A sound wave is the result of compressed air pressure propagating away from its source of compression. It can be displayed as amplitude (as the size of vibration) against time:
 
 







Amplitude (measured in dB, vertical axis) as a function of time (horizontal)

(adapted from: http://sprg.ssl.berkeley.edu/marsmic/HTML/lr/spec1.html#spectrogram)



 

• Frequency, i.e. the times a sound wave crosses zero vertically. Frequency is expressed in Hz, i.e. how many times per second a sound wave travels from its starting point to the plus-peak, down to the minus-peak and up to its zero-crossing. A range like this consists of 360°, which means that it could be displayed in a circle.

• Phase, i.e. the angle of rotation of a periodic signal value, measured in degrees (0 ... 360°) or in radians (0 ... 2p , i.e. 0 ... 6.282...)
• Phase shift: Most waveforms are not sinusoidal but can analysed as the sum of two or more sine waves. Usually their phases then have different starting points, the difference between which can be called their phase shift.

What are simple sound waves?

 
Simple signals consist of one sine wave only and they can be calculated by the formula:


f
 
 

 
According to Fourier's Theorem complex signals can be represented as the point by point sum of a possibly infinite number of sinusoid signals:
 
 

x_n = c + m₁ ( sin (t₁ + Q₁) + c + m_n ( sin (t_n + j _n))
 

 
The sampling frequency determines the limit of audio frequencies that can be reproduced digitally. One of the most important rules of sampling is called the Nyquist Theorem (or sampling theorem), which states that the highest frequency which can be accurately represented is one-half of the sampling rate. The Nyquist frequency for a given signal is twice the frequency of the highest frequency component in the signal.

In other words, there must be at least 2 measurements within one phase. If not, an aliasing effect occurs, which leads to the distortion of the frequencies in the signal, by introducing spurious low frequency artefacts corresponding to the difference between the sampling frequency and the signal frequency. In the visual domain this corresponds to the moiré effect with silk, some types of patterning on television screens, wheels turning backwards in films.
 
 

 
A spectrum is a function of frequency, often expressed in Pa/Hz (if from a sound). In a spectrum amplitude (loudness) is displayed as a function of frequency (cf. fig. 3). A spectrum is also called 2D-spectrogram. From the point of view of time a spectrum is a snapshot of amplitudes relating to the frequencies they occur at.
 

 
A spectrum is a function of frequency, often expressed in Pa/Hz (if from a sound). In a spectrum amplitude (loudness) is displayed as a function of frequency:
 
 






fig. 3: a spectrum

(source: http://sprg.ssl.berkeley.edu/marsmic/HTML/lr/spec1.html#spectrogram)

 
A 3D-spectrogram is also called sonagramme and it displays the features amplitude, frequency and time in one diagram. Frequency (Hz) is displayed as a function of time (ms). Amplitude comes into play by the use of colour (therefore these types of spectrograms are also called colour spectrograms).
 
 





fig. 4: a colour spectrogram


 

 
Pitch is the perceptual correlate of the frequency of vibration of the vocal folds. The frequency is determined by sub-glottal pressure and by laryngeal adjustments governing the length, tension and mass of the vocal of the folds themselves. Pitch lowering is associated with reduced tension in the vocal folds. Pitch is largely determined by the fundamental frequency of the sound, but the relationship between pitch and fundamental frequency is non-linear and varies with the frequency involved. Pitch is measured in cycles per second (cps). Pitch and frequency have a subtle difference and are often used interchangeable. However, they describe changes in air pressure. Scientists tend to use the word "frequency", musicians rather say "pitch".
 

 
Fundamental frequency (F0) is defined as the lowest frequency of the sine waves composing a complex sine wave. The two higher frequency components are the second and third harmonics, the fundamental frequency is also called first harmonic.
 

Signal annotation describes the process of assigning properties like orthographic letters, phonemes or break indices to sound signals.