


Advanced Data Processing 

Fourier Transforms 





Transforms 

Time è Frequency 

Inverse Transform 

Frequency è Time 

Uses 

Filtering signals 

Looking for periodic information 





Work on vector of data 

Assume evenly spaced 

fft() 

needs 2^{n} data points 

Produces 2^{n1} complex points in
frequency domain with phase and amplitude information 





Output of fft() 

Vector of frequency components 

Df =
1/duration 





Take fft() of signal 

Manipulate transformed signal 

Take inverse of manipulated signal 







2 different techniques 

Frequency Domain Filter 

Allow certain range of frequencies 

Principle Component Filter 

Only allow components > given amplitude 




Make Vector of filter 





Apply and take inverse fft() 




Only take components > cut off value 

