Topic: MATLAB coding, signals and systems, sampling, Fourier analysis, FFT, new transform techniques

Purpose of the assessment:

The purpose of this assignment is to motivate students to learn MATLAB programming and how to use software to solve problems numerically. In summary, the learning outcomes in this project include:

a. Simulate digital communication applications using MATLAB.
b. Explain the need for sampling.
c. Apply the principles used in the generation, transmission and reception of signals.
d. Demonstrate analytical and problem solving skills.
e. Demonstrate the ability to work efficiently and effectively in team environment.
f. Prove the ability to apply content learned during their studies to solve problems.
g. Develop research and lifelong learning skills.
h. Develop the skill to write professionally-looking technical reports.

Description of the assessment:

Questions

1. Study the 5 pulses below which have not been drawn to scale.

(a) What is the duration of each signal?
(b) Express each of the signals as a function of s(t).
(c) State all the operations applied on s(t) to obtain each of the other signals.
(d) Find the energies of each of the signals.
(e) What is the effect on the energy of a signal if its sign is changed? Shifted in time? Scaled in amplitude? Or scaled in time?

2. State and explain the law or theorem governing sampling of a signal, and its application in digital communications.

3. Explain Fourier theory and its importance in digital communications.

4. Differences between Fourier Transform, Discrete-time Fourier Transform (DFT) and Fast Fourier Transform (FFT).

5. Consider the signal x(t) = 4Λ(t/4) - Λ(t), with a time period of 8.

(a) Determine the Fourier transform of x(t) analytically and plot the spectrum of x(t)

(b) Using MATLAB, determine the Fourier transform numerically and plot the result.
[Note that the FFT is usually used to compute the DFT to reduce processing]. Explain how you proceed with your work. In particular, explain how you chose:
- The sampling period Ts
- The sampling frequency fs
- The number of samples used in the FFT
- The spectral sampling interval (i.e. sampling interval of X(f))
- The law or theorem governing sampling of a signal

(c) Identify and write any functions that your MATLAB code calls.

6. Discuss the new techniques are available for signal analysis and how they claim to outperform DFT/FFT.

II Requirements

The requirements are found in the marking scheme table below.

Suggested approach:

1. Students are required to analyze the questions given individually and with their team members in order to thoroughly understand the subject matter and solve the questions.

2. The student must research and learn anything unknown that is required to complete the assignment.

3. Each team is required to submit a concise technical report while being mindful of word limit.

Submission Guidelines:

Your assignment should be completed according to the General Guidelines for Presentation of Academic Work.

1. successful completion of required tasks

2. quality of figures (no copy-and-paste graphics allowed!)
a. comments
b. meaningful names

3. accompanying documentation including
a. table of contents and page numbers
b. a front page - indicating your names.
c. list of references used (IEEE referencing style) as an evidence of research depth.

4. The assignment must be submitted in soft (electronic) as .doc file on Moodle page provided at MIT intranet. The page numbers of the assignment must be clear on each page.