55-701181 Digital Signal Processing Assessment Answer

Question:

Module learning outcomes to be assessed:

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.  

i)Make critical judgement about the operational parameters and potential applications of adaptive discrete systems for solving engineering problems.  

ii)Design and apply digital filter by critically considering the characteristics of the desired signal and the noise.

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 Objective: A brief (few lines) 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 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: his 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.

Appendices: Results and analysis that do not fit well in the main body of the report can go in the appendices. Appendices could include your Matlab© code.

Notes: Marks will be awarded by considering the quality and standard of the work and the report. This work is an individual assignment. Therefore, evidence of collusion with others will be considered as plagiarism and dealt with according with the University regulations. You are required to submit your individual report to the module's Blackboard site by or before specified deadline. Do not send your report as email attachment.

Digital Signal Processing : 55-701181-AF  

Academic year: 2020-21

This is an individual work.

Submit this report in Microsoft Word format to the module's blackboard by or before stated deadline. Name your report with the filename format:

Firstname_Surname_Student_ID.docx

Do not send your report as email attachment or any form other than submission via the Blackboard.

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.

The signal to be processed a piece of music obtained from the site (please note this music has restrictions for its use):

Section (A) System design and analysis  

Marking scheme: This section has 8 parts. Each part carries 5 marks.  Total mark for this section is 40% of overall mark.

A1 Use Matlab© to plot the music signal. Plot is distribution. Plot also a normal (Gaussian) distribution, comment on their closeness.   

A2  Using Matlab©  take three significantly large sections of the music signal and determine their closeness by determining a correlation coefficient matrix. Comment on findings..

A3 Design a 2nd order lowpass Butterworth digital filter, cutoff frequency fc=1000 Hz and sample rate defined by the signal sample rate(use Matlab© for this task).  NB. You can determine sample rate on loading the signal.

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 three 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)=y(-2)=x(-1)=x(-2)=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. Using Matlab© demonstrate 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 system's operation.  

Section (B) Signal analysis

Marking scheme: This section has 3 parts. Parts B1 has 10 marks, Parts B2 and B3 have 15 marks. Total mark for this section is 40% of overall mark.

B1 Using Matlab© demonstrate how signal length affect estimation of signal magnitude spectrum. Determine magnitude spectra of three separate sections of the music signal and explain whether the signal is stationary.  

B2 Windowing is used as part of frequency spectrum estimation to reduce spectral leakage. Use different windows in determining the music signal power spectra and explain observations. Indicate the features of each window used.  

B3 Explain a limitation of Fourier analysis in representing non-stationary signal and outline how this limitation can be dealt with using Short-time Fourier Transform (STFT or spectrogram) and wavelet transform. With the aid of Matlab© obtain the STFT and wavelet transform the music signal. You must indicate the parameters involved in these representations and the manner the affect the two (STFT and wavelet) transforms.    

Section (C) Investigation into characteristics of digital filters

Marking scheme: This section has one part.  Total mark for this section is 20% of overall mark.

C1 Use an adaptive linear combiner to train and then categorise iris flower feature set provided to you. Comment on strength and limitation of ALC as a signal processing tool.  

Guide to the Report Structure

THIS IS AN INDIVIDUAL WORK & REPORT

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 Objective: A brief (few lines) 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 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: his 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.

Appendices: Results and analysis that do not fit well in the main body of the report can go in the appendices. Appendices could include your Matlab© code.

Notes: Marks will be awarded by considering the quality and standard of the work and the report. This work is an individual assignment. Therefore, evidence of collusion with others will be considered as plagiarism and dealt with according with the University regulations. You are required to submit your individual report to the module's Blackboard site by or before specified deadline. Do not send your report as email attachment.