Chapter 11.1(a) One dimensional, multichannel, discrete time, and digital.(b) Multi dimensional, single channel, continuous-time, analog.(c) One dimensional, single channel, continuous-time, analog.(d) One dimensional, single channel, continuous-time, analog.(e) One dimensional, multichannel, discrete-time, digital.1.2(a)f=0.01π2π=1200⇒periodic withNp= 200.(b)f=30π105(12π) =17⇒periodic withNp= 7.(c)f=3π2π=32⇒periodic withNp= 2.(d)f=32π⇒non-periodic.(e)f=62π10(12π) =3110⇒periodic withNp= 10.1.3(a) Periodic with periodTp=2π5.(b)f=52π⇒non-periodic.(c)f=112π⇒non-periodic.(d)cos(n8) is non-periodic;cos(πn8) is periodic; Their product is non-periodic.(e)cos(πn2) is periodic with periodNp=4sin(πn8) is periodic with periodNp=16cos(πn4+π3) is periodic with periodNp=8Therefore, x(n) is periodic with periodNp=16. (16 is the least common multiple of 4,8,16).1.4(a)w=2πkNimplies thatf=kN. Letα=GCD of (k, N),i.e.,k=k′α, N=N′α.Then,f=k′N′,which implies thatN′=Nα .3Preview Mode
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