A periodic signal x[n] of fundamental  period N can be represented by its Fourier series

If you consider this a representation of x[n]

(a) Is x₁ [n] = x[n ˆ’ N₀] for any value of N₀ periodic? If so use the Fourier series of x[n] to obtain the Fourier series coefficients of x₁[n].

(b) Let x₂[n] = x[n] ˆ’ x[n ˆ’ 1] , i.e., the finite difference. Determine if  x₂[n] is periodic, and if so find its Fourier series coefficients.

(c) If x₃[n] = x[n]( ˆ’ 1)ⁿ, is x₃ [n] periodic? if so determine its Fourier  series coefficients.

(d) Let x₄[n] = sign[cos(0.5Ï€n)] where sign(ξ) is a function that gives 1 when ξ ‰¥ 0 and €“ 1 when ξ < 0. Determine the Fourier coefficients of x₄ [n] if periodic.

(e) Let x[n] = sign[cos(0.5Ï€n)], and N₀ = 3. Use MATLAB to find the  Fourier series coefficients for x_i[n], i = 1, 2, 3.

Transcribed Image Text:

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