Full scale
Encyclopedia
In electronics and signal processing, full scale or full code represents the maximum amplitude a system can present.
fixed point
binary representation, this occurs when all bit
s 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 to floating point software instead of using binary. 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.
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 unsignedUnsigned
Unsigned can refer to:* An unsigned artist is a musical artist or group not attached or signed to a record label* Similarly, the contractual condition of any personnel, property or domains....
fixed point
Fixed-point arithmetic
In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the radix point...
binary representation, this occurs when all bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
s are 1s, but this is a simplified analysis. Full scale also occurs when the minimum value (or maximum rarefaction
Rarefaction
Rarefaction is the reduction of a medium's density, or the opposite of compression.A natural example of this is as a phase in a sound wave or phonon. Half of a sound wave is made up of the compression of the medium, and the other half is the decompression or rarefaction of the medium.Another...
amplitude) is reached, which would be represented as all 0s. Further, many digital systems use other digital encoding methods, such as two's complement
Two's complement
The two's complement of a binary number is defined as the value obtained by subtracting the number from a large power of two...
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
Clipping
-Words:* Clipping , the cutting-out of articles from a paper publication* Clipping , shortening the articulation of a speech sound, usually a vowel* Clipping , the formation of a new word by shortening it, e.g...
. However, this can be avoided if a DAW switches to floating point software instead of using binary. 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
Anti-aliasing filter
An anti-aliasing filter is a filter used before a signal sampler, to restrict the bandwidth of a signal to approximately satisfy the sampling theorem....
, resampling
Sample rate conversion
Sample rate conversion is the process of converting a signal from one sampling rate to another, while changing the information carried by the signal as little as possible...
, or reconstruction filter
Reconstruction filter
In a mixed-signal system , a reconstruction filter is used to construct a smooth analogue signal from a digital input, as in the case of a digital to analogue converter or other sampled data output device....
, which may increase peak amplitude slightly due to the Gibbs phenomenon
Gibbs phenomenon
In mathematics, the Gibbs phenomenon, named after the American physicist J. Willard Gibbs, is the peculiar manner in which the Fourier series of a piecewise continuously differentiable periodic function behaves at a jump discontinuity: the nth partial sum of the Fourier series has large...
(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
Galvanometer
A galvanometer is a type of ammeter: an instrument for detecting and measuring electric current. It is an analog electromechanical transducer that produces a rotary deflection of some type of pointer in response to electric current flowing through its coil in a magnetic field. .Galvanometers were...
.
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.