Consider the periodic signal g(t), for which one period is shown in the figure below
where A=1 and π»π = π. π πππ. This signal can be expanded in a trigonometric Fourier series as:
π (ππ ππ¨π¬ ππππ + ππ π¬π’π§ ππππ)
π=π
Now, consider the approximate signal:
π²
ππ(π) = ππ + ∑(ππ ππ¨π¬ ππππ + ππ π¬π’π§ ππππ)
π=π
1. Find ππ, ππ, ππ, ππ, ππ, ππ, πππ
ππ (you can use matlab or any other code to find numerical values of the coefficients)
2. Use matlab to plot π(π) and ππ(π) for K = 3, on the same figure for one cycle of π(π).
3. The mean square error between π(π) and ππ(π) is defined as
π π»π π
π΄πΊπ¬ = (∫ (π(π) − ππ(π)) π
π)
π»π π
Find the mean square error for K=1, 2, and 3. Summarize your results in a table.
4. If ππ(π) (when K = 3) is multiplied by the carrier π(π) = ππ ππ¨π¬ ππ
(πππ)π followed by an ideal bandpass filter to generate the single sideband signal π(π), find s(t) and its spectrum.
