Question

If X(k) is the N point DFT of a sequence whose Fourier series coefficients is given by ck, then which of the following is true?

(a) X(k)=Nck

(b) X(k)=ck/N

(c) X(k)=N/ck

(d) None of the mentioned

I have been asked this question in semester exam.

Enquiry is from Sampling Rate Conversion by a Rational Factor I/D in division Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

The correct choice is (a) X(k)=Nck

Easy explanation: The Fourier series coefficients are given by the expression

ck=\(\frac{1}{N} \sum_{n=0}^{N-1} x(n)e^{-j2πkn/N} = \frac{1}{N}X(k)=> X(k)=Nc_k\)