log10Signal

Log10signal is a representation used in signal processing that denotes the base-10 logarithm of a signal’s magnitude. It is commonly applied to time-domain or frequency-domain data to compress large dynamic ranges and to emphasize relative changes on a logarithmic scale. In practice, a small positive offset is often added to the magnitude before taking the logarithm to avoid undefined values at zero.

Mathematically, for a real-valued time signal x(t) or its samples x[n], one computes the magnitude m[n] = |x[n]| and then forms L[n] = log10(m[n] + ε), where ε is a small constant. For complex signals or frequency-domain representations, such as a spectrum X(f) with magnitude M(f) = |X(f)|, the corresponding log10signal is L(f) = log10(M(f) + ε). This transformation preserves the order of positive magnitudes but loses phase information.

Relation to decibel scales is common but distinct. The standard amplitude in decibels is A_dB = 20 log10(|x|), so log10signal equals A_dB divided by 20 for amplitude representations. For power, P_dB = 10 log10(P). Thus log10signal provides a logarithmic, magnitude-based view that is related to decibel scales but is not itself a conventional decibel measure.

Applications include visualization of signals and spectrums (for example, log-m magnitude spectrograms), dynamic-range compression in analysis, and preprocessing for machine learning where log-scaled inputs can stabilize variance. Limitations include loss of phase information and sensitivity to the chosen ε, which can affect low-magnitude values. See also decibel scale and log-scale concepts.