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Challenge08_Fourier

# Challenge08_Fourier - Digital Signal Processing Dr Fred J...

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Digital Signal Processing Dr. Fred J. Taylor, Professor Lesson Title: Fourier Transform Challenge Challenge: [08] Background: You are working with a group of mechanical engineers (a.k.a., barbarians) that are attempting to measure the frequency response of a large mechanical system (e.g., airframe). You tell them how your vast knowledge of the DFT makes analyzing the system a trivial exercise. To demonstrate your skills, you propose to run an experiment that is completely unconventional, one that only you know how it works. You take a 440 Hz tuning fork, digitize a section of the signal at 8 kHz (satisfying the Nyquist Sampling Theorem), and then process the data using a Matlab 1034-sample DFT showing that you don’t need a 1024 point FFT. The returned spectrum is shown in Figure 1. One of the observers asks “Where the peak is located?” You measure and report that the spectral peak is located at the 57 harmonic. “What frequency is that?” asks a mechanical engineer. You answer, “441 Hz.” “Not 440 Hz?” the mechanical engineer says

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