Fundamental Concepts
Acoustics
periodic acoustic waveform – airs pressure varying with a repeated pattern
cycle – one repetition of a waveform
frequency – number of cycles per second of wave traveling through the air, measured in hertz
fundamental frequency – lowest frequency in a periodic waveform
overtone series – naturally occurring acoustic phenomenon of frequencies in whole number ratios above a sounded fundamental, first eight partials of the harmonic series:
intervals – relationship between two fundamental frequency
cents – logarithmic unit of measurement (converts from the linear scale of frequency in a scale related to the way that frequency is perceived), conversion from frequency ratios to cents (where R is the decimal equivalent of the ratio)
cents = log R x 1200/log 2
log R = cents / 1200/log 2
Example: log 3/2 x 1200/log 2; log 1.5 X 1200/log 2; 701.995 (Perfect Fifth)
range of human hearing for pitch – 20-20,000 Hz (below 0–20 Hz heard as rhythm; above 20,000 Hz imperceptible; upper range decreases as people ago)
phase – starting point is initial phase, measured in degrees across the entire cycle: measured by radians (360 degrees = 2pi)
amplitude – amount of air pressure change
decibels – relative unit of measurement of power: # of decibels = 10 x log10(level/reference level)
Digital Conversion
analog-to-digital converter – quantization of acoustic signal to binary values
sampling rate – number of times an analog signal is measured per second
nyquist frequency – half of the sampling rate
alisaing/foldover – if the original frequency > 1/2 sampling frequency: new frequency = sampling frequency-original frequency
Image from: http://people.cs.clemson.edu/~tadavis/cs809/aa/aliasing3.gif
lowpass anti-aliasing filter – used to ensure that there are not any frequencies above the nyquist frequency
bit depth – number of bits used to describe the amplitude: lower bit rate creates a greater quantization of amplitude values
Image from: http://en.wikipedia.org/wiki/Audio_bit_depth#mediaviewer/File:4-bit-linear-PCM.svg