Finished (:D) fig_invariance_log_hp.pdf.

Added movable label string to time_bar().
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j-hartling
2026-03-23 15:38:49 +01:00
parent a276883454
commit dc4443aa17
18 changed files with 389 additions and 247 deletions

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@@ -47,6 +47,12 @@
% \newcommand{\eref}[1]{\mbox{\cref{#1}}}
% \newcommand{\eref}[1]{\mbox{Eq.\,\ref{#1}}}
% Subplot lettering:
\newcommand{\figa}{\textbf{a}}
\newcommand{\figb}{\textbf{b}}
\newcommand{\figc}{\textbf{c}}
\newcommand{\figd}{\textbf{d}}
% Math shorthands - Standard symbols:
\newcommand{\dec}{\log_{10}} % Logarithm base 10
\newcommand{\infint}{\int_{-\infty}^{+\infty}} % Indefinite integral
@@ -625,23 +631,25 @@ the signal for reliable song recognition.
\includegraphics[width=\textwidth]{figures/fig_invariance_log_hp.pdf}
\caption{\textbf{Intensity invariance by logarithmic compression and
adaptation is restricted by the noise floor.}
Envelope $\env(t)$ is transformed into logarihmically
compressed envelope $\db(t)$ and further into
intensity-adapted envelope $\adapt(t)$. Indicated time
scale is $5\,$s for both \textbf{a} and \textbf{b} (black
bars).
\textbf{a}:~Ideally, if $\env(t)$ consists only of song
component $\soc(t)$ rescaled by $\sca$, then $\adapt(t)$
is fully intensity-invariant across all $\sca$.
\textbf{b}:~In practice, $\env(t)$ also contains
fixed-scale noise component $\noc(t)$, which limits the
effective intensity invariance of $\adapt(t)$ to
sufficiently large $\sca$.
\textbf{c}:~Ratios of the SD of each representation in
\textbf{b} at a given $\sca$ relative to the SD of the
representation for $\sca=0$ (solid lines). The same ratios
for the ideal $\adapt(t)$ in \textbf{a} are shown for
comparison (dashed line).
Synthetic input $\filt(t)$ consists of song component
$\soc(t)$ scaled by $\sca$ with (\figc{} and \figd) or
without (\figa{} and \figb) additive noise component
$\noc(t)$. Input $\filt(t)$ is transformed into envelope
$\env(t)$, logarithmically compressed envelope $\db(t)$,
and intensity-adapted envelope $\adapt(t)$.
\textbf{Left}:~$\env(t)$, $\db(t)$, and $\adapt(t)$ for
different scales $\sca$.
\textbf{Right}:~Ratios of the standard deviation of
$\env(t)$, $\db(t)$, and $\adapt(t)$ relative to the
respective reference standard deviation for input
$\filt(t)=\noc(t)$.
\figa{} and \figb:~Ideally, if $\filt(t)=\sca\cdot\soc(t)$, then
$\adapt(t)$ is intensity-invariant across all $\sca$.
\figc{} and \figd:~In practice, if
$\filt(t)=\sca\cdot\soc(t)+\noc(t)$, the intensity
invariance of $\adapt(t)$ is limited to sufficiently large
$\sca$. Shaded area indicates saturation of $\adapt(t)$ at
$95\,\%$ curve span.
}
\label{fig:inv_log-hp}
\end{figure}