数字信号处理英文版课后答案 (2)

《数字信号处理英文版课后答案 (2)》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、Chapter2Solutions2.1Theminimumsamplingrateistwicethemaximumfrequencyinthesignal,or44.1kHz.2.2(a)Since=2f=20rad/sec,thefrequencyofthesignalf=3.18Hz.TheNyquistrateforthesignalis6.37Hz5000(b),sof=833.3Hz.TheNyquistrateis1666.7Hz.33000(c),sof=214.3Hz.TheNyquistrateis428.6Hz.71

2、12.3(a)T125sSf8000S(b)Themaximumrecoverablefrequencyishalfthesamplingrate,or4000kHz.2.4=4000rad/sec,sof=4000/(2)=2000/Hz,andT=/2000sec.Therefore,fiveperiodscover5/2000=/400sec.Forthissignal,theNyquistsamplingrateis2(2000/)=4000/Hz,sothesamplingrateinthiscaseisfS=4(4000

3、/)=16000/Hz.Therefore,thetotalnumberofsamplescollectedinfiveperiodsis(16000/samples/sec)(/400sec)=40.2.5=2500rad/sec,sof=2500/(2)=1250Hz,andT=1/1250sec.Therefore,fiveperiodscover5/1250sec.Forthissignal,theNyquistsamplingrateis2(1250)=2500Hz,sothesamplingrateinthiscaseisfS=

4、7/8(2500)=2187.5Hz.Thetotalnumberofsamplescollectedis(2187.5samples/sec)(5/1250sec)=8.75.Thismeansonlyeightsamplesarecollectedwhilefiveperiodsoftheanalogsignalelapse.Infact,forthissignal,anintegernumberofsamplescanneverbecollectedinanintegernumberofanalogperiods.2.6Copiesofthespec

5、trumoccursymmetricallyaroundeverymultipleofthesamplingfrequency.Magnitude10.90.80.70.60.50.40.30.20.10-200020040060080010001200Frequency2.7CopiesofthesignalappearatkfS±f.Inotherwords,copiesofthespectrumappeararoundeverymultipleofthesamplingrate.(a)ThesamplingratemeetsNyquistrequir

6、ements,sonoaliasingoccurs.0102030405060708090100110120130140150Frequency,kHz(b)Thesamplingrateistoolowforthissignal,soaliasingoccurs.Spectralimagesareshownbydashedlines,whilethefinalspectrumisshownasasolidline.0102030405060708090100110120130140150Frequency,kHz2.8Thecellphonesignal

7、isband-limited.Thetransmissionrangeis30kHzwide.Theminimumsamplingratemustbeatleast60kHz.Inthiscase,a60kHzsamplingrateisadequate.Abasebandcopyofthetransmissioncanberecoveredbyafilterwitha30kHzcut-off.…0306090120899970900000900030f(kHz)2.9(a)Copiesofthesignalat300Hzappearat…,10003

8、00,0300,1000300,2000300Hz,….Th