Digital Sound, ADC/DAC and MIDI

An analogue signal varies continuously in the model; a digital representation uses discrete encoded values. An ADC measures a signal at selected times and quantises each measurement to an available amplitude level. Sampling rate counts samples per second, while sample resolution or bit depth determines available amplitude codes.

A DAC converts numerical sample values into a corresponding analogue output signal, normally followed by appropriate reconstruction filtering. Greater bit depth reduces quantisation step size for a fixed amplitude range. Greater sample rate supports a wider band of frequencies; it is not the same as increasing amplitude precision.

The Nyquist sampling principle concerns a band-limited signal: sampling must be at least twice its highest frequency in the ideal model, with practical systems using suitable filtering and margin. Inadequate sampling can cause aliasing, making different original frequencies indistinguishable in the samples.

Raw audio bits=sample rate×bit depth×duration×channels. Stereo normally has two channels under this model. Divide by eight for bytes and state whether headers or compression are excluded. A higher sample rate increases raw storage even when the actual sound contains little high-frequency content.

MIDI represents events such as note-on, note-off, pitch, timing and control changes, rather than directly sampling the resulting sound waveform. A synthesiser or instrument interprets those events. Compact event files can be easy to edit or transpose, but reproduction depends on the sound source and configuration.

MIDI is not a general substitute for recording speech or every arbitrary acoustic detail. A recorded performance waveform preserves different information from an instruction to play a note. Compare the representation’s purpose and required playback system rather than stating that one always has universally better sound.

Attempt the task before opening its worked response. Record each change of state, explain the rule used, and check the result against the original requirements. Code examples labelled Python 3 use that language’s conventions; pseudocode states its own assumptions.