ELEC6218 Signal Processing
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ELEC6218 Signal Processing
Statistical Signal Processing Coursework
Submission Details
This assignment contributes 10% of your final mark for the ELEC6218 Signal Processing mod- ule.
You are required to produce a write-up, which needs to include the derivations, calculations, explanations and Matlab code, that are requested in the questions below.
When you are finished, you need to submit the assignment at C-BASS
https://handin.ecs.soton.ac.uk/handin/2122/ELEC6218/1/ before 4pm on Tuesday 11/01/2022. You only need to make an electronic submission.
If you notice any mistakes in this document or have any queries about it, please email me at [email protected].
Mohammed El-Hajjar
Learning Outcomes
1. Apply maximum likelihood estimation technique;
2. Implement your estimator in Matlab for verification and testing.
Table 1: Marking Scheme
|
Accuracy of results: Are the obtained results correct? Is the formulation correct? |
50% |
|
Interpretation of results: How well are the questions posed in the assignment answered? Do you answer all parts of the questions? Do you include the required derivations? Do you explain your derivations when requested? |
50% |
Amplitude and frequency estimation of a sinusoidal signal
Consider a sinusoidal signal x[n] embedded in White Gaussian noise (WGN), which can be represented as
x[n] = A cos(2πf0n) + w[n], n = 0, 1, 2, . . . , N - 1,
where A > 0 is the amplitude, 0 < f0 < 0.5 is the frequency and w[n] is the WGN with mean 0 and variance σ 2 .
1. Find the maximum likelihood estimate (MLE) of the amplitude A and the frequency f0 of the sinusoidal signal.
2. Consider a sinusoid x[n] = 1.25 cos(2 × π × 0.15 × n) + w[n], with w[n] having a variance σ 2 = 0.1 and N = 200.
(a) Write a Matlab code that implements your MLE estimate in part 1 above to find Aˆ and fˆ0 , which represent the estimates of the A and f0 .
(b) Include in your write up the output values of your Matlab code for Aˆ and fˆ0 .
Hint: An idempotent matrix A has the following characteristic: A2 = A.
In your analysis, you will get a matrix of the form╱I - H(HT H)− 1 HT、. This will be idempotent matrix.
2022-01-06
Statistical Signal Processing Coursework