Reference no: EM133687081 , Length: word count:2000

Digital Signal Processing

Learning outcome 1: Analyse and design discrete systems, mathematically express them using a number of suitable approaches, critically analyse their frequency response and transfer function properties and use z-transform techniques to investigate stability.

Learning outcome 2: Make critical judgement about the operational parameters and potential of adaptive discrete systems for solving engineering problems.

Learning outcome 3: Make critical judgement about the operational parameters and potential applications of adaptive discrete systems for solving engineering problems.

Learning outcome 4: Design and apply digital filter by critically considering the characteristics of the desired signal and the noise.

Guide to the Report Structure

The report should have the following format and structure and features.

Presentation: Ensure your report is scientifically presented (figures, grammar, English, format etc. Ensure you have properly and adequately referenced your work. Use the SHU suggested style of referencing throughout.
Aims and Objectives: A brief (few sentences) indicating of what was the purpose of the study. What were investigated?

Introduction: This outlines the background to the investigation. The introduction needs to cover a brief theory of the related topics used in the study. You would have to do a literature search to obtain more information when writing this part. Use the university recommended referencing APA style. Ensure your report is properly and adequately referenced.

Methodology: This is partially contained within your assignment sheet. You may refer directly to the part in the assignment sheet. However, you need to augment these and describe the tasks you did in a more detail. You may wish to elaborate of some of the tasks you performed to obtain you results.

Results: This may include tables of readings, waveforms, graphs, figures, and observations etc. These need to be clearly and carefully presented. Always plot your results as it is easier to look at a diagram than a list of numbers. Make sure your graphs are scientifically labelled (do not forget labels for axes).Critical discussion of results: You need to explain your findings and observations critically. Do they conform to theory?. If there are discrepancies, determine by how much and explain the cause. To explain some of your findings you may have to do further readings.

Conclusions: You need to summarise your findings in a reflective manner and explain what you understood by doing the work.
References: Ensure your report is correctly and adequately referenced using the University suggested style.

Introduction
The purpose of this coursework is to further develop and build on your digital signal processing knowledge and expertise in solving practical engineering problems.

This work has 3 parts outlined in A, B and C. You are required to complete all parts, carefully noting your observations, and producing a scientific individual report to critically explain them.

Section (A) Design and analysis

A1 The web site teachingheartauscultation has examples of heart sounds representing heart normal sound and examples of abnormal heart sounds. Your Blackboard (under the Assessment folder) has examples of these heart sounds. The audioread function in Matlab© can be used to plot an example (adultCase1.mp3) of these signal. The format of this function is[x,fs] = audioread(filename);filename can be defined as filename= 'adultCASE1.mp3';The function returns the heart sound signal x and sample rate fs. The sample rate for this signal is 11025 samples per second.

Plot couple more of the heart sounds and visually examine their characteristic differences. For each signal, ensure the sample rate is 11025 samples per second.

Select one of the heart signals and use Matlab to explore to what extent its samples are from a normal (Gaussian) distribution. You need to use at least one statistical method and two visual methods (plots) to carry out this investigation. Critically comments on findings.

A2 Explain what correlation coefficient is, and determine correlation coefficient of any two heart signals. Explain what are limits of correlation coefficient measure when investigating similarity between signals.
A3 Using Matlab , design a 1st order lowpass Butterworth digital filter, cutoff frequency fc=200 Hz, sample rate fs=11,025.

A4 Determine (using Matlab ), the filter's difference equation coefficients (values of B and A matrices) and write the filter's difference equation.

A5 Determine (using Matlab) the first four values of the system's unit sample response. Then manually (without Matlab©) determine these values. Compare the values obtained (using Matlab) with those obtained manually. Assume y(-1)=x(-1)=0. Comment on the similarity between the two sets of results.

A6 Plot (using Matlab ) the filter's frequency response (magnitude and phase) between 0 and fs/2 Hz. Carry out a literature search to explore whether your plotted frequency response conforms to the theory and comment on your findings. Demonstrate using Matlab© plots, how the filter's order, affects its magnitude and phase responses. Determine the values (magnitude and phase) associated with the filter's magnitude response at cut-off frequency and the compare them with those obtained manually. Critically explain findings.

A7 Manually (without Matlab ) determine the filter's transfer function.

A8 Plot (using Matlab) the system's pole-zero diagram. Comment on the information that can be obtained from this diagram. Carry out a brief literature search to explore how the locations of poles and zeros affect a discrete system's operation.

Section (B) Filter design and signal analysis

B1 Using the Matlab Digital Signal Processing User Guide document (available freely from the Internet) and other information sources, obtain the power frequency spectra for any two of the heart signals. Critically comment on observations. Using Maltlab© plots, demonstrate how signal length affects the accuracy of power spectrum.

B2 Using your digital signal processing expertise, devise a method to automatically (i.e. using Matlab©) determine heart rate from two heart rate signals.

B3 Obtain the Short-time Fourier transform and wavelet transform of a heart rate signal and compare the effectiveness of each approach in representing the signal. Briefly explore how the parameters of each approach affect its performance.