialized Lowpass FIR Filters

• Chapter Seven. Specialized Lowpass FIR Filters
• FREQUENCY SAMPLING FILTERS: THE LOST ART
• INTERPOLATED LOWPASS FIR FILTERS
• REFERENCES

Chapter Eight. Quadrature Signals

• Chapter Eight. Quadrature Signals
• WHY CARE ABOUT QUADRATURE SIGNALS?
• THE NOTATION OF COMPLEX NUMBERS
• REPRESENTING REAL SIGNALS USING COMPLEX PHASORS
• A FEW THOUGHTS ON NEGATIVE FREQUENCY
• QUADRATURE SIGNALS IN THE FREQUENCY DOMAIN
• BANDPASS QUADRATURE SIGNALS IN THE FREQUENCY DOMAIN
• COMPLEX DOWN-CONVERSION
• A COMPLEX DOWN-CONVERSION EXAMPLE
• AN ALTERNATE DOWN-CONVERSION METHOD
• REFERENCES

Chapter Nine. The Discrete Hilbert Transform

• Chapter Nine. The Discrete Hilbert Transform
• HILBERT TRANSFORM DEFINITION
• WHY CARE ABOUT THE HILBERT TRANSFORM?
• IMPULSE RESPONSE OF A HILBERT TRANSFORMER
• DESIGNING A DISCRETE HILBERT TRANSFORMER
• TIME-DOMAIN ANALYTIC SIGNAL GENERATION
• COMPARING ANALYTIC SIGNAL GENERATION METHODS
• REFERENCES

Chapter Ten. Sample Rate Conversion

• Chapter Ten. Sample Rate Conversion
• DECIMATION
• INTERPOLATION
• COMBINING DECIMATION AND INTERPOLATION
• POLYPHASE FILTERS
• CASCADED INTEGRATOR-COMB FILTERS
• REFERENCES

Chapter Eleven. Signal Averaging

• Chapter Eleven. Signal Averaging
• COHERENT AVERAGING
• INCOHERENT AVERAGING
• AVERAGING MULTIPLE FAST FOURIER TRANSFORMS
• FILTERING ASPECTS OF TIME-DOMAIN AVERAGING
• EXPONENTIAL AVERAGING
• REFERENCES

Chapter Twelve. Digital Data Formats and Their Effects

• Chapter Twelve. Digital Data Formats and Their Effects
• FIXED-POINT BINARY FORMATS
• BINARY NUMBER PRECISION AND DYNAMIC RANGE
• EFFECTS OF FINITE FIXED-POINT BINARY WORD LENGTH
• FLOATING-POINT BINARY FORMATS
• BLOCK FLOATING-POINT BINARY FORMAT
• REFERENCES

Chapter Thirteen. Digital Signal Processing Tricks

• Chapter Thirteen. Digital Signal Processing Tricks
• FREQUENCY TRANSLATION WITHOUT MULTIPLICATION
• HIGH-SPEED VECTOR MAGNITUDE APPROXIMATION
• FREQUENCY-DOMAIN WINDOWING
• FAST MULTIPLICATION OF COMPLEX NUMBERS
• EFFICIENTLY PERFORMING THE FFT OF REAL SEQUENCES
• COMPUTING THE INVERSE FFT USING THE FORWARD FFT
• SIMPLIFIED FIR FILTER STRUCTURE
• REDUCING A/D CONVERTER QUANTIZATION NOISE
• A/D CONVERTER TESTING TECHNIQUES
• FAST FIR FILTERING USING THE FFT
• GENERATING NORMALLY DISTRIBUTED RANDOM DATA
• ZERO-PHASE FILTERING
• SHARPENED FIR FILTERS
• INTERPOLATING A BANDPASS SIGNAL
• SPECTRAL PEAK LOCATION ALGORITHM
• COMPUTING FFT TWIDDLE FACTORS
• SINGLE TONE DETECTION
• THE SLIDING DFT
• THE ZOOM FFT
• A PRACTICAL SPECTRUM ANALYZER
• AN EFFICIENT ARCTANGENT APPROXIMATION
• FREQUENCY DEMODULATION ALGORITHMS
• DC REMOVAL
• IMPROVING TRADITIONAL CIC FILTERS
• SMOOTHING IMPULSIVE NOISE
• EFFICIENT POLYNOMIAL EVALUATION
• DESIGNING VERY HIGH-ORDER FIR FILTERS
• TIME-DOMAIN INTERPOLATION USING THE FFT
• FREQUENCY TRANSLATION USING DECIMATION
• AUTOMATIC GAIN CONTROL (AGC)
• APPROXIMATE ENVELOPE DETECTION
• A QUADRATURE OSCILLATOR
• DUAL-MODE AVERAGING
• REFERENCES

Appendix A. The Arithmetic of Complex Numbers

• Appendix A. The Arithmetic of Complex Numbers
• Section A.1. GRAPHICAL REPRESENTATION OF REAL AND COMPLEX NUMBERS
• Section A.2. ARITHMETIC REPRESENTATION OF COMPLEX NUMBERS
• Section A.3. ARITHMETIC OPERATIONS OF COMPLEX NUMBERS
• Section A.4. SOME PRACTICAL IMPLICATIONS OF USING COMPLEX NUMBERS
• REFERENCES

Appendix B. Closed Form of a Geometric Series

• Appendix B. Closed Form of a Geometric Series

Appendix C. Time Reversal and the DFT

• Appendix C. Time Reversal and the DFT

Appendix D. Mean, Variance, and Standard Deviation

• Appendix D. Mean, Variance, and Standard Deviation
• Section D.1. STATISTICAL MEASURES
• Section D.2. STANDARD DEVIATION, OR RMS, OF A CONTINUOUS SINEWAVE
• Section D.3. THE MEAN AND VARIANCE OF RANDOM FUNCTIONS
• Section D.4. THE NORMAL PROBABILITY DENSITY FUNCTION
• REFERENCES

Appendix E. Decibels (dB and dBm)

• Appendix E. Decibels (dB and dBm)
• Section E.1. USING LOGARITHMS TO DETERMINE RELATIVE SIGNAL POWER
• Section E.2. SOME USEFUL DECIBEL NUMBERS
• Section E.3. ABSOLUTE POWER USING DECIBELS

Appendix F. Digital Filter Terminology

• Appendix F. Digital Filter Terminology
• REFERENCES

Appendix G. Frequency Sampling Filter Derivations

• Appendix G. Frequency Sampling Filter Derivations
• Section G.1. FREQUENCY RESPONSE OF A COMB FILTER
• Section G.2. SINGLE COMPLEX FSF FREQUENCY RESPONSE
• Section G.3. MULTISECTION COMPLEX FSF PHASE
• Section G.4. MULTISECTION COMPLEX FSF FREQUENCY RESPONSE
• Section G.5. REAL FSF TRANSFER FUNCTION
• Section G.6. TYPE-IV FSF FREQUENCY RESPONSE

Appendix H. Frequency Sampling Filter Design Tables

• Appendix H. Frequency Sampling Filter Design Tables

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Understanding Digital Signal Processing (2nd Edition)

ISBN: 0131089897
EAN: 2147483647

Year: 2004
Pages: 183

Authors: Richard G. Lyons

BUY ON AMAZON

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Interprocess Communications in Linux: The Nooks and Crannies

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• Introduction
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• Executing Remote Commands at a System Level

Qshell for iSeries

• Running Qshell
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• Commands
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Introducing Microsoft Office InfoPath 2003 (Bpg-Other)

• Presenting InfoPath 2003 SP-1
• Filling Out Forms
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• Working with Advanced Form Elements
• Writing Advanced Event Handlers

A+ Fast Pass

• Domain 2 Diagnosing and Troubleshooting
• Domain 3 Preventive Maintenance
• Domain 6 Basic Networking
• Domain 1 Operating System Fundamentals
• Domain 4 Networks

Cisco IOS in a Nutshell (In a Nutshell (OReilly))

• Command-Line Completion
• The Enable Password
• Enabling SNMP
• Autonomous System (AS) Numbers
• Quick Reference

The Oracle Hackers Handbook: Hacking and Defending Oracle

• Attacking the Authentication Process
• Indirect Privilege Escalation
• Attacking Oracle PL/SQL Web Applications
• Running Operating System Commands
• Accessing the Network

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