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Proofs of Parseval’s Theorem & the Convolution Theorem
wwwf.imperial.ac.ukProofs of Parseval’s Theorem & the Convolution Theorem (using the integral representation of the δ-function) 1 The generalization of Parseval’s theorem The result is Z f(t)g(t)∗dt= 1 2π Z ∞ −∞ f(ω)g(ω)∗dω (1) This has many names but is often called Plancherel’s formula.
Tutorial 7 - Sampling
www.ee.ic.ac.ukPYKC – 11 Feb 08 2 E2.5 Signals & Linear Systems Tutorial Sheet 7 – Sampling (Lectures 12 - 13) 1.* By applying the Parseval’s theorem, show that
Signal Transmission through LTI Systems
www.ee.ic.ac.ukPYKC 20-Feb-11 E2.5 Signals & Linear Systems Lecture 12 Slide 9 Parseval’s Theorem The energy of a signal x(t) can be derived in time or frequency domain: