# Full Scale - Electronics and Signal Processing

Electronics and Signal Processing

In digital systems, a signal is said to be at digital full scale when it has reached the maximum (or minimum) representable value. In an unsigned fixed point binary representation, this occurs when all bits are 1s, but this is a simplified analysis. Full scale also occurs when the minimum value (or maximum rarefaction amplitude) is reached, which would be represented as all 0s. Further, many digital systems use other digital encoding methods, such as two's complement wherein all 1s or all 0s actually occur around the zero crossing, and the maximum and minimum values are not as simply described.

Once a signal has reached digital full scale all headroom has been utilized, and any further increase in amplitude results 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.