Question 1 A binary signal is transmitted along a twisted pair of copper wires, with a potential difference of -1 V representing binary 0 and a potential difference of +1 V

representing binary 1. This signal is affected by thermal noise, which can be assumed to follow a Gaussian distribution. You can assume that the noise level is not a function of frequency. Part a: Create a routine in MATLAB which models this system and where the user can vary the signal power, bandwidth and temperature. Produce a plot which shows the maximum possible information rate as a function of temperature: At a fixed bandwidth If the bandwidth is doubled If the bandwidth is reduced to a half of the original value Produce a plot which shows the probability of a bit error as a function of temperature: At a fixed bandwidth If the bandwidth is doubled If the bandwidth is reduced to a half of the original value You should make a recommendation for the operating characteristics (signal power, bandwidth and temperature) of the system. Please note that there is no right or wrong answer for this part of the question - I am interested in your reasoning, not the precise numerical value. Part b: Then, assuming that the attenuation of a signal is 3dB per km, write a Matlab code that produces a graph that shows how the signal to noise varies with distance for the operating characteristics that you have chosen. Your submission should include: • A detailed description of your work, including any plots which are needed to clearly explain your work • A single .m file for part a which can be run in MATLAB which contains your routine. This.m file should contain any comments which the user needs to be able to easily run this file and reproduce your results A single .m file for part b which can be run in MATLAB which contains your routine. This.m file should contain any comments which the user needs to be able to easily run this file and reproduce your results If you find that you are unable to complete part a, then you can still attempt part b if you select a reasonable value for signal power and temperature. You can find such reasonable values in the lecture notes and/or seminar questions.