Electric signal
The musical instrument disturbs the air and generates an alternating pressure (sound pressure) which is converted into an electrical signal. The amplitude of the signal will change over time. This change relationship indicates that a trajectory of amplitude change with time will be generated on a rectangular coordinate with a linear scale on the amplitude vertical axis and the horizontal time axis.

A line can be divided into an infinite number of the line segments. In each segment, there are an infinite number of points Any point on the line segment and the trend of this point extending to the next point constitute an infinitesimal line segment.

Any infinitesimal line segment on the track of the music electrical signal can be represented by a sine wave of a certain frequency and represents a frequency component.

Technically, we use sine waves to interpret electrical music signals. This is because the sine wave has only a single frequency component on the spectrogram and can be regarded as the purest signal. In this way, we can more conveniently follow the trajectory guided by the theory of electronic technology and accept the specifications of various laws in various aspects such as equipment design and analysis.

However, music information involves both the time domain and the frequency domain. The frequency and amplitude of music sounds will change over time. In music electrical signals, the appearance of a certain frequency component does not necessarily continue to the end of the entire sine wave fluctuation cycle (360 degrees). In other words, every time the frequency components appear in the music electrical signal, they are not always in the unit of the entire sine wave fluctuation period.

Spectrum
Frequency component: Any infinitesimal line segment on the track of the music electrical signal can be represented by a sine wave of a certain frequency and represents a frequency component.

A time axis can be divided into infinite time periods. Each period contains an infinite number of time points.

• At each point in time, there is always a frequency component.
• In each period, there is always one or more frequency components.
• For each specific period, there is always a corresponding frequency spectrum.

Spectrum in a specific period:
In any period on the time axis, there is always a corresponding piece of music signal track. All frequency components corresponding to any segment of the music signal track constitute a specific time period spectrum corresponding to this time period.

Time-frequency information spectrum:
the frequency spectrum of each period arranged on the time axis, and the amplitude of each frequency component of them is superimposed and accumulated with the previous period spectrum in time sequence. This process constitutes a three-dimensional time-frequency information spectrum in which the amplitude of each frequency component changes with time.

Instantaneous frequency spectrum: the time-frequency information spectrum cutting surface at a specific time point on the time axis, which represents the instantaneous frequency spectrum of a music time-frequency information at that time point.

At any point on the time axis, where there is always a corresponding instantaneous frequency spectrum of music time-frequency information.

Created by Chen

Last revision date: Aug-2019