June 14, 2015
June 14, 2015
June 17, 2015
Computing & Information Technology
26.123.1 - 26.123.11
A Taste of Python - Discrete and Fast Fourier TransformsThis paper attempts to present the development and application of a practical teaching moduleintroducing Python programming techniques to electronics, computer, and bioengineeringstudents before they encounter digital signal processing and its applications in junior or seniorlevel courses.The Fourier transform takes a signal in the time domain, switches it into the frequency domain,and vice versa. Fourier Transforms are extensively used in engineering and science in a widevariety of fields including acoustics, digital signal processing, image processing, geophysicalprocessing, wavelet theory, and optics and astronomy. The Discrete Fourier Transform (DFT) isan essential digital signal processing tool and is highly desirable if the integral form of theFourier Transform cannot be expressed as a mathematical equation. The key to spectral analysisis to choose a window length that suits the signal to be analyzed, since the length of the windowused for DFT calculations has a strong impact on the information the DFT can provide. Theoperation count of the DFT algorithm is time intensive, and as such a number of Fast FourierTransform methods have been developed to perform DFT efficiently.This paper will explain how this learning and teaching module was instrumental in progressivelearning for students by presenting Python programming and the general theory of the FourierTransform in order to demonstrate how the DFT and FFT algorithms are derived and computedthrough leverage of the Python computing features. This paper thereby serves as an interestingand innovative way to expose computer information systems and technology students toadvanced python programming. These students first took a freshman level course and wereintended to be exposed to basic peripheral interfacing using Raspberry Pi and Raspbianoperating system. This module helped students learn the advanced features of Pythonprogramming while having fun learning the Discrete and Fast Fourier Transforms. Finally theresults of the survey analyzing this learning methodology will also be discussed.With proper guidance, monitoring, and diligent care, the engineering technology students wereexposed earlier to Python programming and the basics of DSP. This will go a long way inmotivating them, eliminating their fear, improving their understanding, and reinforcing the bestpractices in implementing digital filtering by fast convolution, spectral analysis, seismic dataprocessing, wavelet video compression, fingerprint image compression, and other advancedtopics in DFT and FFT real time applications 2.Bibliography1. Shakib, J., Muqri, M., Leveraging the Power of Java in the Enterprise, American Society for Engineering Education, AC 2010-1701.2. Muqri M., Shakib, J., A taste of Java Discrete and Fast Fourier Transforms, Lynn, Paul A., American Society for Engineering Education, AC 2010-1701.3. Fuerst, Wolfgang, Introductory Digital Signal Processing with Computer Applications, John Wiley & Sons, 1994.4. R. Meyer, H.W. Schuessler, and K. Schwarz. (1990). FFT Implmentation on DSP chips – Theory and Practice. IEEE International Conference on Acoustics, Speech, and Signal Processing.5. H.V. Sorensen and C.S. Burrus. (1993, March). Efficient computation of the DFT with only a subset of input or output points. IEEE Transactions on Signal Processing, 41(3), 1184-1200.6. Joyce Van de Vegte, Fundamentals of Digital Signal Processing, Prentice Hall, 2002.
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