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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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View Full Document 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 .
 Spring '11
 LaFleur

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