(lecture 7) Digitizing Sound: From Analog to Digital Conversion to Timbre

Analog to Digital Conversion of Sound

Analog vs. Digital Sound

• Analog Sound: Refers to sound waves traveling through the air as compressions and rarefactions. This is the physical reality of sound.

• Digital Sound: The conversion of analog sound into a series of numbers that a computer can read and process.

• Analog-to-Digital Conversion (ADC): The process of transforming analog sound into its digital counterpart. This conversion is typically initiated by a microphone, which detects air pressure changes (analog) and converts them into an electrical signal, which is then digitized.

  • Historical Context: In earlier times, oscilloscopes visually represented air pressure variations as continuous lines on a graph. Post-World War II, efforts intensified to digitize sound and develop computational equations for computer coding.

Quantifying Sound: Sampling Rate and Bit Depth

Harry Nyquist and the Nyquist Theorem

• Harry Nyquist: A Swedish physicist who worked at Bell Labs from the late 1800s to the mid-1900s. He pioneered modern sound recording, and his theorem and algorithms form the basis for most contemporary recordings.

• Purpose: Nyquist's work addressed how often air pressure changes must be measured (sampled) to accurately convert and replicate analog sound into a digital format.

• Human Hearing Range: Humans can typically hear frequencies from $20 ext{ Hz}$ to $20,000 ext{ Hz}$. High frequencies, like the shimmer of a cymbal or complex orchestral sounds, extend up to $20,000 ext{ Hz}$.

• Nyquist Theorem: States that the sampling rate must be at least double the highest frequency of interest in the sound to be accurately represented digitally without confusion with other frequencies.

  • Formula: $\text{Sampling Rate} = 2 \times \text{Highest Frequency of Interest}$.

  • Example: For the human hearing range, which extends to $20,000 ext{ Hz}$, the required sampling rate would be $2 \times 20,000 ext{ Hz} = 40,000 ext{ Hz}$. To ensure full coverage, a standard sampling rate of $44,100$ times per second is commonly used, which adequately captures all frequencies up to $20,000 ext{ Hz}$.

  • Implication: If the sampling rate is too low, the digital representation can be confused with other frequencies, leading to inaccurate reconstruction of the sound.

• Sampling Rate Definition: How often (per second) air pressure changes are measured and stored in a computer.

  • Visual Representation: Imagine a sine wave (compressions and rarefactions). Sampling involves taking discrete measurements (represented as 'x's) at specific points in time. The computer only has these numerical values, losing information between the sampling points.

  • Software Application: Programs like Praat allow users to set the sampling rate. For instance, if only interested in frequencies up to $5,000 ext{ Hz}$ (common for speech analysis), a sampling rate of $10,000 ext{ Hz}$ would suffice ($2 \times 5,000 ext{ Hz}$). Research papers reporting acoustic data typically specify their sampling rate and frequency range.

Bit Depth

• Definition: Bit depth determines the maximum dynamic range of an audio file, essentially how many amplitude levels can be assigned to each sample point.

• Function: It creates an arbitrary scale (e.g., in decibels) to quantify the pressure variation at each measured sample.

• Common Bit Depths and Dynamic Range:

  • $16 ext{ bit}$: Provides a dynamic range of over $90 ext{ dB}$ (specifically, $96 ext{ dB}$). This is generally sufficient for most speech and music recordings, covering approximately $99.9\%$ of measurable sound intensity.

  • $24 ext{ bit}$: Offers a wider dynamic range than $16 ext{ bit}$.

  • $32 ext{ bit}$: Considered