Find discrete time Fourier series coefficient of the following sequence h[k] = 1 k ≤ N 10 N+1 ≤ k ≤ Ko - N - 1, With a fundamental period K₁> (2N+1)

The Discrete Time Fourier Series (DTFS) coefficients are given by the formula:

Cn = (1/K₁) Σ (from k=0 to K₁-1) x[k] e^(-j2πnk/K₁)

where x[k] is the sequence and K₁ is the fundamental period.

Given the sequence h[k] = 1 for k ≤ N and h[k] = 10 for N+1 ≤ k ≤ K₁ - N - 1, we can calculate the DTFS coefficients.

First, we calculate the sum for k ≤ N:

Σ (from k=0 to N) e^(-j2πnk/K₁) = e^0 + e^(-j2πn/K₁) + e^(-j2πn2/K₁) + ... + e^(-j2πnN/K₁)

Next, we calculate the sum for N+1 ≤ k ≤ K₁ - N - 1:

Σ (from k=N+1 to K₁ - N - 1) 10 e^(-j2πnk/K₁) = 10(e^(-j2πn(N+1)/K₁) + e^(-j2πn(N+2)/K₁) + ... + e^(-j2πn(K₁ - N - 1)/K₁))

Adding these two sums together and dividing by K₁ gives the DTFS coefficient Cn.