Discrete Signals

Fourier Analysis · Axiom Academy

From the continuous analog world to the digital realm of computers Look around you - your phone, computer, smartwatch, and digital camera all process signals. But there's a fundamental truth about digital devices... Click any device to explore how it works with numbers Let's visualize the difference. Click the buttons below to switch between a continuous analog signal and its discrete digital representation. Use the slider to control how many samples we take per second. Watch how the quality of our discrete representation changes! The Language of Discrete Signals Just as continuous signals use different notation, discrete signals have their own mathematical language. Parentheses () indicate continuous time Square brackets [] indicate discrete samples Example: If we sample a 5 Hz sine wave at 20 samples/second, then where n = 0, 1, 2, 3, ... By converting continuous signals to sequences of numbers, we unlock the power of computers to analyze, modify, and transmit information with perfect accuracy and incredible speed. Just as we used Fourier series and transforms to analyze continuous signals, we need new tools for discrete signals: the Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) . These are the algorithms behind spectrograms, audio compression, and frequency analysis on computers.

This is the written version of the interactive lesson above. See the full Fourier Analysis course.