Transcription of Exercises in Signals
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Exercises in Signals
Exercises in Signals , Systems, and TransformsIvan W. SelesnickLast edit: October 27, 2014 Contents1 discrete - time Signals and System More Z Inverse Di erence Complex Frequency Summary Simple System More Continuous- time Signals and System Laplace Di erential Complex Frequency Simple System Fourier Fourier Fourier The Sampling Theorem15011 discrete - time Signals and an accurate sketch of each of the discrete - time Signals (a)x(n)=u(n+ 3) + (n 1)(b)x(n)= (n+ 3) + (n 1)(c)x(n)=2n (n 4)(d)x(n)=2n u( n 2)(e)x(n)=( 1)nu( n 4).(f)x(n)=2 (n+ 4) (n 2) +u(n 3)(g)x(n)=1Xk=04 (n 3k 1)(h)x(n)=1Xk= 1( 1)k (n 3k) a sketch of each of the following Signals (a)x(n)=1Xk= 1( )|k| (n k)(b)x(n) = cos( n)u(n)(c)x(n)=u(n) 2u(n 4) +u(n 8) (n),x1(n),x2(n), andx3(n)wherex(n)=u(n+ 4) u(n),x1(n)=x(n 3),x2(n)=x(5 n),x3(n)=nXk= 1x(k) (n) andx1(n)wherex(n)=( )nu(n),x1(n)=nXk= 1x(k) (n) andx1(n)wherex(n)=n[ (n 5) + (n 3)],x1(n)=nXk= 1x(k) a sketch of each of the following Signals (a)f(n)=1Xk=0( )k (n 3k)(b)g(n)=1Xk= 1( )|k| (n 3k)(c)x(n) = cos( n)u(n)(d)x(n) = cos( n)u(n) discrete - time Signals in plot the discrete - time impulse function:n = -10:10;f = (n == 0);stem(n,f)Usestemto plot the discrete - time step function:f = (n >= 0);stem(n,f)Make stem plots of the following Signals .
1.2.7 The impulse response of a discrete-time LTI system is h(n)=2(n)+3(n1)+(n2). Find and sketch the output of this system when the input is the signal
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