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FourierSeries2_2009

FourierSeries2_2009 - More on Fourier Series Knowing the...

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More on Fourier Series Knowing the Fourier Series for “simple” waveforms (square waves, triangle waves, etc.), we can also determine the Fourier series representation of more “complicated” waveforms through adding, subtracting, differentiation, or integration of these waveforms. Also, knowing the frequency domain representation of these Signals allows us to predict the behavior when it is passed through an LTI system (filter) that alters the signal. We think of this filter has altering the signal’s magnitudes and phases as a function of frequency.
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Filtering Low-pass filters w w w High-pass filters w w w
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Band-reject filters w w w Filtering Band-pass filters w w w
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Filtering Filtering clearly alters the frequency domain representation of our signal. This in turn alters our time domain signal. Example square wave: = + - - - + = 1 1 ) 1 2 ( 2 cos 1 2 ) 1 ( 2 2 1 ) ( n n t n T n t f π π
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First Ten Harmonics Time Domain Frequency Domain
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Time Domain Frequency Domain First Ten Harmonics-LPF
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Time Domain Frequency Domain First Ten Harmonics-HPF The time signal looks a bit confusing, better understood in frequency domain.
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