How Digital Signal Processing Turns Sound Waves Into Numbers—and Back

A violinist plays an A above middle C, vibrating the string exactly 440 times per second. A microphone converts that vibrating air pressure into a wobbling electrical voltage. But a computer cannot store a smooth, continuously wobbling voltage — it can only store numbers. To record that note digitally, a converter has to measure the voltage 44,100 times every single second and write down each measurement as a number. That process, called sampling, is the foundation of every streamed song, podcast, and video call you have ever heard.

By the end of this lesson, you will be able to: - Explain what an analog-to-digital converter does to a sound wave - State the Nyquist-Shannon sampling rule and explain why 44.1kHz is used for CD-quality audio - Describe what bit depth measures and compare 16-bit to 24-bit audio - Calculate the amount of data a short digital audio recording actually requires

Sound is a pressure wave — molecules of air bumping into each other in a pattern that repeats. A microphone's diaphragm physically moves back and forth with that pressure wave, and a magnet-and-coil or capacitor system inside converts that motion into a matching electrical voltage. At this stage, the signal is analog: it can take any value at any instant, just like the sound wave it represents. Digital signal processing exists because computers cannot work with any value at any instant — they need discrete, countable numbers.

An analog-to-digital converter (ADC) measures, or samples, the incoming voltage at a fixed rate, called the sample rate, measured in Hertz (Hz) or kilohertz (kHz). CD-quality audio uses a sample rate of 44,100 samples per second, written 44.1kHz. Video and streaming audio commonly use 48kHz. The choice is not random: in 1928, engineer Harry Nyquist proved that to accurately capture a wave, you must sample at least twice as fast as its highest frequency. Human hearing tops out around 20,000 Hz (20kHz), so a sample rate needs to be at least 40kHz to faithfully capture everything we can hear — 44.1kHz builds in a small safety margin above that minimum.

Sample rate controls how often a sound is measured; bit depth controls how precisely each individual measurement is recorded. CD audio uses 16-bit depth, which allows 65,536 possible loudness values for each sample. Professional studios often record at 24-bit depth, allowing more than 16.7 million possible values — giving engineers far more room to adjust volume later without introducing audible distortion called quantization noise. More bits means a more accurate snapshot of the wave at that instant, the same way a ruler marked in millimeters is more precise than one marked only in centimeters.

44.1kHz became the CD standard in the early 1980s partly because it fit neatly onto the video-based equipment Sony and Philips used to store early digital audio masters. Film and television production largely standardized on 48kHz instead, because it divides evenly into common video frame rates. High-resolution music production sometimes uses 96kHz or even 192kHz, giving engineers extra headroom for processing effects like pitch-shifting before the higher frequencies are filtered back out for final release. None of these higher rates make audio more audible to human ears beyond the Nyquist minimum — they exist mainly to give editing software more data to work with before problems like aliasing can appear.