Sound exists in the physical world as changes in air pressure. A vibrating object creates these pressure changes, which travel through the air. ```text Physical vibration ↓ Air pressure changes ↓ Sound wave ↓ Eardrum ↓ Hearing ``` The physical sound wave is continuous. But computers work with digital data. A computer needs sound to be represented using numbers. ``` Physical Sound ↓ Analog Signal ↓ Measurements ↓ Numbers ↓ Digital Audio ``` So the central question is: How can a continuous sound wave be represented using discrete numbers? # Continuous Sound A continuous signal changes continuously over time. For example, a simplified sound waveform might look like: Amplitude ↑ | | /\ | / \ | / \ ---|-----/------\------→ Time | / \ | / \ The important idea is that the waveform exists continuously. There is a value at every moment in time. Conceptually: Time ────────────────────────────→ There are no gaps between one point and another. Physical sound is continuous. # Sound as an Analog Signal Before sound enters a computer, it can be represented as an analog electrical signal. A microphone converts changes in air pressure into changes in electrical voltage. ``` Sound ↓ Microphone ↓ Electrical signal ↓ Analog waveform ``` The electrical signal follows the changing sound. At this stage, the signal is still continuous. ``` Sound ↓ Continuous physical waveform ↓ Continuous analog electrical signal ``` # From Continuous to Discrete A computer cannot normally store the continuous waveform directly. Instead, it takes measurements of the waveform. Continuous waveform /\ / \ / \ ----/------\--------- / \ / \ Measurements • • • ----•------•--------- • • Each measurement gives us a value for the amplitude. ``` For example: 0.12 0.25 0.41 0.52 0.48 0.31 0.10 -0.15 ... ``` These numbers represent the amplitude of the sound at particular moments in time. This is the basic idea behind digital audio. Digital audio represents a sound waveform using numerical measurements. # Continuous vs. Discrete | Characteristic | Continuous | Discrete | |---|---|---| | **Time** | Continuous | Specific measurement points | | **Amplitude** | Continuous range | Numerical values | | **Representation** | Waveform | Samples / numbers | | **Example** | Analog signal | Digital audio | | **Computer processing** | Analog circuits | Numerical processing | A simple way to remember the difference: **CONTINUOUS** : The signal exists continuously. **DISCRETE** : The signal is represented at specific points. # From Sound to Digital Audio A simplified recording system looks like this: ``` Sound ↓ Microphone ↓ Analog electrical signal ↓ A/D Converter ↓ Digital audio ↓ Numbers ↓ Computer ``` The important transition is: ``` CONTINUOUS ↓ Measurements ↓ DISCRETE ↓ Numbers ``` The device that performs the analog-to-digital conversion is called an: **ADC** — Analog-to-Digital Converter Conceptually: ``` Analog signal ↓ ADC ↓ Digital numbers ``` # Sampling Now we arrive at an important question. When should the computer take those measurements? The process of measuring a signal at specific points in time is called Sampling. For example: Continuous waveform /\ / \ / \ ----/------\--------- / \ / \ Sampling points • • • ----•------•--------- • • The computer takes measurements at regular intervals. Each measurement becomes a sample. ``` Sample 1 → 0.12 Sample 2 → 0.25 Sample 3 → 0.41 Sample 4 → 0.52 Sample 5 → 0.48 ... ``` So, a sample is a measurement of the signal at a particular point in time. # Sample Rate The number of samples taken per second is called the **sample rate**. For example: ``` 44.1 kHz ↓ 44,100 samples per second ``` Another common sample rate is: ``` 48 kHz ↓ 48,000 samples per second ``` Conceptually: ``` Lower sample rate • • • • Higher sample rate • • • • • • • • • • ``` A higher sample rate means that the system takes more measurements per second. **Sample rate** tells us how frequently the signal is measured. By the way, what numerical value do we assign to each measurement? This leads to another important concept called **quantization**. Quantization assigns each sample a numerical value that represents the signal's **amplitude**, or its instantaneous level. Conceptually: ``` Continuous sound ↓ Sampling ↓ Discrete time ↓ Quantization ↓ Discrete numerical values ```