Question

If x(t) has the Fourier transform X(jw), and p(t) is periodic with fundamental frequency ω₀ and Fourier series representation, what is the Fourier transform of p(t)?

a) P(jω)
b) X(jω₀)
c) P(jω₀)
d) X(jω)

Answer 1

The Fourier transform of a periodic function p(t) is a series of impulses represented by P(jω), which consists of the fundamental frequency and its harmonics.

Step-by-step explanation:

The question revolves around the concept of Fourier transforms and Fourier series representations of periodic functions in the context of signal processing. Fourier series can represent any periodic function as a sum of sine and cosine functions with different amplitudes, frequencies, and phase shifts. Furthermore, the Fourier transform of a periodic function, such as p(t), is a series of impulses at the fundamental frequency ω0 and its harmonics (integer multiples of the fundamental frequency). In this case, the correct answer to the Fourier transform of p(t) would be P(jω), where P(jω) is a series of impulses at frequencies multiple of ω0. This implies that the correct option would be ‘a’, which corresponds to P(jω).