Target Signal f^T(t)
f^T(t)=NΣn=1 Acos(nwt)
f1+f2+f3+f4
Periodic function => a weigted sum of sines and cosines of different frequencies
transform f(t) it a F(w)
frequency spectrum of the function f
a reversible operation
For every w from – to ∞(infinity) F(w) holds the amplitude A and phase a sine function
Frequency Domain of a signal
g(t)= sin(2pwt) + 1/3sin(2p(3w)t)
Convolution Theorem and the Fourier Transform
Fourier transform of a convolution of two functions = product of their fourier transforms
F[g * h] = F[g]F[h]
F^-1[gh] = F^-1[g]*F-1[h]
Using the Frequency spectra
low-pass, high-pass, band-pass filtering
