====== Prednaska 2 -Fourier transform ======

==== Fourier transform ====
time{t} -> frequency
  * diracuv impuls
  * jednotkovy skok

== square ==
  * 1(x+k)-1(x-k) <=> 1/pi*u sin (2piku) \\
  * vypocet fourier - sinc [[http://en.wikipedia.org/wiki/Sinc_function]] \\

=== Linearita ===
<m>af(x)+bf(x) doubleleftright aF(u)+bF(u)</m>

=== Praselval's theorem (Parsevalova rovnost) ===

=== Convolution theorem (Konvolucni teorem) ===

=== Shift theorem (Posunuti v obraze) === 


==== Fourier transform 2D ====
position{x,y} <==> frequency & orientation{u,v}
<m>Omicron(N^4)</m>

==== Fast Fourier transform ====
<m>Omicron(N^2log N)</m>

==== Samling theorem (Vzorkovaci teorem) ====
Nyquist frequency: <m>f_max <= 1/2delta</m>