Analysis of heart sounds enables a number of dysfunctions in the blood circulation system to be investigated. Heart sounds are recorded by acoustic sensors placed on the chest, close to the heart location.  In this coursework, you will design a system to process a heart sound signal available on your blackboard.

This assignment has three parts. In part A you will plot the heart signal, design and analyse the system that processes the signal. In part B you will investigate spectral analysis and issues that affect its accuracy. In part C you will investigate how short-time frequency is performed.

Part (A) System design

In order to better interpret your results you need to be familiar with the signal you are processing. Carry out a brief (0.5 a page) literature review of heart sounds and explain how heart sounds are produced and what are their time characteristics and frequency components.

1. Use matlab to plot the heart sound signal provided. Relate the time domain features of the signal plot to those you found in your literature review (you may need to zoom into the signal). The signal is processed with a system with transfer function H(z)= (0.05397z + 0.05397)/(z-0.8921). The sample rate for the system is 11025.
2. Using pen and paper, determine the system's poles and zero and its frequency response.
3. Using pen and paper, determine the system's difference equation.
4. Using matlab, plot the system's pole-zero diagram. Investigate what information can be obtained from this diagram (you should do a literature search).
5. Use matlab to plot the system frequency response. The -3dB point should correspond to 200 Hz. Determine its magnitude and phase at 200 Hz. By carefully considering the features of the frequency response, explain the function of the system.
6. Use matlab to determine the first three values of the system's unit sample response. Then using pen and paper determine the values. Compare the values obtained by using matlab with those obtained using pen and paper. Are there any difference?.
7. Process the input signal with the system. Compare the input and output signals and explain differences.
8. Investigate how increasing the order of the system affect its transfer function, pole zero diagram and frequency response. Relate your finding with suitable references.

Critically discuss all your operations (use appropriate references to support your discussions).

Part (C) Signal Analysis

The frequency spectrum of a full amplitude modulated (AM) sinusoidal signal is

where E_c=10 volts and E_m=4 volts are carrier and modulating signal amplitudes, fc=1000 Hz and f_m=500 Hz are carrier and modulating signal frequencies.

Generate the AM signal and then investigate its magnitude frequency spectrum. In your investigation you need to demonstrate spectral leakage, scalloping (picket fence) effect and the manner they could be dealt with.

Gradually reduce f_m value from 500 Hz and plot the magnitude spectrum of the AM signal. Explain what happens to the spectrum at very low the values (say 10 Hz) of f_m.

You must critically discuss all your observations.

Part (D) Short-Time Fourier Transform (STFT)

Carry out a literature review to identify the shortcoming of Fourier Transform in determining the frequency spectrum of a signal that is not stationary and how Short-Time Fourier Transform (STFT) deals with this limitation.

Obtain the STFT of the AM signal and investigate how parameters of STFT affect its operation.