Overview

How does your phone turn your voice into radio waves? How does Spotify compress music? How does an MRI see inside your body? It’s all signal processing.

Core Idea

Fourier Transform: Any complex wave can be broken down into a sum of simple sine waves. It converts a signal from the Time Domain (what happens when) to the Frequency Domain (what pitch is it).

Formal Definition (if applicable)

Nyquist-Shannon Sampling Theorem: To perfectly reconstruct a signal, you must sample it at a rate at least twice its highest frequency. (CDs sample at 44.1 kHz to capture human hearing up to 22 kHz).

Intuition

  • Filter: Sunglasses filter out UV light. Audio filters remove hiss (high frequency) or rumble (low frequency).
  • Compression: Removing parts of the signal humans can’t perceive (MP3, JPEG).

Examples

  • Noise Cancellation: Headphones recording outside noise and playing the inverse wave to cancel it out.
  • Auto-Tune: Pitch correction.
  • Image Processing: Photoshop filters, edge detection in self-driving cars.

Common Misconceptions

  • “Digital is always better.” (Analog vinyl records have infinite resolution, though they have noise. Digital is discrete.)
  • “Zoom and Enhance.” (You can’t create information that isn’t there. CSI lied to you.)
  • DSP (Digital Signal Processor): A specialized chip for math.
  • Convolution: A mathematical operation used in filtering and reverb.
  • Modulation: Encoding information onto a carrier wave (AM/FM radio).

Applications

  • Telecommunications: 5G, Wi-Fi.
  • Audio/Video: Streaming, recording.
  • Medical Imaging: CT scans, Ultrasound.

Criticism / Limitations

Processing introduces latency (delay). Heavy compression introduces artifacts (blocky video).

Further Reading

  • Oppenheim & Schafer, Discrete-Time Signal Processing
  • Lyons, Understanding Digital Signal Processing