Fourier series Periodic functions and signals may be expanded into a series of sine and cosine functions http://www.falstad.com/fourier/12/
http://www.falstad.com/fourier/j2/ Fourier series • Periodic functions and signals may be expanded into a series of sine and cosine functions
The Fourier transform a transform takes one function(or signal) and turns it into another function(or signal)
The Fourier Transform • A transform takes one function (or signal) and turns it into another function (or signal)
The Fourier transform a transform takes one function(or signal) and turns it into another function(or signal) Continuous fourier transform close your eyes if you don t like integrals
The Fourier Transform • A transform takes one function (or signal) and turns it into another function (or signal) • Continuous Fourier Transform: close your eyes if you don’t like integrals
The Fourier transform a transform takes one function(or signal) and turns it into another function(or signal) Continuous fourier transform H(= h()e2mdt h()=「H()=2mdf
The Fourier Transform • A transform takes one function (or signal) and turns it into another function (or signal) • Continuous Fourier Transform: ( ) ( ) ( ) ( ) − − − = = h t H f e df H f h t e dt ift ift 2 2
The Fourier transform a transform takes one function(or signal) and turns it into another function(or signal) The discrete Fourier transform Hn=∑he 2mikn/N H 2m//N
• A transform takes one function (or signal) and turns it into another function (or signal) • The Discrete Fourier Transform: The Fourier Transform − = − − = = = 1 0 2 1 0 2 1 N n ikn N k n N k ikn N n k H e N h H h e