{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"FMP\"\n", "\"AudioLabs\"\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"C3\"\n", "

Logarithmic Compression

\n", "
\n", "\n", "
\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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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import os \n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "import librosa, librosa.display\n", "from numba import jit\n", "%matplotlib inline\n", "\n", "v = np.arange(1001) / 100\n", "\n", "@jit(nopython=True)\n", "def log_compression(v, gamma=1.0):\n", " \"\"\"Logarithmically compresses a value or array\n", "\n", " Notebook: C3/C3S1_LogCompression.ipynb\n", "\n", " Args:\n", " v (float or np.ndarray): Value or array\n", " gamma (float): Compression factor (Default value = 1.0)\n", "\n", " Returns:\n", " v_compressed (float or np.ndarray): Compressed value or array\n", " \"\"\"\n", " return np.log(1 + gamma * v)\n", "\n", "\n", "plt.figure(figsize=(5, 5))\n", "plt.plot(v, v, color='black', linestyle=':', label='Identity')\n", "plt.plot(v, log_compression(v, gamma=1), color='blue', label='$\\gamma$ = 1')\n", "plt.plot(v, log_compression(v, gamma=10), color='gray', label='$\\gamma$ = 10')\n", "plt.plot(v, log_compression(v, gamma=100), color='red', label='$\\gamma$ = 100')\n", "plt.xlabel('Original values')\n", "plt.ylabel('Compressed values')\n", "plt.xlim([v[0], v[-1]])\n", "plt.ylim([v[0], v[-1]])\n", "# plt.tick_params(direction='in')\n", "plt.legend(loc='upper left', fontsize=12)\n", "plt.tight_layout()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compressed Spectrogram\n", "\n", "For a representation with positive values such as a spectrogram, one obtains a compressed version by applying the function $\\Gamma_\\gamma$ to each of the values. For example, for a [spectrogram](../C2/C2_STFT-Basic.html) $\\mathcal{Y}$, the compressed version is the concatenation $\\Gamma_\\gamma \\circ \\mathcal{Y}$ defined by \n", "\n", "\\begin{equation}\n", " (\\Gamma_\\gamma\\circ \\mathcal{Y})(n,k):=\\log(1+ \\gamma \\cdot \\mathcal{Y}(n,k))\n", "\\end{equation}\n", "\n", "with $n$ being the time frame parameter and $k$ the frequency bin parameter. A suitable choice of $\\gamma$ very much depends on the data characteristics and the application in mind. In particular, in the presence of noise one needs to find a good balance between enhancing the weak but relevant signal components while not amplifying the undesired noise components too much. As an illustrating example, we consider a recording of the note C4 played by a piano. The following figure shows the resulting spectrogram as well as compressed versions using different constants $\\gamma$.\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:49:52.565165Z", "iopub.status.busy": "2024-02-15T08:49:52.564897Z", "iopub.status.idle": "2024-02-15T08:49:53.503045Z", "shell.execute_reply": "2024-02-15T08:49:53.502521Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x, Fs = librosa.load(os.path.join('..', 'data', 'C3', 'FMP_C3_NoteC4_Piano.wav'))\n", "\n", "N = 1024\n", "H = 512\n", "X = librosa.stft(x, n_fft=N, hop_length=H, win_length=N, window='hann', pad_mode='constant', center=True)\n", "T_coef = np.arange(X.shape[1]) * H / Fs\n", "K = N // 2\n", "F_coef = np.arange(K + 1) * Fs / N\n", "Y = np.abs(X) ** 2\n", "\n", "plt.figure(figsize=(11, 3))\n", "extent = [T_coef[0], T_coef[-1], F_coef[0], F_coef[-1]]\n", "gamma_set = [0, 1, 100, 10000]\n", "M = len(gamma_set)\n", "Y = np.abs(X)\n", "\n", "for m in range(M):\n", " ax = plt.subplot(1, M, m + 1)\n", " gamma = gamma_set[m]\n", " if gamma == 0:\n", " Y_compressed = Y\n", " title = 'No compression'\n", " else:\n", " Y_compressed = log_compression(Y, gamma=gamma)\n", " title = '$\\gamma$=%d' % gamma\n", " plt.imshow(Y_compressed, cmap='gray_r', aspect='auto', origin='lower', extent=extent)\n", " plt.xlabel('Time (seconds)')\n", " plt.ylim([0, 4000])\n", " plt.clim([0, Y_compressed.max()])\n", " plt.ylabel('Frequency (Hz)')\n", " plt.colorbar()\n", " plt.title(title)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While the partials (the horizontal lines) are hardly visible in the original spectrogram, they clearly pop up in the compressed versions. Also, the note transient (the vertical line at time position $t=0.9$) emerges when increasing the constant $\\gamma$. As a downside, noise-like sound components are also enhanced when compressing the spectrogram. A suitable choice of $\\gamma$ very much depends on the data characteristics and the application in mind. In particular, in the presence of noise one needs to find a good balance between enhancing the weak but relevant signal components while not amplifying the undesired noise components too much." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compressed Chromagram\n", "\n", "Next, we consider a [chromagram](../C3/C3S1_SpecLogFreq-Chromagram.html) $\\mathcal{C}$ and its compressed version $\\Gamma_\\gamma \\circ \\mathcal{C}$ defined by \n", "\n", "\\begin{equation}\n", " (\\Gamma_\\gamma\\circ \\mathcal{C})(n,c):=\\log(1+ \\gamma \\cdot \\mathcal{C}(n,c)). \n", "\\end{equation}\n", "\n", "As an example, we consider a piano recording of a C major scale.\n", "\n", "\"C1\"\n", "\n", "
\n", "\n", "\n", "\n", "The following figure shows a chromagram as well as compressed versions using different constants $\\gamma$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:49:53.505768Z", "iopub.status.busy": "2024-02-15T08:49:53.505580Z", "iopub.status.idle": "2024-02-15T08:49:54.566374Z", "shell.execute_reply": "2024-02-15T08:49:54.565805Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Fs = 22050\n", "fn_wav = os.path.join('..', 'data', 'C3', 'FMP_C3_F08_C-major-scale_pause.wav')\n", "x, Fs = librosa.load(fn_wav, sr=Fs)\n", "\n", "N = 4096\n", "H = 512\n", "C = librosa.feature.chroma_stft(y=x, sr=Fs, tuning=0, norm=None, hop_length=H, n_fft=N)\n", "C = C / C.max()\n", "\n", "plt.figure(figsize=(8, 8))\n", "gamma_set = [0, 10, 1000, 100000]\n", "M = len(gamma_set)\n", "Y = np.abs(X)\n", "\n", "for m in range(M):\n", " ax = plt.subplot(M, 1, m + 1)\n", " gamma = gamma_set[m]\n", " if gamma == 0:\n", " C_compressed = C\n", " title = 'No compression'\n", " else:\n", " C_compressed = log_compression(C, gamma=gamma)\n", " title = '$\\gamma$=%d' % gamma\n", " librosa.display.specshow(C_compressed, x_axis='time', \n", " y_axis='chroma', cmap='gray_r', sr=Fs, hop_length=H)\n", " plt.xlabel('Time (seconds)')\n", " plt.ylabel('Chroma')\n", " plt.clim([0, np.max(C_compressed)])\n", " plt.title(title)\n", " plt.colorbar()\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further Notes\n", "\n", "* Logarithmic compression is a simple, yet powerful tool that is widely used for various music processing tasks. We use this concept throughout the FMP notebooks. A prominent example is the [FMP notebook on chord recognition)](../C5/C5S3_ChordRec_Beatles.html), which presents a case study based on the Beatles corpus to investigates how different chroma variants effect chord recognition results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "Acknowledgment: This notebook was created by Meinard Müller.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "
\"C0\"\"C1\"\"C2\"\"C3\"\"C4\"\"C5\"\"C6\"\"C7\"\"C8\"
" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.16" } }, "nbformat": 4, "nbformat_minor": 1 }