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snickersnee
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Homework Statement
How can I figure out the Fourier transform of the following:
I'd prefer to use tables if at all possible.
1. [itex]d(z)=d_{eff}sign[\cos[2\pi z]/\Lambda])[/itex]
(note this is one function inside another one.)
2. [itex]d(z)=d_{eff}(1/2)(sign[\cos[2\pi z]/\Lambda]+1)[/itex]
3. [itex]d(z)=d_{eff}\frac{1}{2}a\{u(z)-u(z-\frac{\Lambda}{2})\}+\frac{1}{2}b\{u(z-\frac{\Lambda}{2}))-u(z-\Lambda)\}[/itex]
d_eff, a, b and Lambda (the period) are constants. u(z) is the step function. (I'm using it to model a square wave)
Homework Equations
See above
The Attempt at a Solution
I took this class a long time ago. There were some kind of rules about what to do if a constant is added, or multiplied by a constant, or if functions are nested, please refresh my memory. For example, if two functions are added in time domain, does that also mean they are added in frequency domain?
FT of step function is this: [itex]\sum_{n\ odd}\frac{4}{n\pi}e^{iwt}-e^{-iwt}[/itex]
FT of signum function: 1/(pi*i*f)
I need the exponential form but I can convert.
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