# 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. However, this can be avoided if a DAW switches from integer to floating-point arithmetic. This usually entails some loss of precision although the final precision should still be significantly better than that which is needed for the final music processing.

The signal passes through an anti-aliasing, resampling, or reconstruction filter, which may increase peak amplitude slightly due to the Gibbs phenomenon (The Gibbs Phenomenon is a mathematical concept and only applies to one point so in practice it is irrelevant to real life circuits and devices). 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.

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.

If a proper (no clipping/saturation) analog signal is converted to digital via A/D with sufficient samples, and then reconverted to analog via D/A then 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.)[1]