Full scale


In electronics and signal processing, full scale or full code represents the maximum amplitude a system can represent.
In digital systems, 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.
In analog systems, full scale may be defined by the maximum voltage available, or the maximum deflection or indication of an analog instrument such as a moving coil meter or galvanometer.

Binary represenation

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.
Signal processing in digital audio workstations often uses floating-point arithmetic, which can include values past full-scale, to avoid clipping in intermediate processing stages. In a floating-point 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. In the analog domain there is no peak/clipping problem unless the d/a analog circuitry was badly designed. In the digital domain there are no peaks created by these conversions.
If a proper 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.