Spectrum Analyzer: MATLAB Exercise 2.8 2002/06/03 2003/08/01 11:25:58.722 GMT-5 Swaroop Appadwedula appadwed@uiuc.edu Douglas L. Jones dl-jones@uiuc.edu Michael L. Kramer kramer@ifp.uiuc.edu Dima Moussa dmoussa@uiuc.edu Brian Wade bwade@uiuc.edu Jake Janevitz jake@janevitz.com Daniel Grobe Sachs sachs@uiuc.edu Matthew J. Berry mjberry@uiuc.edu Mark A. Haun markhaun@uiuc.edu Swaroop Appadwedula appadwed@uiuc.edu Douglas L. Jones dl-jones@uiuc.edu Daniel Grobe Sachs sachs@uiuc.edu Matthew J. Berry mjberry@uiuc.edu Mark D. Butala butala@uiuc.edu Ricardo Anthony Radaelli-Sanchez ricky@alumni.rice.edu Robert L. Morrison rlmorris@uiuc.edu Fourier transform Fast Fourier transform FFT Discrete Fourier Transform DFT Discrete Time Fourier Transform DTFT boxcar hamming mainlobe sidelobe twiddle-factor bit-reversed windowing zero-pad DSP You will investigate the effects of windowing and zero-padding on the Discrete Fourier Transform of a signal.

MATLAB Exercise Since the DFT is a sampled version of the spectrum of a digital signal, it has certain sampling effects. To explore these sampling effects more thoroughly, we consider the effect of multiplying the time signal by different window functions and the effect of using zero-padding to increase the length (and thus the number of sample points) of the DFT. Using the following MATLAB script as an example, plot the squared-magnitude response of the following test cases over the digital frequencies ω c 8 3 8 . rectangular window with no zero-padding hamming window with no zero-padding rectangular window with zero-padding by factor of four (i.e., 1024-point FFT) hamming window window with zero-padding by factor of four Window sequences can be generated in MATLAB by using the boxcar and hamming functions. Make sure you understand what every line in the script does. What signals are plotted? You should be able to describe the tradeoff between mainlobe width and sidelobe behavior for the various window functions. Does zero-padding increase frequency resolution? Are we getting something for free? What is the relationship between the DFT, X k , and the DTFT, X ω , of a sequence x n ?