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Added and described two single-kernel Thresh-LP invariance figures in main.tex.

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j-hartling
2026-03-11 15:21:22 +01:00
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@@ -248,17 +248,21 @@
\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 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 }
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces \textbf {Intensity invariance by logarithmic compression and adaptation is restricted by the noise floor.} 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}{}{}{}}
\newlabel{eq:feat_avg}{{16}{13}{}{}{}}
\newlabel{eq:feat_prop}{{17}{13}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces \textbf {Intensity invariance by thresholding and temporal averaging depends on the threshold value.} Kernel response $c_i(t)$ is rescaled by $\alpha $ and transformed into binary response $b_i(t)$ and further into feature $f_i(t)$. Threshold value $\Theta _i$ is set to different percentiles of the the distribution of $c_i(t)$ at $\alpha =1$. Darker colors indicate higher values of $\Theta _i$. Indicated time scale of $500\,$ms is the same for \textbf {a}-\textbf {c} (black bar). \textbf {a}:~50th percentile. \textbf {b}:~75th percentile. \textbf {c}:~100th percentile. \textbf {d}:~Average value of $f_i(t)$ during the song for the different $\Theta _i$ in \textbf {a}-\textbf {c}. }}{13}{}\protected@file@percent }
\newlabel{fig:inv_thresh-lp_single}{{5}{13}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces \textbf {Intensity invariance by thresholding and temporal averaging depends on noise.} Kernel response $c_i(t)$ is rescaled by $\alpha $, mixed with fixed-scale noise component $\eta (t)$, and transformed into binary response $b_i(t)$ and further into feature $f_i(t)$. Threshold value $\Theta _i$ is set to different percentiles of the the distribution of $c_i(t)$ at $\alpha =1$. Darker colors indicate higher values of $\Theta _i$. Indicated time scale of $500\,$ms is the same for \textbf {a}-\textbf {c} (black bar). \textbf {a}:~50th percentile. \textbf {b}:~75th percentile. \textbf {c}:~100th percentile. \textbf {d}:~Average value of $f_i(t)$ during the song for the different $\Theta _i$ in \textbf {a}-\textbf {c}. }}{14}{}\protected@file@percent }
\newlabel{fig:inv_thresh-lp_single_noise}{{6}{14}{}{}{}}
\newlabel{eq:pdf_split}{{15}{15}{}{}{}}
\newlabel{eq:feat_avg}{{16}{15}{}{}{}}
\newlabel{eq:feat_prop}{{17}{15}{}{}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {4}Discriminating species-specific song\\patterns in feature space}{14}{}\protected@file@percent }
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