Technical Report: Harmonic Signals and Convolution Analysis

This assignment is to be written as a technical report that you will submit as the coursework component of this module. This technical report should be properly formatted and should include contents page, introduction, results, discussions and conclusions. All figures and tables are to be numbered and provided with a respective legend. Any simulation results, tables and plots obtained from practical work should also be included. Do not include screen snapshots in your report. The report is to be written using a suitable text editor such as Microsoft Word and submission is done electronically using Turnitin on Blackboard.

The two parts will be equally weighted. The tasks are detailed in the following pages.

Task 1

1) Determine the members of the family of harmonically related complex exponential signals in discrete time that share a common period of N = 7.

2) Use MATLAB (or similar technical software) to plot each member. Use the range from O to 7 for the independent variable. On each plot, superimpose the continuous-time counterpart of each member.

3) Based on the theory, compare the second (m = 2) and fifth (m = 5) members of the family, and judge which one oscillates faster. Explain how this can be seen from the graphs of the 2 signals.

4) Based on the theory, compare the fourth (m = 4) and fifth (m = 5) members of the family, and judge which one oscillates faster. Explain how this can be seen from the graphs of the 2 signals.

Task 2

1) Use MATLAB (or similar technical software) to plot the following two signals:

2) Convolve the above 2 signals by hand. Then, use MATLAB (or similar technical software) to convolve the 2 signals using the builtin convolution function. Compare the 2 results. (You should attach your hand-written solution as a scanned image in the form of a Figure within your technical report).