(New page: ==Multiplication Property of Continuous - Time Fourier Series== Suppose that x(t) and y(t) are both periodic with Period '''T''' and that *<math>x(t)\Longleftrightarrow a_k</math>, and.....) |
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Since the product '''<math>x(t)y(t)</math>''' is also periodic with period '''T''', we can expand it in a Fourier series with Fourier series coefficients '''<math>h_k</math>''' expressed in terms of those for x(t) and y(t). The result is.. | Since the product '''<math>x(t)y(t)</math>''' is also periodic with period '''T''', we can expand it in a Fourier series with Fourier series coefficients '''<math>h_k</math>''' expressed in terms of those for x(t) and y(t). The result is.. | ||
| − | *<math>x(t)y(t)\Longleftrightarrow h_k = \ | + | *<math>x(t)y(t)\Longleftrightarrow h_k = \sum_{l=-\infty}^\infty a_lb_{k-l}</math> |
Revision as of 09:20, 8 July 2009
Multiplication Property of Continuous - Time Fourier Series
Suppose that x(t) and y(t) are both periodic with Period T and that
- $ x(t)\Longleftrightarrow a_k $, and...
- $ y(t)\Longleftrightarrow b_k $
Since the product $ x(t)y(t) $ is also periodic with period T, we can expand it in a Fourier series with Fourier series coefficients $ h_k $ expressed in terms of those for x(t) and y(t). The result is..
- $ x(t)y(t)\Longleftrightarrow h_k = \sum_{l=-\infty}^\infty a_lb_{k-l} $
