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When a time shift is applied to a periodic signal x(t), the period T of the signal is preserved.<br> | When a time shift is applied to a periodic signal x(t), the period T of the signal is preserved.<br> | ||
The Fourier series coefficients <math>b_{k}</math> of the resulting signal y(t)=x(t-<math>t_{0}</math>) may be expressed as<br> | The Fourier series coefficients <math>b_{k}</math> of the resulting signal y(t)=x(t-<math>t_{0}</math>) may be expressed as<br> | ||
| − | <math> | + | <math>b_{k}=\frac{1}{T}\int_T x(t-t_{0})e^{-jkw_{0}t}dt</math><br> |
Revision as of 03:27, 9 July 2009
== Time Shifting Property of Continuous-Time Fourier Series ==
When a time shift is applied to a periodic signal x(t), the period T of the signal is preserved.
The Fourier series coefficients $ b_{k} $ of the resulting signal y(t)=x(t-$ t_{0} $) may be expressed as
$ b_{k}=\frac{1}{T}\int_T x(t-t_{0})e^{-jkw_{0}t}dt $
