How to find whether signal x(n)=sin(3pi/4*n)+sin(pi/3*n) is periodic signal or not?
my solution:
x(n+N)=sin(3pi/4*n+N)+sin(pi/3*n+N)
=sin(3pi/4*n)cos(N)+ cos(3pi/4*n)sin(N)+sin(pi/3*n)cos(N)+cos(pi/3*n)sin(N)
=sin(N){cos(3pi/4*n)+cos(pi/3*n)}+cos(N){sin(3pi/4*n)+sin(pi/3)}
at N=2npi
sin(2npi)=0
cos(2npi)=1
= sin(3pi/4*n)+sin(pi/3*n)
=x(n)
hence periodic signal
period=2npi
my solution:
x(n+N)=sin(3pi/4*n+N)+sin(pi/3*n+N)
=sin(3pi/4*n)cos(N)+ cos(3pi/4*n)sin(N)+sin(pi/3*n)cos(N)+cos(pi/3*n)sin(N)
=sin(N){cos(3pi/4*n)+cos(pi/3*n)}+cos(N){sin(3pi/4*n)+sin(pi/3)}
at N=2npi
sin(2npi)=0
cos(2npi)=1
= sin(3pi/4*n)+sin(pi/3*n)
=x(n)
hence periodic signal
period=2npi
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