Question

Consider the periodic continuous-time signal x(t) = 4 - (t - 2n)$^2$ for $2n \le t < 2(n + 1)$ for all integers $n$. (a) Determine the continuous-time Fourier series (CTFS) coefficients for $x(t)$. (b) Use MATLAB to plot the real and imaginary parts and the mag- nitude and phase of the CTFS coefficients for harmonic numbers k = -20, -19, \dots, 20. Include your MATLAB code as part of your solution. (c) Use MATLAB to form the partial sums $x_N(t)$ of the CTFS and plot the partial sums with the signal $x(t)$ for N = 1, 2, 5, 10, 50 and for $0 \le t < 2$. Include your MATLAB code as part of your solution. (d) Use MATLAB to plot the MSE of the partial sums you calculated previously as a function of N for N = 1, 2, \dots, 50.

          Consider the periodic continuous-time signal
x(t) = 4 - (t - 2n)$^2$ for $2n \le t < 2(n + 1)$
for all integers $n$.
(a) Determine the continuous-time Fourier series (CTFS) coefficients
for $x(t)$.
(b) Use MATLAB to plot the real and imaginary parts and the mag-
nitude and phase of the CTFS coefficients for harmonic numbers
k = -20, -19, \dots, 20. Include your MATLAB code as part of
your solution.
(c) Use MATLAB to form the partial sums $x_N(t)$ of the CTFS and
plot the partial sums with the signal $x(t)$ for N = 1, 2, 5, 10, 50
and for $0 \le t < 2$. Include your MATLAB code as part of your
solution.
(d) Use MATLAB to plot the MSE of the partial sums you calculated
previously as a function of N for N = 1, 2, \dots, 50.

Consider the periodic continuous-time signal
x(t) = 4 - (t - 2n)^2 for 2n ≤ t < 2(n + 1)
for all integers n.
(a) Determine the continuous-time Fourier series (CTFS) coefficients
for x(t).
(b) Use MATLAB to plot the real and imaginary parts and the mag-
nitude and phase of the CTFS coefficients for harmonic numbers
k = -20, -19, …, 20. Include your MATLAB code as part of
your solution.
(c) Use MATLAB to form the partial sums xN(t) of the CTFS and
plot the partial sums with the signal x(t) for N = 1, 2, 5, 10, 50
and for 0 ≤ t < 2. Include your MATLAB code as part of your
solution.
(d) Use MATLAB to plot the MSE of the partial sums you calculated
previously as a function of N for N = 1, 2, …, 50.

Added by Curtis F.

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