electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...

and

signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...

, full scale represents the maximum

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...

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 (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 A digital audio workstation (DAW) is an electronic device or application software used for Sound recording and reproduction, recording, editing and producing audio files. DAWs come in a wide variety of configurations from a single software pro ...

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 ...

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 Ringing may mean: Vibrations * Ringing (signal), unwanted oscillation of a signal, leading to ringing artifacts * Vibration of a harmonic oscillator ** Bell ringing * Ringing (telephony), the sound of a telephone bell * Ringing (medicine), a ring ...

. 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 {{electronics-stub