Show that [ int_{-infty}^{infty} t x^{*}(t) x^{prime}(t) d t=-int_{-infty}^{infty} f X^{*}(f) X^{prime}(f) d f ] where (X(f))
Question:
Show that
\[
\int_{-\infty}^{\infty} t x^{*}(t) x^{\prime}(t) d t=-\int_{-\infty}^{\infty} f X^{*}(f) X^{\prime}(f) d f
\]
where \(X(f)\) is the FT of \(x(t)\), and \(x^{\prime}(t)\) is its derivative with respect to time. The function \(X^{\prime}(f)\) is the derivative of \(X(f)\) with respect to frequency.
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Related Book For
Radar Systems Analysis And Design Using MATLAB
ISBN: 9780367507930
4th Edition
Authors: Bassem R. Mahafza
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