信号与系统课堂练习

Onclassexercise

Theperiodofx[n]=cos(πn/8)+sin(2n)is,x(t)=cos(4πt)+sin(4t)is?

Theexpressionforx(t)illustratedinFigure1is?

-112

2

1

consideracontinuous-timesystemwithinputx(t)andoutputy(t)relatedbythissystemmaybe().

Linear,time-variant,causal,stable

Linear,time-variant,notcausal,unstable

Nonlinear,time-variant,causal,stable

Linear,time-variant,causal,unstatble

ConsideranLTIsystemwithunitimpulseresponseh(t)illustratedinFigure2.iftheinputisx(t)=u(t),theouput()?

h(t)

1

0t

-112

Theconvolutionintegraly(t)=[u(t)-u(t-1)]*[u(t-1)-u(t-3)]is()

(t-1)u(t-1)+(t-2)u(t-2)-(t-3)u(t-3)-(t-4)u(t-4)

tu(t)-(t-1)u(t-1)-(t-2)u(t-2)+(t-3)u(t-3)

(t-1)u(t-1)-(t-2)u(t-2)-(t-3)u(t-3)+(t-4)u(t-4)

tu(t)+(t-1)u(t-1)-(t-2)u(t-2)-(t-3)u(t-3)

6.

1(b)–1(c)–0.5(d)0.5

7.ConsideranLTIsystemwhoseinputx[n]andunitimpulseresponseh[n]aregivenbyx[n]={3,2,1},n=-1,0,1h[n]={-1,2,3},n=0,1,2Theoutputy[n]=x[n]*h[n]is?

Consideracontinuous-timesystemSwhosefrequencyresponseis

1,|ω|<=100π

H(jω)=

0,otherwise

x(t)=∑akej6kπt,iftheoutputy(t)=x(t),wecanjustifythatforwhatvaluesofkisitguaranteedthatak=0.

9.Letx(t)beaperiodicsignalwithfundamentalfrequencyω0andFourierseriescoefficientsak.TheFourierseiescoefficientsofx(1-t)is?

ConsideraCTLTIsystemwithimpulseresponseiftheinputtheFSrepresentationoftheoutputy(t)is().

is()

ConsideranLTIsystemwithunitimpulseresponseiftheinput,theoutputy(t)is()

ConsideraCTLTIsystemwithfrequencyresponseinthefollowingfigure.Whentheinputisaperiodicsignalx(t)withfundamentalperiodT=1andFScoefficients,itisfoundy(t)=x(t),Theinputsignalx(t)satisfy().

(a)(b)=0,k=0(c)(d)

1

π

-π

14.Thesystem:maybe()

(a)Linear(b)TI(c)NC(d)Stable

15.ConsideraCTLTIsystemwhosefrequencyresponseis.Whentheinputis,itisfoundy(t)=0.Whichofthefollowingstatementsaretrue()

(a)(b)(c)(d)

16.WearegivenacertainLTIsystemwithunitimpulseresponse,and.WhichofthefollowingstatementsisFALSE()

(a)