ME301BeamVibration112SupplementFourierTransforms

# - 1.12 Supplement on Introduction to Fourier Transforms A number of experiments generate a cyclic voltage vs time such as an electrical tachometer

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1.12. Supplement on Introduction to Fourier Transforms A number of experiments generate a cyclic voltage vs. time such as an electrical tachometer and vibrating wing accelerometer. The signal can have a dominant frequency with a wave shape such as sine, square or sawtooth. The signal could also be corrupted by high frequency noise or 60 [Hz] electrical noise from the laboratory. Fourier analysis offers a method for breaking the signal down into a set of individual sine (or cosine) waves of different frequencies by determining wave amplitudes. To learn about Fourier Analysis, consider the common signal of an on/off square wave The fundamental frequency is the inverse of the period, , and the duty cycle is the time, d, the signal is ‘on’ compared to the cycle period (duty cycle, , is usually in percent) Using a Fourier cosine series, the square wave of voltage versus time is comprised of many superimposed cosine waves. With a unit step square wave, the series is where the amplitude and frequency of the component cosine waves are The magnitude of these amplitudes being related to wave number, m , gives a frequency domain plot (x,y)=( f , A magnitude) or (x,y)=( m wave number, A magnitude). It takes

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many waves in the series for the V(t) to appear as a square wave. A special case is the duty cycle of 50% or 0.5 where the series simplifies to only odd terms. The
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## This note was uploaded on 02/07/2011 for the course AE/ME 301 taught by Professor Lafleur during the Spring '11 term at Clarkson University .

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- 1.12 Supplement on Introduction to Fourier Transforms A number of experiments generate a cyclic voltage vs time such as an electrical tachometer

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