Transcription of Fourier Series Square Wave Example The Fourier series of a ...
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University of California, San DiegoJ. ConnellyFourier Series Square Wave ExampleThe Fourier Series of a Square wave with period1isf(t)=1+4 1Xn=1noddsin( nt)nIn what follows, we plot1+4 2N 1Xn=1noddsin( nt)nforN=1,2,..,10,25,50,75,100, 1000 , +4 1Xn=1noddsin( nt)n 2 1 Series of Square wave with 1 terms of sum21+4 3Xn=1noddsin( nt)n 2 1 Series of Square wave with 2 terms of sum31+4 5Xn=1noddsin( nt)n 2 1 Series of Square wave with 3 terms of sum41+4 7Xn=1noddsin( nt)n 2 1 Series of Square wave with 4 terms of sum51+4 9Xn=1noddsin( nt)n 2 1 Series of Square wave with 5 terms of sum61+4 11Xn=1noddsin( nt)n 2 1 Series of Square wave with 6 terms of sum71+4 13Xn=1noddsin( nt)n 2 1 Series of Square wave with 7 terms of sum81+4 15Xn=1noddsin( nt)n 2 1 Series of Square wave with 8 terms of sum91+4 17Xn=1noddsin( nt)n 2 1 Series of Square wave with 9 terms of sum101+4 19Xn=1noddsin( nt)n 2 1 Series of Square wave with 10 terms of sum111+4 49Xn=1noddsin( nt)n 2 1 Series of Square wave with 25 terms of sum121+4 99Xn=1noddsin( nt)
Fourier Series Sawtooth Wave Example The Fourier series of a sawtooth wave with period 1 is f(t)= 1 2 1 ⇡ X1 n=1 sin(2⇡nt) n In what follows, we plot 1 2 1 ⇡ XN n=1 sin(2⇡nt) n for N =1,2,...,10,25,50,75,100,1000,10000. 1
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