Question

Consider the following discrete signal with Tₛ =0.1sec : 3) x(n)={ 1 1 1} a periodic signal with N=3.

Find the Fourier series coefficients.

Answer 1

The Fourier series coefficients for the given periodic signal with N=3 are c0=1, c1=0, and c2=0.

Step-by-step explanation:

The Fourier series coefficients can be found by using the formula:

ck = (1/N) * ∑N-1n=0 x(n) * e-j2πkn/N

For the given signal x(n)={1, 1, 1}, with N=3, the Fourier series coefficients are:

c0 = (1/3) * (1 + 1 + 1) = 1

c1 = (1/3) * (1 * e-j2π1/3 + 1 * e-j2π2/3 + 1 * e-j2π3/3) = (1/3) * (1 + (-1/2) + (-1/2)) = 0

c2 = (1/3) * (1 * e-j2π2/3 + 1 * e-j2π4/3 + 1 * e-j2π6/3) = (1/3) * (-1/2 + (-1/2) + 1) = 0