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<math>X^* (jw)=[\int\limits_{-\infty}^{\infty}x(t)e^{(-\jmath wt)}dt]^*</math> | <math>X^* (jw)=[\int\limits_{-\infty}^{\infty}x(t)e^{(-\jmath wt)}dt]^*</math> | ||
− | <math>X^* (jw)=\int\limits_{-\infty}^{\infty}x(t)e^{(\jmath wt)}dt | + | <math>X^* (jw)=\int\limits_{-\infty}^{\infty}x^* (t)e^{(\jmath wt)}dt</math> |
+ | |||
Replacing w with -w, | Replacing w with -w, | ||
− | <math>X^* (-jw)=\int\limits_{-\infty}^{\infty}x(t)e^{(-\jmath wt)}dt | + | <math>X^* (-jw)=\int\limits_{-\infty}^{\infty}x^* (t)e^{(-\jmath wt)}dt</math> |
Revision as of 04:27, 9 July 2009
Conjugation Property and Conjugate Symmetry
The conjugation property states that if the $ \mathcal{F} $ of x(t) will be equal to X(jw) then, the $ \mathcal{F} $ of x*(t) will be equal to X*(-jw) This property follows from the evaluation of the complex conjugate of $ X^* (jw)=[\int\limits_{-\infty}^{\infty}x(t)e^{(-\jmath wt)}dt]^* $ $ X^* (jw)=\int\limits_{-\infty}^{\infty}x^* (t)e^{(\jmath wt)}dt $ Replacing w with -w, $ X^* (-jw)=\int\limits_{-\infty}^{\infty}x^* (t)e^{(-\jmath wt)}dt $