railway RRB JE (CBT I + CBT II) Mock Test 2024 Signals and Systems Discrete Fourier Transform (DFT) and Discrete Fourier Series (DFS) Definition of Discrete Fourier Series (DFS)
If xin(t) = sin(2*π*4000*t) + 0.75 * sin(2*π*5000*t + π /4) is sampled with Fs = 16000 Hz, calculate X(0) if X(m) = \(\mathop \sum \limits_{n = 0}^{N - 1} x\left( n \right){e^{-j2\pi nm/N}}\) when N=8, where x(n)= xin(nts)
1
0.0 – j 4.0
2
0.0 – j 0.0
3
1.414 + j 1.414
4
0.0 + j 4.0