Digital Sound Representation

Digital Sound

• A digital sound is a sequence of numeric values representing the amplitude of an original waveform at discrete, evenly spaced points in time.
• It is created by taking repeated measures or samples of voltage amplitude of a continuously varying (analog) signal at a particular sample rate (Fsr).

Digital Representation of Sound

• The precision of digital sound depends on two parameters: sample rate (Fsr) and bit size (bit depth).
• Higher Fsr and bit size result in larger file sizes.
• The higher the sampling rate, the more precisely the digitized sound represents temporal changes in the amplitude of the original sound.

Sample Rate and Nyquist Frequency

• Sample rate must be more than twice as high as the highest frequency (Nyquist frequency) contained in the signal.
• Typical sampling rate of recorders is 44 kHz, where the Nyquist frequency is 22 kHz.
• Nyquist Frequency (NF) is equal to half the frequency at which the signal was digitized (sample rate, Fsr) - NF = ½ Fsr.

Bit Size

• The precision of a sample depends on the sample bit size or bit depth.
• An 8-bit sample can resolve 256 different amplitude values; a 16-bit converter can resolve 65,536 values.
• 16-bit is the minimum value for bioacoustic research.

Digital Audio Formats

• There are three types of digital audio formats: uncompressed, lossless compression, and lossy compression.
• Uncompressed audio file formats store both sound and silence, have large file sizes, and are suitable for storing and archiving original recordings and acoustic research.
• Examples of uncompressed formats: WAV, AIFF, PCM, RAW, AU.

Lossless Compression Audio Formats

• Lossless compression audio formats compress audio files without losing quality, have smaller sizes, and are suitable for acoustic research.
• Examples of lossless compression formats: FLAC, ALAC, APE, M4A.

Lossy Compression Audio File Formats

• Lossy compression audio file formats compress audio files by removing some of the sound data, resulting in small file sizes, but are not suitable for storing original sounds or acoustic research.
• Examples of lossy compression formats: MP3, MP4, WMA, 3GP, OGG, OGA, AT3.

The Fast-Fourier-Transformation (FFT)

• The FFT is an equation that takes sample inputs and outputs their respective frequency components.
• It requires a fixed number of sample inputs (FFT size or sample size) to perform Fourier calculations.
• FFT is used to plot power spectrum and spectrogram and allows frequency-related parameters of the sound to be measured.
• The frequency and time resolution of spectra or spectrogram is dictated by the Heisenberg Uncertainty Principle.

Learn about digital sound, its representation, and the parameters that affect its precision. Understand how analog signals are converted to digital samples and the importance of sample rate and amplitude.