In
electronics and
signal processing, full scale represents the maximum
amplitude a system can represent.
In
digital system
Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics and analog signals.
Digital electronic circuits are usually ...
s, a signal is said to be at digital full scale when its magnitude has reached the maximum representable value. Once a signal has reached digital full scale, all
headroom has been utilized, and any further increase in amplitude will result in an error known as
clipping. The amplitude of a digital signal can be represented in percent, full scale, or
decibels, full scale (dBFS).
In analog systems, full scale may be defined by the maximum voltage available, or the maximum deflection (full scale deflection or FSD) or indication of an analog instrument such as a moving coil meter or
galvanometer.
Binary representation
Since
binary integer representation range is asymmetrical, full scale is defined using the maximum positive value that can be represented. For example,
16-bit PCM audio is centered on the value 0, and can contain values from −32,768 to +32,767. A signal is at full-scale if it reaches from −32,767 to +32,767. (This means that −32,768, the lowest possible value, slightly ''exceeds'' full-scale.)
Signal processing in
digital audio workstations often uses
floating-point arithmetic
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...
, which can include values past full-scale, to avoid clipping in intermediate processing stages. In a
floating-point
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can b ...
representation, a full-scale signal is typically defined to reach from −1.0 to +1.0.
Processing
The signal passes through an
anti-aliasing,
resampling, or
reconstruction filter, which may increase peak amplitude slightly due to
ringing.
It is possible for the ''analog'' signal ''represented by'' the digital data to exceed digital full scale even if the digital data does not, and vice versa. Converting to the analog domain, there is no clipping problem as long as the
D/A analog circuitry is well designed. In the digital domain, there are no peaks created by these conversions.
If a full-scale analog signal is converted to digital via
A/D with sufficient samples, and then reconverted to analog via
D/A, the
Nyquist theorem guarantees that there will be no problem in the analog domain due to "peak" issues because the restored analog signal will be an exact copy of the original analog signal. (However, if the signal is
normalized in the digital domain, it may contain "intersample peaks" which exceed full scale after analog reconstruction.)
References
Digital signal processing
Digital audio
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