Question

What is the frequency shifting property of continuous time fourier series?

(a) Multiplication in the time domain by a real sinusoid

(b) Multiplication in the time domain by a complex sinusoid

(c) Multiplication in the time domain by a sinusoid

(d) Addition in the time domain by a complex sinusoid

The question was posed to me during an interview for a job.

I'd like to ask this question from Fourier Series Properties topic in portion Fourier Series of Signals and Systems

Answer 1

Correct choice is (b) Multiplication in the time domain by a complex sinusoid

Best explanation: If x(t) and y(t) are two periodic signals with coefficients Xn  and Yn,

Then y(t)= e^jmwtx(t)↔Yn=Xn-m.

Hence, we can see that a frequency shift corresponds to multiplication in the time domain by complex sinusoid whose frequency is equal to the time shift.