show how to get the answer A continuous time signal ft cos

show how to get the answer.

A continuous time signal f(t) = cos 2 pi t is sampled every T = 1/4 sec for 8 samples beginning at t=0. Write an expression for the DFT of the resulting sequence. Evaluate this expression for n = 2 (F_2).

Solution

>> n=0:1:7;
>> Ts=1/4;
>> t=n*Ts;
>> fn=cos(2*pi*t);
>> fft(fn)

ans =

-0.0000            -0.0000             4.0000 - 0.0000i   0.0000             0.0000             0.0000             4.0000 + 0.0000i -0.0000

F=4 at n=2