Signals and Sys...

Let x(t) be a signal with Nyquist rate ω₀. The Nyquist rate of the signal x(t) + x (t – ω₀) is

If signal x(t) = 2 + cos (50 πt) is sampled with sampling frequency 40 Hz, then the sampled discrete time signal x[n] will be given by:

The difference in the number of complex multipliers required for 16-point DFT and 16-point radix-2 FFT is:

Let x(n) be a 8-point real sequence with 8-point DFT X(K) and x(n) satisfies the symmetry

\(x\left[ {n + \frac{N}{2}} \right] = -x\left( n \right)\) n = 0,1,2,3,

Let x(n), defined for n = 0, 1 . . . . 7 have a DFT as shown:

X(k) = [1, 1-j, 1, 0, 1, 0, 1, 1+j]

The first six points of the 8 point DFT of a real-valued sequence are 5, 1 – 3j, 0, 3 – 4j, 0 and 3 + 4j. The last two points of the DFT will be respectively: