Discrete Fourier Transform (DFT)

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Presentation transcript:

Discrete Fourier Transform (DFT) Because every piece of data ever collected in any lab is discrete

Cool Fourier Animations! Basic idea of Fourier Analysis https://www.youtube.com/watch?v=ZRZIz81nXo4 https://phet.colorado.edu/en/simulation/fourier https://www.youtube.com/watch?v=LznjC4Lo7lE Trippy animation! https://www.youtube.com/watch?v=cUD1gMAl6W4 Cool Fourier Animations!

Continuous Function vs. Discrete Sampling Image credit: http://www.sp4comm.org/webversion/livre.html

Continuous vs Discrete 2T periodic Discrete x(k) k Continuous vs Discrete Image credit: https://flylib.com/books/en/2.729.1/discrete_sequences_and_their_notation.html

f(t) = continuous time signal f(k) = discrete time signal k = integer time index ts = sampling period fs = 1/ts = sampling frequency 2T = fundamental period of f(t) N = number of samples to complete 1 oscillation at fundamental period 2T = Nts n = harmonic number Definitions for DFT

Nyquist Frequency Image credit: http://zone.ni.com/reference/de-XX/help/371361H-0113/lvanlsconcepts/aliasing/