Flashcards
Fourier Transforms
Cards in this deck (12)
- 1Define the Fourier Transform
- 2Define the inverse fourier transform
- 3Describe what the Fourier transform does to a signal (function of time)Decomposes it into the frequencies that make it up.
- 4If s(t) is real, its Fourier transform S(f) satisfies...S(f)=S*(−f) where S* is the complex conjugate of S.
- 5How does a time delay effect the Fourier transform of a signal?
- 6How does a frequency delay effect the inverse Fourier transform of a signal?
- 7Describe the Laplace transformThe Laplace transform maps a function f(t) to a function F(s) of the COMPLEX variable s, where s=σ+jω.
- 8Given a Laplace transform L: f(t) --> F(s) to a function F of the COMPLEX variable s=σ+jω. How do we derive the Fourier transform of f(t)?If we set the real part, σ=0 the result is the Fourier transform F(jω).
NB: only if the formula for the LT of f(t) exists (is non infinite) for σ=0 - 9Laplace TransformWhere s=σ+jω is complex
- 10What does the Laplace transform do?It converts linear differential equations
in t into algebraic equation in s, which provides a method for solving them. - 11Inverse Laplace transform
- 12What conditions must be satisfied in order to apply the Laplace transform?
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- PhD Comms (Maths) Flashcards on Fourier Transforms, created by L H on 15/01/2018.
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- L H
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- Created by L H · Jan 10, 2018
- Copied by L H · Jan 15, 2018
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