User:David R. Keller/Sandbox

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Distributions[edit]

Signal Fourier transform
unitary, angular frequency
Fourier transform
unitary, ordinary frequency
Remarks




301 denotes the Dirac delta distribution.
302 Dual of rule 301.
303 This follows from and 103 and 301.
304 Follows from rules 101 and 303 using Euler's formula:
305 Also from 101 and 303 using
306 Here, is a natural number. is the -th distribution derivative of the Dirac delta. This rule follows from rules 107 and 302. Combining this rule with 1, we can transform all polynomials.
307 Here is the sign function; note that this is consistent with rules 107 and 302.
308 Generalization of rule 307.
309 The dual of rule 307.
310 Here is the Heaviside unit step function; this follows from rules 101 and 309.
311 is the Heaviside unit step function and .
312 The Dirac comb — helpful for explaining or understanding the transition from continuous to discrete time.