Jean Baptiste Joseph Fourier

The Discrete Fourier Transform

La Théorie Analitique de la Chaleur (correct)

The Big Idea

The Analytic Theory of Heat

Functions can only be expressed as a sum of sines of different frequencies

Any function that periodically repeats itself can be expressed as a sum of sines and cosines of different frequencies each multiplied by a different coefficient (correct)

Functions can be expressed as a sum of sines and cosines of the same frequency

Functions can be expressed as a sum of sines and cosines with fixed coefficients

The transformation of a continuous function f(x, y) into the frequency domain

The transformation of a continuous function f(x, y) into the time domain

The transformation of a discrete function f(x, y) into the time domain

The transformation of a discrete function f(x, y) into the frequency domain (correct)

<p>$F(u, v) = \sum_{x=0}^{M-1} \sum_{y=0}^{N-1} f(x, y)e^{-j2\pi(ux/M + vy/N)}$</p> Signup and view all the answers

<p>We get closer and closer to the original function as we add more and more frequencies</p> Signup and view all the answers