The objective of this assessment is for each student to undertake an investigative review of the literature and study and familiarize with the techniques of decimation and interpolation.
2 Part A: Review of Decimation and Interpolation techniques
In this part, student must review some of the basic interpolation techniques. The student must select one of the following study areas:
1- A detailed review of algorithms for image interpolation using Discrete cosine transform (DCT) and fast Fourier transform (FFT).
2- A detailed review of polynomial interpolations techniques (including spline) and their applications.
3- A detailed review of Inverse Distance Weighting interpolation (IDW) and Kriging method and their applications.
Compare and contrast the various methods in use in a written report of not less than four (4) A4 pages with single line spacing length. Do not use Wikipedia for this assessment.
3 Part B: Signal decimation Using Matlab
1. Load the signal “x” into your workspace using the command “load original_signal.mat”. “x” has 200000 samples with a sampling frequency of 24 Mega samples per second, taken from a modulated baseband signal.
2. Plot the first 2000 samples of this signal.
3. Decimate the signal 3 times using the command “y=x(1:3:end);”
4. Find the power spectrum of “x” and “y” using the MATLAB periodogram and draw them in dB on one axis. Set the FFT size 512. Discuss the similarities and differences of the spectrums.
5. Zero pad (up-sample) the “y” signal sample with 2 zeros in the middle of the adjacent samples, to increase the sampling frequency by 3, and call the resultant signal “zy”.
6. Load a root raised cosine filter impulse response, h, from the given file “rrc_filter.mat” into your workspace using the command “load rrc_filter.mat;”
7. Filter your signal (“zy”) using the command “yzf=conv(x,h);”.
8. Find the power spectrum of “yzf” and “yz” in dB and draw them on one axis.
9. Discuss the zero-padding and filtering effects on the signal spectrum.
10 Use the cubic spline interpolation in MATLAB to interpolate the signal “y” using the command “ys= interp1(1: length(y), y,1:1/3:length(y), ‘spline’);”.
11. Draw the spectrum of “ys” and compare it with the result of the section 8.
12. Repeat the sections 10 and 11 by changing the method to ‘linear’ and ‘nearest’.
13. Filter the signals “ys” in section 12 with the given filter and find and draw the spectrums and discuss the results.
14. Give an overview of the work you have done and discuss the strength and weakness of each of the used interpolation methods in Part B.
4 Format of Report
Your report should be in three parts: Part I, literature review report; Part II detail of your Matlab code works and Part III an overview of the work you have done on Part B and discuss on the strength and weakness of each used interpolation methods. Your report should have a reference list at the end of the report. The report should not be more than 10 A4 pages long (11-point font size using Calibri font type).