Discrete Fourier Transform by Hand: Unraveling the Math Behind Signal Processing

The Discrete Fourier Transform (DFT) is a cornerstone of signal processing, but its complex mathematical formulation often obscures its simplicity. This hands-on exercise reveals that DFT is essentially a series of matrix multiplications, making it accessible to compute by hand. By comparing DFT with learned transforms in neural networks, the article highlights how both can process signals effectively. It walks through inverse DFT to convert frequency-domain signals to time domain and then demonstrates DFT's ability to recover the original frequency components, demystifying the process step by step.