EEGR4124 Project 5, DFT 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
  •        // 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" buttun 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.

  • Implement the 20log10|FFT| button, plot 80 dB full-scale (chop off below this by setting min = max - 80dB).
    Hint: dB = 10 log10(power ) = 20 log10(voltage) Center the frequency domain so the center of the plot corresponds to zero frequency (dc). Also note that the functions fft() and ifft() are provided for you in Myclass.java. Do not try to take the log of zero.
  • Be careful with the fft() method, since it is unique in MyClass. The fft() method returns a result on the stack, so you must use it in a command like a.equals(b.fft()) to fetch the result off the stack using the equals() method. The fft should be taken on the displayed data (dispData)
  • Take great care in implementing this 20log10|FFT| button, since it will be`used throughout the rest of thesemester!
  • Do not forget to place dc (zero frequency) in the middle of the display.  Hint: for the easiest method of shifting the spectrum, see the left side of item 3 in Table 2.2 for a frequency shift of pi.
  • Take 20log10|FFT| of box16.au (length 16 box),
    plot this ( P1 ).
    (Hint: see Fig. 2.19 on p. 45.)
    What is the dc value in dB ( Q1 ).? Explain (show calculations) your results
    What discrete-time frequency is the first null ( Q2 ).? Explain (show calculations) your results (in rad/sample).
    Assume sampling rate is 8000 samples/second, what is the analog frequency of the first null ( Q3 ).?  (in Hz)
    How many dB down is the first sidelobe ( Q4 )?  Hint: see Eq. 2.123, Fig. 2.19, and Table 2.3 line 9 on p. 62.
    Compare all of these results with theoretical. .
  • Take 20log10|FFT| of sin3264.au (32 and 64 cycle sinewaves added) , plot this ( P2 ).
    What are the discrete-time (rad/sample) frequencies of the two sinusoidal components ( Q5 )?  Recall that the sample rate of the audio files is 8000 samples/second.  What are the continuous-time  (Hz) frequencies of the two sinusoidal components ( Q6 )?
  • Convolve box16.au with sin3264.au, plot this ( P3 ).
    Take 20log10|FFT| of the result, plot this ( P4 ).
    Explain the results.
  • Convolve box16.au with rand5sin64.au (noise+64cycles sine), plot this ( P5 ).
    Take 20log10|FFT| of the result, plot this ( P6 ).
    Plot 20log10|FFT| of rand5sin64.au ( P7 ).
    ( Q7 ) How many dB did the P6  signal-to-noise ratio improve relative to the P7 signal-to-noise ratio? (when comparing P6 with P7, signal-to-noise dB is the difference between the strong signal at low frequency and the noise level at pi/2 for each of the 2 plots)
  • What did Philo Taylor Farnsworth demonstrate on September 3, 1928? ( Q8 )

  • 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.
     
    Copyright 2009 T.P. Weldon