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sp_S15_mud

sp_S15_mud - Lecture S15 Muddiest Points General Comments...

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[ } ( )] = Lecture S15 Muddiest Points General Comments Today, we started looking at Fourier transforms. In simplest form, FTs are just Laplace transforms with s replaced by . This can be done legitimately for any stable signal. But there’s more to it than that — we can define the FT for almost stable signals, which is important for the analysis of many communications problems, such as modulation. Responses to Muddiest-Part-of-the-Lecture Cards (10 cards) 1. Is the Fourier transform at all related to Fourier series? (1 student) Yes! We got at Fourier transforms via Laplace transforms, but we could have gotten to them via Fourier series. Brieﬂy, Fourier series can represent periodic series, with period, say, T . If we let the period T go to infinity, the Fourier series summation becomes the Fourier transform integral. 2. Direct vs. indirect transforms? (1) The direct transform is F −∞ } ( ) −| ω The inverse (not indirect) transform is F −∞ [ G ( | ω )] = −∞ ω ) + | ω ω G ( | 3. Can you explain

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sp_S15_mud - Lecture S15 Muddiest Points General Comments...

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