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EEE 6209 Advanced Signal Processing

Coursework 2020

Dr Charith Abhayaratne

1

EEE 6209

Advanced Signal Processing

Coursework 2018-19: EEE6209-001

Dr Charith Abhayaratne

21/03/2020

Total Marks: 100 (This contributes to 25% of the overall module marks)

TITLE: Signal Noise removal

Due Date: 8

th

May 2020 at 16.00 via Blackboard EEE6209 coursework submission link

The aim of the coursework exercise is to explore and apply transform domain processing for signal

denoising. Each of you has been assigned an individual signal. The number of the signal allocated to you

can be found in “My Grades” section in MOLE EEE6209 pages. Download the “signals” file from MOLE

coursework folder and choose the MAT file (x.mat, where x is your signal number). Also download the

noise file (noise.MAT) from MOLE coursework folder. Two variables can be found in the signal MAT file.

They are the signal assigned to you and the signal number, n. The noise MAT file contains the noise signal

(V) to corrupt the signal assigned to you.

Add noise, V, to your test signal, A, to get the corrupted image, B, as follows:

B= A+ V.

You have to complete 3 tasks:

1. Analyse the original signal A, to understand its time-domain and frequency domain characteristics.

2. Use the Fourier transform-based techniques to remove the noise in signal, B, to recover the original

signal, A.

3. Explore the multi resolution analysis based on the Discrete Cosine Transform (DCT) you learned in

lectures (Topic 02) to remove noise in signal, B, to recover the original signal, A.

You are required to submit a short report (not more than 2000 words in text and not exceeding 6 –A4

pages) including your findings in above 3 tasks.

For each task, you are required to do the following sub tasks and write your answers in the report. Do not

copy text from the task descriptions. Just use the relevant sub task number (e.g., 1.1, 1.2, etc.)

Task 1: Signal analysis task –

1.1 What is the identification number of the signal assigned to you?

1.2 Show the plots of original and noisy signals

1.3 Filter the original signal, A, using the 2 point moving difference filter, with filter coefficients,

(0.5, -0.5) for n=0 and 1, respectively. Show the plots of the filtered signal output.

1.4 Explain what you have learned from the plot in 1.3.

1.5 Use your answers to 1.3 and 1.4 above to segment the signal, A, into smaller segments and show

the plots of the segment.

1.6 Compute the FFT of A and it segments (as in 1.4 above) and show the plots of the magnitude of the

FFT.

1.7 Using your observations in 1.3 to 1.6, comment about frequency domain and the time domain

properties of the signal A;

1.8 Compute the Peak Signal to noise ratio (PSNR) for the noisy signal and its segments. The

definition of PSNR is given at the end of this document.

1.9 Taking the analysis of the signal you did, suggest possible methods for noise removal.

EEE 6209 Advanced Signal Processing

Coursework 2020

Dr Charith Abhayaratne

2

Task 2: Fourier domain noise removal – In this case, you have to assume the noise is spread in all

frequencies. You may want to verify this in your report. Noise magnitude in frequency domain may be

smaller than that of the useful signal components. With this assumption, you can implement a method to

remove the noise in the Fourier domain. For this task you may want to consider the signal segments as in

Task 1 as opposed to the overall signal.

2.1 In your report, explain how you use the Fourier Transform to remove the noise in signal, B, to recover

the original signal, A;

2.2 Show the plot the recovered signal;

2.3 If your technique uses any parameter values, for example, threshold values, you need to show the result

for several different values of the parameter;

2.4 Compute the PSNR values for the recovered signal segments for different parameter values;

2.5 Discuss the performance of the Fourier transform –based noise removal algorithm and the choice of its

parameter values.

Task3: Use the 1D N-point DCT on the signal segments to remove the noise, where N can be any integer

number.

3.1 In your report, explain how you use the DCT to remove the noise from the signal segments.

3.2 Explain how the thresholds are chosen.

3.3 Include a block diagram of the noise removal algorithm

3.4 Plot the recovered signal

3.5 If your technique uses any parameter values, for example different values of N or thresholds, you need

to show the result for several different values of the parameters;

3.6 Compute the PSNR values for the recovered signal segments for different parameter values;

3.7 Discuss the performance of the DCT –based noise removal algorithm and the choice of its parameter

values.

3.8 Finally, provide an overall comparison and discussion on the performance of Fourier –based denoising

and DCT denoising.

The marking scheme is as follows:

Textual parts:

Task 1 Methodology, results, analysis and discussion 30 marks

Task 2 Methodology 10 marks

Task 2 Results, analysis and discussion 20 marks

Task 3 Methodology 15 marks

Task 3 Results, analysis and discussion 15 marks

Overall Conclusions and recommendations 10 marks

Figures part:

Accuracy of Task 1 figures 25 marks

Accuracy of Task 2 figures 25 marks

Accuracy of Task 3 figures 25 marks

Quality of figures 25 marks

Overall marks = 0.7x(Textual part marks) + 0.3x(Figures part marks)

USEFUL ADVICE

- PSNR definition: The PSNR of two signals, x and y, are computed as below:

where p is the peak signal value. For this exercise consider p=255.

EEE 6209 Advanced Signal Processing

Coursework 2020

Dr Charith Abhayaratne

Where L is the signal length.

- DO NOT provide Matlab codes with your report. Instead use pseudo codes to explain your

methodology and algorithms.

- DO NOT copy and paste any text from this document. Doing so will result in a matching in

Turnitin reports leading to deduction of marks by the department’s plagiarism assessment

committee. Therefore just use the question numbers, 1.1, 1.2,….. etc

- All your numerical answers should include the appropriate units (For example, PSNR values in

dB). All the plots should include x-axis label, y-axis label, plot title and a legend if you are showing

multiple plots in the same figure. Not following these instructions may result in penalty marks.

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