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Unformatted text preview: 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. Filtering Lowpass filters w w w Highpass filters w w w Bandreject filters w w w Filtering Bandpass filters w w w 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 First Ten Harmonics Time Domain Frequency Domain Time Domain Frequency Domain First Ten HarmonicsLPF Time Domain Frequency Domain First Ten HarmonicsHPF The time signal looks a bit confusing, better understood in frequency domain. N_harmonics = 10; %number of harmonics...
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This note was uploaded on 06/08/2009 for the course BME 513 taught by Professor Yen during the Spring '07 term at USC.
 Spring '07
 Yen

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