Digital Audio Basics

Digitization of Sound

• Crucial for multimedia presentations.
• Introduces basic concepts and digitization of sound.
• Explores MIDI for capturing, storing, and playing back musical notes.

Sound

• Wave phenomenon involving air molecule compression and expansion.
• Longitudinal pressure wave.
• Takes on continuous values.
• Requires a medium (e.g., air) to propagate.
• Wave properties: reflection, refraction, diffraction.
• Digital representation: digitized representations of audio information.

Ear Mechanics

• Ear canal amplifies speech frequencies, protects eardrum.
• Middle ear (ossicles: hammer, anvil, stirrup) amplifies vibrations.
• Inner ear (cochlea) transforms vibrations to electrical impulses via hair cells.

Digitization

• Conversion to stream of numbers (integers).
• Analog signal: continuous pressure wave measurement.
• Sound is 1D (amplitude vs. time).

Sampling and Quantization

• Signal must be sampled in time and amplitude.
• Sampling: measuring at evenly-spaced intervals (sampling frequency).
  • Typical audio sampling rates: 8 kHz - 48 kHz (Nyquist theorem).
• Quantization: sampling in amplitude to represent signal as discrete values.

Pitch and Frequency

• Frequency: absolute measure.
• Pitch: perceptual, subjective quality.
  • Linked by setting "A" above middle C to 440 Hz.
  • Octave: doubling the frequency.
• Harmonics: integral multiples of fundamental frequency.

Audio Data Digitization

• Key questions:
  1. Sampling rate?
  2. Quantization fineness and uniformity?
  3. Audio data format (file format)?

Nyquist Theorem

• Sampling rate must be at least twice the maximum frequency content.
• Sampling_rate >= 2 * f_{max}
• Alias frequency: incorrect frequency due to under-sampling.
• Band-limited signal: sampling rate should be at least $2(f<em>2 - f</em>1)$, where $f<em>1$ and $f</em>2$ are the lower and upper frequency limits.

Signal to Noise Ratio (SNR)

• Measure of signal quality.
• Ratio of correct signal power to noise.
• Measured in decibels (dB).
• $SNR<em>{dB} = 10 * log</em>{10}(A<em>{signal}^2 / A</em>{noise}^2)$

Audio Filtering

• Prior to sampling, filters remove unwanted frequencies.
  • Speech: 50Hz to 10kHz (band-pass filter).
  • Music: 20Hz to 20kHz.
• Lowpass filter used after DA conversion to remove high frequencies.

Digital to Analog Conversion

• Methods:
  1. FM (Frequency Modulation)
  2. WaveTable

Frequency Modulation (FM)

• Varying carrier signal frequency with modulating signal.
• Complex signals created by modulating frequencies.
• Uses envelope function $A(t)$ for loudness over time and $I(t)$ for harmonics.

Wave Table Synthesis

• Storing digital samples of real instrument sounds.
• Allows software manipulation: combining, editing, enhancing sounds.
• Better sound reproduction than FM synthesis.

MIDI: Musical Instrument Digital Interface

• Protocol for controlling and communicating between electronic music devices.
• Scripting language coding "events" (pitch, duration, volume).
• Supported by most synthesizers.
• MIDI file: sequence of MIDI instructions (messages).

MIDI Concepts

• Channels: 16 channels (0-15) to separate messages, associated with instruments.
• System messages: general messages for all instruments (tuning, timing).
• Multi-voice instruments: can play multiple notes at once.

General MIDI

• Standard mapping specifying instruments associated with channels.
• Note On message: channel, pitch, velocity (volume).
• Percussion: pitch data indicates drum type.
• Note On message: status byte (channel, pitch), followed by two data bytes.
• Followed by Note Off message (pitch, velocity).
• MIDI status byte: 128-255; data bytes: 0-127.
• Actual MIDI bytes are 10-bit (0 start, 0 stop).
• Programmability: devices can change envelope describing sound amplitude over time.