Description

Faculty of Engineering and Technology
Department of Electrical and Computer Engineering
Communication Systems ENEE 3309

Consider the periodic signal g(t), for which one period is shown in the figure below

where A=1 and 𝑻𝟎 = 𝟎. 𝟏 𝒔𝒆𝒄. This signal can be expanded in a trigonometric Fourier series as:
𝒈 (𝒂𝒏 𝐜𝐨𝐬 𝒏𝝎𝟎𝒕 + 𝒃𝒏 𝐬𝐢𝐧 𝒏𝝎𝟎𝒕)
𝒏=𝟏
Now, consider the approximate signal:
𝑲
𝒈𝒂(𝒕) = 𝒂𝟎 + ∑(𝒂𝒏 𝐜𝐨𝐬 𝒏𝝎𝟎𝒕 + 𝒃𝒏 𝐬𝐢𝐧 𝒏𝝎𝟎𝒕)
𝒏=𝟏
1. Find 𝒂𝟎, 𝒂𝟏, 𝒂𝟐, 𝒂𝟑, 𝒃𝟏, 𝒃𝟐, 𝒂𝒏𝒅 𝒃𝟑 (you can use matlab or any other code to find numerical values of the coefficients)
2. Use matlab to plot 𝒈(𝒕) and 𝒈𝒂(𝒕) for K = 3, on the same figure for one cycle of 𝒈(𝒕).
3. The mean square error between 𝒈(𝒕) and 𝒈𝒂(𝒕) is defined as
𝟏 𝑻𝟎 𝟐
𝑴𝑺𝑬 = (∫ (𝒈(𝒕) − 𝒈𝒂(𝒕)) 𝒅𝒕)
𝑻𝟎 𝟎
Find the mean square error for K=1, 2, and 3. Summarize your results in a table.
4. If 𝒈𝒂(𝒕) (when K = 3) is multiplied by the carrier 𝒄(𝒕) = 𝟏𝟎 𝐜𝐨𝐬 𝟐𝝅(𝟐𝟎𝟎)𝒕 followed by an ideal bandpass filter to generate the single sideband signal 𝒔(𝒕), find s(t) and its spectrum.