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Determine the fundamental period of the following signals: (i) x(t)=cos(π3t)+sin(π4t) (ii) x[n]=cos2[πan]

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 05

Year : DEC 2014

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i )

Since sin(t)=cos(tπ2) sin(πt4)=cos(πt4π2)x(t)=cos(π3t)+cos(πt4π2)

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T=T1T2=68=34

Since T it is a rational ∴ signal is periodic

∴ Fundamental period (T)=T1=34T2=6.

ii )

x[n]=cos2π8n

cos2π8n=1+cos(2πn8)2=1+cos(πn4)2=0.5+0.5cos(πn4)w=π42πf=π4f=1/8

Fundamental period T = 8.

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