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Finished a good part of analysis and figure for Thresh-LP invariance (WIP).

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j-hartling
2026-03-06 14:47:22 +01:00
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@@ -248,7 +248,7 @@
\newlabel{eq:toy_log}{{12}{11}{}{}{}}
\newlabel{eq:toy_highpass}{{13}{11}{}{}{}}
\newlabel{eq:toy_snr}{{14}{11}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces \textbf {Intensity invariance by logarithmic compression and adaptation.} \textbf {a}:~Synthetic envelopes resulting from the mixture of song component $s(t)$ with scale $\alpha $ and noise component $\eta (t)$ with fixed scale. \textbf {b}:~Corresponding logarithmically scaled envelopes. \textbf {c}:~Corresponding intensity-adapted envelopes. \textbf {d}:~Absolute SNRs of each representation relative to the representation without song component ($\alpha =0$). \textbf {e}:~Same SNRs as in \textbf {d} but normalized to the maximum SNR for each representation. \textbf {f}:~Relative amplification of normalized SNRs relative to the normalized SNRs of the initial envelope. }}{12}{}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces \textbf {Intensity invariance by logarithmic compression and adaptation is restricted by the noise floor.} Synthetic envelope $x_{\text {env}}(t)$ is transformed into logarihmically compressed envelope $x_{\text {dB}}(t)$ and further into intensity-adapted envelope $x_{\text {adapt}}(t)$. Indicated time scale is $5\,$s for both \textbf {a} and \textbf {b} (black bars). \textbf {a}:~Ideally, if $x_{\text {env}}(t)$ consists only of song component $s(t)$ rescaled by $\alpha $, then $x_{\text {adapt}}(t)$ is fully intensity-invariant across all $\alpha $. \textbf {b}:~In practice, $x_{\text {env}}(t)$ also contains fixed-scale noise component $\eta (t)$, which limits the effective intensity invariance of $x_{\text {adapt}}(t)$ to sufficiently large $\alpha $. \textbf {c}:~Ratios of the SD of each representation in \textbf {b} at a given $\alpha $ relative to the SD of the representation for $\alpha =0$ (solid lines). The same ratios for the ideal $x_{\text {adapt}}(t)$ in \textbf {a} are shown for comparison (dashed line). }}{12}{}\protected@file@percent }
\newlabel{fig:inv_log-hp}{{4}{12}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Thresholding nonlinearity \& temporal averaging}{12}{}\protected@file@percent }
\newlabel{eq:pdf_split}{{15}{13}{}{}{}}