Circular Convolution and FFT

ECGR4124 Project 6, Circular Convolution and FFT

Form the same groups of 3 as before. Members of any group must be all graduate or all undergrad.

Do NOT use "zoom" feature on any plots unless specifically requested.

Preliminary tasks

Run NetBeans 5.5, or a later version (Start>AllPrograms>MosaicXp>Programming>Netbeans>NetBeans55)
Make a copy of your previous project from within NetBeans, and name this new project p4DSPsoundv55a. To do this, right-click the project in the ProjectPane, and select CopyProject.
Close the old project (right-clicl>CloseProject)
Clean and build the new project (NetBeans>Build>CleanAndBuildMainProject)
Hopefully there will be no errors. Use this new copy to build project 4.
To greatly speed up execution, you may comment out the following three lines in method refreshdisplay() of DSPsoundv55aUI.java. However, this trick will disable the writing of the data files f1.txt, f2.txt, and disp.txt. It seems that the MOSAIC afs file-system is very slow when these files are written, for some reason.

       // inData1.writeraw("f1.txt");
       // inData2.writeraw("f2.txt");
       // dispData.writeraw("disp.txt");

Write your explanations on a seperate answer sheet as described in the report requirements below, 2 or 3 sentences should suffice for most explanations.
Use "Write PNG" button on the interface to save the plots as ".png" graphics files to be included in your reports. Do NOT chop off portions of the printout. Do not use "print screen" or copy/paste, since this will cause you to lose resolution on the printouts.
Make sure that your 20log10|FFT| from project 2 is working correctly, with DC (zero-frequncy) in the center of the plot. To test this, you should get the following results for box64.au. If you do not get the following result, see the instructor or TA.

Implement convolution using the FFT and steps (a)-(c) on page 660.
Implement this as the F2 button.
This is a circular convolution.

Circular convolve box16.au with sin3264.au, plot the results ( P1 ).
Compare the results here with the results using a linear convolution from the previous project.
Notice the difference at the beginning of the waveform.

Circular convolve box32.au with box64.au, and plot it ( P2 ).
Consider why the results different from linear convolution earlier. Especially consider what happens when the linear convolution first begins filtring the signal.

Implement a 2000 Hz positive frequency shift using Eq. 6 in Table 8.2. (time domain is easiest) Hint: dont forget to convert from Hz to rad/sample.
Implement this as the F3 button.
Use this new function to shift sin32.au.
Take 20log10|FFT| of the result.
Plot the resulting frequency spectrum ( P3 ).

Implement a backward difference (Eq. 2.77).

Implement as the F4 button.
Apply this to imp32.au, then plot 20log10|FFT| ( P4 ).
Compare this result to the predicted result.
( Q1 ) What is the theoretical dc response |H(w)| for the backward difference system?
( Q2 ) What is the theoretical response |H(w)| at frequency w=pi rad/sample for the backward difference system?
( Q3 ) What is the theoretical response |H(w)| in dB at frequency w=pi rad/sample for the backward difference system?
Apply the backward difference to rand5sin64.au, then plot 20log10|FFT| ( P5 ).
Notice the inrease in high-frequency noise spectrum relative to the low frequencies comparing P5 with the original spectrum.

What system did J. Presper Eckert Jr. invent and complete in late 1945? ( Q4 )

Report

Use the Project Report Template (also shown as pdf file)

Include the plot numbers P1, P2, etc in captions, along with a short description!
Write a cover sheet + 1 page executive summary ONLY!!! Describe any unresolved issues.
Place answers to all questions on one or more consequitive sheets of paper at the front of the report!
Do NOT scatter the question answer sheets throughout the report, keep them together
Do NOT use "zoom" feature on any plots unless specifically requested.
Make sure that you include question numbers and plot numbers on all sheets!
I will only look on the question answer-sheets for any discussion.
All extraneous material WILL BE IGNORED!
Do not write any discussion, except directly on the question answer-sheets or 1 page summary.
Do not add extraneous pages.
Do not put explanations on plots unless specifically directed to do so.
Include any problems or unresolved issues in the summary.

ECGR4124 Project 6, Circular Convolution and FFT

Copyright 2009 T.P. Weldon