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If x(t) has CTFS coefficients <math>a_k</math> and y(t) has CTFS coefficients <math>b_k</math>, | If x(t) has CTFS coefficients <math>a_k</math> and y(t) has CTFS coefficients <math>b_k</math>, | ||
| − | then the Fourier series coefficients <math>b_k</math> of the resulting signal y(t)=x(t-<math>t_0</math>) | + | then the Fourier series coefficients <math>b_k</math> of the resulting signal y(t) = x(t - <math>t_0</math>) |
| − | may be expressed as <math>b_k | + | may be expressed as <math>b_k = \left ( \frac{1}{T} \right ) \int \limits_T x \left ( t - t_0 \right ) e^{-j k w_0 t}\, dt</math>. |
Revision as of 02:41, 23 July 2009
CTFS Time Shifting Property
If x(t) has CTFS coefficients $ a_k $ and y(t) has CTFS coefficients $ b_k $,
then the Fourier series coefficients $ b_k $ of the resulting signal y(t) = x(t - $ t_0 $)
may be expressed as $ b_k = \left ( \frac{1}{T} \right ) \int \limits_T x \left ( t - t_0 \right ) e^{-j k w_0 t}\, dt $.
