The signal xt 5 cos8 pi t is sampled eight times starting a

The signal x(t) = 5 cos(8 pi t) is sampled eight times starting at t = 0 using a sampling period of 0.1 second. (a) Compute the DFT of the sample sequence. (b) Use MATLAB to confirm the results of part (a).

Solution

MATLAB code:

t=0:0.1:0.7   
x=5*cos(8*pi*t);
DFTx=fft(x)

DFT vale of the given function:

[2.5000 + 0.0000i 2.6492 + 0.8057i 3.4549 + 2.1353i 15.4409 +11.9860i -5.5902 + 0.0000i 15.4409 -11.9860i

3.4549 - 2.1353i 2.6492 - 0.8057i]