_Signal_FAQ11_Xk_&_X(f)

_Signal_FAQ11_Xk_&_X(f) - f δ , right? The k th slice...

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When we derived the FT from the FS, the spectrum becomes a function of f . But it was a function of k and f 0 . Is there a contradiction there? Run the demonstration program. Does the spectral density at the bottom depend on 0 T as 0 T or 0 0 f ? It tends towards a curve independent of the width 0 f , right? The curve is given by ( 29 f j f X π 2 2 1 + = , where f is 0 kf . There is no contradiction and corresponds to the same thing that happens in calculus. Suppose we want to find the area under the curve of ( 29 f y versus f . What do we do? We divide the f axis into slices with width 0 f or, more commonly used,
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Unformatted text preview: f δ , right? The k th slice is at kf f = . The height or value of the function for this slice is ( 29 ( 29 ( 29 f y kf y f y y k = = = . The area of the k th slice is ( 29 ( 29 f f y f f y f y k = = . The total area is ( 29 ∑ ∑ ∞-∞ = ∞-∞ = = k k k f f y f y . We replace this sum with the integration sign and we write this as follows, right? ( 29 ( 29 ∫ ∑ ∑ ∞ ∞-∞-∞ = ∞-∞ = ⇒ = df f y f f y f y k k k Does the integration depends on f ?...
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This note was uploaded on 08/02/2009 for the course ECE EE2009 taught by Professor Prof.c.c.ko during the Fall '07 term at National University of Singapore.

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