(New page: <math>a_k=\frac{1}{T}\int_0^Tx(t)e^{-jk\omega_0t}dt</math>. And the equation for fourier series of a function is as follows: <math>x(t)=\sum_{k=-\infty}^{\infty}a_ke^{jk\omega_0t}</mat...)
 
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<math>a_k=\frac{1}{T}\int_0^Tx(t)e^{-jk\omega_0t}dt</math>.
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<math>x[n]=-0.5cos(3\pin)+sin(3\pin)\!</math>.
  
  
And the equation for fourier series of a function is as follows:
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<math>x[n]=-\frac{1}{2}[\frac{e^{j3\pin}+e^{-j3\pin}}{2}]+\frac{e^{j3\pin}-e^{-3\pin}}{j2}</math>
  
  
<math>x(t)=\sum_{k=-\infty}^{\infty}a_ke^{jk\omega_0t}</math>
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<math>x[n]=-\frac{1}{4}e^{j3\pin}-\frac{1}{4}e^{-j3\pin}+\frac{1}{j2}e^{3\pin}-\frac{1}{j2}e^{-j3\pin}</math>
 
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We first put our signal into the first equation, and we get this monster:
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<math>a_0=\frac{1}{2\pi}\int_0^{2\pi}[4cos(2t) + (3j)sin(3t)]e^{0}dt</math>
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Revision as of 15:29, 26 September 2008

$ x[n]=-0.5cos(3\pin)+sin(3\pin)\! $.


$ x[n]=-\frac{1}{2}[\frac{e^{j3\pin}+e^{-j3\pin}}{2}]+\frac{e^{j3\pin}-e^{-3\pin}}{j2} $


$ x[n]=-\frac{1}{4}e^{j3\pin}-\frac{1}{4}e^{-j3\pin}+\frac{1}{j2}e^{3\pin}-\frac{1}{j2}e^{-j3\pin} $

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett