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Since binary integer representation range is asymmetrical, full scale is defined using the maximum positive value that can be represented. [1] [2] 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.
Best rational approximants for π (green circle), e (blue diamond), ϕ (pink oblong), (√3)/2 (grey hexagon), 1/√2 (red octagon) and 1/√3 (orange triangle) calculated from their continued fraction expansions, plotted as slopes y/x with errors from their true values (black dashes)
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
The red lines indicate full scale, and the waveform is shown before and after hard clipping (grey and black outlines respectively). Decibels relative to full scale ( dBFS or dB FS ) is a unit of measurement for amplitude levels in digital systems, such as pulse-code modulation (PCM), which have a defined maximum peak level.
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale.. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation.
The most common test signals that fulfill this are full amplitude triangle waves and sawtooth waves. For example, a 16-bit ADC has a maximum signal-to-quantization-noise ratio of 6.02 × 16 = 96.3 dB. When the input signal is a full-amplitude sine wave the distribution of the signal is no longer uniform, and the corresponding equation is instead
In contrast to the mean absolute percentage error, SMAPE has both a lower and an upper bound. Indeed, the formula above provides a result between 0% and 200%. Indeed, the formula above provides a result between 0% and 200%.