impulse train

Work in Progress

Summary

DFT pairs

CTFT of impulse train

impulse train <-> impulse train

Concept

Single impulse

kronecker delta
a linear map

Shifted impulse

Train of impulses

periodic - impulse every period

DFT of impulse train

is an impulse train in the other domain
smaller sampling time -> larger sampling frequency

DFT pairs

Signal to shifted impulse

this is how frequencies can be isolated

Impulse

Constant

Application

DFT pair for sine and cosine

using complex exponential

reflects the even & odd nature of cosine and sine

CTFT of impulse train
TODO

there is one more step that i dont yet understand

Extra

TODO
Impulse train