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Question 1: Using MATLAB produce a composite signal of appropriate length containing a cosine wave of amplitude A at frequency fo, a sine wave of amplitude 0.5A at frequency 5fo, a cosine wave of amplitude 2A at frequency 0.2fo and a large random component, obtained using the MATLAB 'randn( )' function. You may select the values of fo and A yourself.

(i) Produce a diagram of the composite signal and produce diagrams of each individual component of the signal.

Question 1(ii) Produce a diagram of the composite signal and discuss the properties of the DFT in relation to the properties of the components of the composite signal.

Question 1(iii) Design high order MATLAB, 'low pass', 'band pass', and 'high pass' filters to isolate, INDIVIDUALL Y, the signals at frequencies 0.2fo, fo and 5fo from the composite signal. Import your composite signal into SIMULINK and apply the three filters you have designed, in turn, to the composite signal to show how effective your filter designs are at isolating the individual frequency components.

Produce plots of the frequency components that you have isolated in this way. Compare the frequency components that you have isolated in this way with the original frequency components that you produced in (i) above.

Question 2 Write an essay (max 5 pages) on the role of signal processing in an engineering application of your choice. Your essay must be fully referenced.

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