Amplitude Modulation in a Digital Sense

Question:

General instructions:

All of the assessments are via coursework, and the second assessment is based on the second lab. In this lab you will apply what you have learnt in the lectures and you will demonstrate concepts from these lectures in MATLAB. When working on this assessment, make sure that you refer back to the lectures. You will also need to have done the MATLAB on ramp in advance of the lab. This can be found at: https://uk.mathworks.com/learn/tutorials/matlab- onramp.html?s_tid=tah_po_mlonramp
When a question says ‘write a routine in MATLAB’ it means that you should create a .m file, which can be run by any user who opens the file in MATLAB and clicks ‘run’. An example of such a file is fib.m, which has been loaded onto Canvas as an example. fib.m includes clear, concise comments.
 
Anything that can be changed by the user is clearly marked. You should work to the same standards.
This lab is worth 30 % of the module.

Ahead of the lab

Before the lab, make sure that you have read through the lab script, watched the three introductory videos (available on the Canvas page, under the Panopto tab. These are called lab-intro-part-1, labintro-part-2 and lab-intro-part-3) and completed the MATLAB on ramp
(https://uk.mathworks.com/learn/tutorials/matlab-onramp.html?s_tid=tah_po_mlonramp). This will ensure that you get off to a flying start during the lab session.
The videos mentioned here are the same as for the first lab so, if you remember these clearly, then you do not need to watch these again.

Getting the best out of the lab

Prioritise tasks which need to be done in MATLAB – these are the ones where you are most likely to need some help. Leave writing up the various exercises until after the lab session

Submission of work

You will submit a single word document on Canvas which contains your work for this assessment, plus MATLAB (.m) files where these are requested. You are welcome to continue working on this after the lab. You may spend as much time as you like on this, provided that your work is submitted on Canvas by 23:59 on Friday 3rd December 2021.
 
1. Write a routine in MATLAB that calculates the FFT of either a half-cosine pulse, a triangular pulse or a Gaussian pulse. Your routine only needs to do one of these (not all three). The FFT should be  plotted over the negative to positive range.
 
Engineers rarely write code from scratch. It is often more efficient to take and modify a code which already exists. You may, if you wish, take the MATLAB code FT_flat_topped_pulse.m which was used in the lectures and modify this. In this case marks will be awarded for how you modify the code. If you prefer, you may write a MATLAB code from scratch. In this case marks will be awarded for how you construct your code. The full range of marks are available for either approach.
 
2. A useful property of Fourier transforms is linearity, where the addition of two signals in the time domain is equivalent to the addition of two signals in the frequency domain. In other words:
If

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