Discrete Fourier Transform by Hand

Prof. Tom Yeh demonstrates that the Discrete Fourier Transform (DFT), despite involving complex mathematical notation, is fundamentally a series of matrix multiplications that can be calculated by hand. The exercise shows how DFT converts signals between frequency and time domains—contrasting with neural networks like U-Net that learn filters from data, while DFT uses fixed, hand-designed transforms to analyze signals as combinations of cosine waves.