{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "Following Section 3.1.2.1 of [Müller, FMP, Springer 2015], we introduce in this notebook the concept of logarithmic compression.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compression Function\n", "\n", "In music signal processing, the problem with representations such as a spectrogram or chromagram is that its values possess a large dynamic range. As a result, small, but still relevant values may be dominated or obscured by large values. Therefore, one often uses a [**decibel scale**](../C1/C1S3_Dynamics.html), where the idea is to balance out this discrepancy by reducing the difference between large and small values with the effect of enhancing the small values. More generally, one may apply other types of logarithm-based functions, a step often referred to as **logarithmic compression**. Let $\\gamma\\in\\mathbb{R}_{>0}$ be a positive constant, then we define a function $\\Gamma_\\gamma:\\mathbb{R}_{>0} \\to \\mathbb{R}_{>0}$ by\n", "\n", "\\begin{equation}\n", " \\Gamma_\\gamma(v):=\\log(1+ \\gamma \\cdot v)\n", "\\end{equation}\n", "\n", "for some positive value $v\\in\\mathbb{R}_{>0}$. Opposed to the $\\mathrm{dB}$ function, the function $\\Gamma_\\gamma$ yields a positive value $\\Gamma_\\gamma(v)$ for any positive value $v\\in\\mathbb{R}_{>0}$. The degree of compression can be adjusted by the constant $\\gamma$: the larger $\\gamma$, the larger the resulting compression. The following code cell illustrates the compression function $\\Gamma_\\gamma$ for different constants $\\gamma$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:49:49.835759Z", "iopub.status.busy": "2024-02-15T08:49:49.835513Z", "iopub.status.idle": "2024-02-15T08:49:52.535177Z", "shell.execute_reply": "2024-02-15T08:49:52.534584Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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