{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"FMP\"\n", "\"AudioLabs\"\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"C2\"\n", "

Digital Signals: Sampling

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\n", "Analog signals have a continuous range of values in both time and amplitude, which generally leads to an infinite number of values. Since a computer can only store and process a finite number of values, one has to convert the waveform into some discrete representation—a process commonly referred to as digitization. The most common approach for digitizing audio signals consists of two steps called sampling and quantization. In this notebook, following Section 2.2.2.1 of [Müller, FMP, Springer 2015], we explain the concept of sampling in more detail.\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sampling\n", "\n", "In signal processing, the term **sampling** refers to the process of reducing a **continuous-time** (CT) signal to a **discrete-time** (DT) signal, which is defined only on a discrete subset of the time axis. By means of a suitable encoding, one often assumes that this discrete set is a subset $I$ of the set $\\mathbb{Z}$ of integers. Then a DT-signal is defined to be a function $x\\colon I\\to\\mathbb{R}$, where the domain $I$ corresponds to points in time. Since one can extend any DT-signal from the domain $I$ to the domain $\\mathbb{Z}$ simply by setting all values to zeros for points in $\\mathbb{Z}\\setminus I$, we may assume $I=\\mathbb{Z}$.\n", "\n", "The most common sampling procedure to transform a CT-signal $f\\colon\\mathbb{R}\\to\\mathbb{R}$ into a DT-signal $x\\colon\\mathbb{Z}\\to\\mathbb{R}$ is known as **equidistant sampling**. Fixing a positive real number $T>0$, the DT-signal $x$ is obtained by setting \n", "\n", "\\begin{equation}\n", " x(n):= f(n \\cdot T)\n", "\\end{equation}\n", "\n", "for $n\\in\\mathbb{Z}$. The value $x(n)$ is called the **sample** taken at time $t=n\\cdot T$ of the original analog signal $f$. In short, this procedure is also called **$T$-sampling**. The number $T$ is referred to as the **sampling period** and the inverse $F_\\mathrm{s}:=1/T$ as the **sampling rate**. The sampling rate specifies the number of samples per second and is measured in Hertz (Hz). \n", "\n", "In the following code cell, we start with a CT-signal $f$ that is defined via linear interpolation of a DT-signal sampled at a high sampling rate. In the plot, this CT-signal is shown as black curve. Applying equidistant sampling, we obtain the DT-signal $x$ visualized as the red stem plot." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T09:00:45.130949Z", "iopub.status.busy": "2024-02-15T09:00:45.130657Z", "iopub.status.idle": "2024-02-15T09:00:46.679184Z", "shell.execute_reply": "2024-02-15T09:00:46.678603Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.interpolate import interp1d\n", "from matplotlib import pyplot as plt\n", "%matplotlib inline\n", "\n", "def generate_function(Fs, dur=1):\n", " \"\"\"Generate example function\n", "\n", " Notebook: C2/C2S2_DigitalSignalSampling.ipynb\n", "\n", " Args:\n", " Fs (scalar): Sampling rate\n", " dur (float): Duration (in seconds) of signal to be generated (Default value = 1)\n", "\n", " Returns:\n", " x (np.ndarray): Signal\n", " t (np.ndarray): Time axis (in seconds)\n", " \"\"\"\n", " N = int(Fs * dur)\n", " t = np.arange(N) / Fs\n", " x = 1 * np.sin(2 * np.pi * (2 * t - 0))\n", " x += 0.5 * np.sin(2 * np.pi * (6 * t - 0.1))\n", " x += 0.1 * np.sin(2 * np.pi * (20 * t - 0.2))\n", " return x, t\n", "\n", "def sampling_equidistant(x_1, t_1, Fs_2, dur=None):\n", " \"\"\"Equidistant sampling of interpolated signal\n", "\n", " Notebook: C2/C2S2_DigitalSignalSampling.ipynb\n", "\n", " Args:\n", " x_1 (np.ndarray): Signal to be interpolated and sampled\n", " t_1 (np.ndarray): Time axis (in seconds) of x_1\n", " Fs_2 (scalar): Sampling rate used for equidistant sampling\n", " dur (float): Duration (in seconds) of sampled signal (Default value = None)\n", "\n", " Returns:\n", " x (np.ndarray): Sampled signal\n", " t (np.ndarray): Time axis (in seconds) of sampled signal\n", " \"\"\"\n", " if dur is None:\n", " dur = len(t_1) * t_1[1]\n", " N = int(Fs_2 * dur)\n", " t_2 = np.arange(N) / Fs_2\n", " x_2 = interp1d(t_1, x_1, kind='linear', fill_value='extrapolate')(t_2)\n", " return x_2, t_2\n", " \n", "Fs_1 = 100\n", "x_1, t_1 = generate_function(Fs=Fs_1, dur=2)\n", "\n", "Fs_2 = 20\n", "x_2, t_2 = sampling_equidistant(x_1, t_1, Fs_2)\n", " \n", "plt.figure(figsize=(8, 2.2))\n", "plt.plot(t_1, x_1, 'k')\n", "plt.title('Original CT-signal')\n", "plt.xlabel('Time (seconds)')\n", "plt.ylim([-1.5, 1.5])\n", "plt.xlim([t_1[0], t_1[-1]])\n", "plt.tight_layout()\n", "\n", "plt.figure(figsize=(8, 2.2))\n", "plt.stem(t_2, x_2, linefmt='r', markerfmt='ro', basefmt='None', use_line_collection=True)\n", "plt.plot(t_1, x_1, 'k', linewidth=1, linestyle='dotted')\n", "plt.title(r'Sampling rate $F_\\mathrm{s} = %.0f$'%Fs_2)\n", "plt.xlabel('Time (seconds)')\n", "plt.ylim([-1.5, 1.5])\n", "plt.xlim([t_1[0], t_1[-1]])\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aliasing\n", "\n", "In general, sampling is a **lossy** operation in the sense that information is lost in this process and that the original CT-signal cannot be recovered from its sampled version. Only if the CT-signal has additional properties in terms of its frequency spectrum (it needs to be **bandlimited**), a perfect reconstruction is possible. This is the assertion of the famous **sampling theorem**, which we explain in more detail at the end of this notebook. The sampling theorem also shows how the original CT-signal can be reconstructed by superimposing suitably shifted $\\mathrm{sinc}$-functions weighted by the samples of the DT-signal.\n", "\n", "Without additional properties, sampling may cause an effect known as **aliasing** where certain frequency components of the signal become indistinguishable. This effect is illustrated by the following figure. Using a high sampling rate, the original CT-signal can be reconstructed with high accuracy. However, when decreasing the sampling rate, the higher-frequency components are not captured well and only a coarse approximation of the original signal remains. This phenomenon is demonstrated by the following example." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T09:00:46.681982Z", "iopub.status.busy": "2024-02-15T09:00:46.681755Z", "iopub.status.idle": "2024-02-15T09:00:47.108489Z", "shell.execute_reply": "2024-02-15T09:00:47.107968Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def reconstruction_sinc(x, t, t_sinc):\n", " \"\"\"Reconstruction from sampled signal using sinc-functions\n", "\n", " Notebook: C2/C2S2_DigitalSignalSampling.ipynb\n", "\n", " Args:\n", " x (np.ndarray): Sampled signal\n", " t (np.ndarray): Equidistant discrete time axis (in seconds) of x\n", " t_sinc (np.ndarray): Equidistant discrete time axis (in seconds) of signal to be reconstructed\n", "\n", " Returns:\n", " x_sinc (np.ndarray): Reconstructed signal having time axis t_sinc\n", " \"\"\"\n", " Fs = 1 / t[1]\n", " x_sinc = np.zeros(len(t_sinc))\n", " for n in range(0, len(t)):\n", " x_sinc += x[n] * np.sinc(Fs * t_sinc - n)\n", " return x_sinc\n", "\n", "def plot_signal_reconstructed(t_1, x_1, t_2, x_2, t_sinc, x_sinc):\n", " plt.figure(figsize=(8, 2.2))\n", " plt.plot(t_1, x_1, 'k', linewidth=1, linestyle='dotted', label='Orignal signal')\n", " plt.stem(t_2, x_2, linefmt='r:', markerfmt='r.', basefmt='None', label='Samples', use_line_collection=True)\n", " plt.plot(t_1, x_sinc, 'b', label='Reconstructed signal')\n", " plt.title(r'Sampling rate $F_\\mathrm{s} = %.0f$'%(1/t_2[1]))\n", " plt.xlabel('Time (seconds)')\n", " plt.ylim([-1.5, 1.5])\n", " plt.xlim([t_1[0], t_1[-1]])\n", " plt.legend(loc='upper right', framealpha=1)\n", " plt.tight_layout()\n", " plt.show()\n", "\n", "Fs_2 = 40\n", "x_2, t_2 = sampling_equidistant(x_1, t_1, Fs_2)\n", "t_sinc = t_1\n", "x_sinc = reconstruction_sinc(x_2, t_2, t_sinc)\n", "plot_signal_reconstructed(t_1, x_1, t_2, x_2, t_sinc, x_sinc);\n", "\n", "Fs_2 = 20\n", "x_2, t_2 = sampling_equidistant(x_1, t_1, Fs_2)\n", "t_sinc = t_1\n", "x_sinc = reconstruction_sinc(x_2, t_2, t_sinc)\n", "plot_signal_reconstructed(t_1, x_1, t_2, x_2, t_sinc, x_sinc);\n", "\n", "Fs_2 = 10\n", "x_2, t_2 = sampling_equidistant(x_1, t_1, Fs_2)\n", "t_sinc = t_1\n", "x_sinc = reconstruction_sinc(x_2, t_2, t_sinc)\n", "plot_signal_reconstructed(t_1, x_1, t_2, x_2, t_sinc, x_sinc);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aliasing effects occur also in other areas such as the visual domain. One famous example is the **wagon-wheel effect**, where a wheel appears to rotate at a slower speed or even backwards when the speed is actually increasing." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T09:00:47.111231Z", "iopub.status.busy": "2024-02-15T09:00:47.110964Z", "iopub.status.idle": "2024-02-15T09:00:47.243757Z", "shell.execute_reply": "2024-02-15T09:00:47.242776Z" } }, "outputs": [ { "data": { "image/jpeg": 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"text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import IPython.display as ipd\n", "ipd.display(ipd.YouTubeVideo('QOwzkND_ooU', width=600, height=450))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next example indicates how aliasing effects the sound quality. We start with a music signal at a high sampling rate ($F_\\mathrm{s}=8192$ Hz), which is then successively reduced by a factor of two." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T09:00:47.247184Z", "iopub.status.busy": "2024-02-15T09:00:47.246884Z", "iopub.status.idle": "2024-02-15T09:00:48.501555Z", "shell.execute_reply": "2024-02-15T09:00:48.501040Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sampling rate Fs = 8000; Number of samples = 26496\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Sampling rate Fs = 4000; Number of samples = 13248\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Sampling rate Fs = 2000; Number of samples = 6624\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Sampling rate Fs = 1000; Number of samples = 3312\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Sampling rate Fs = 500; Number of samples = 1656\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import os\n", "import IPython.display as ipd\n", "import librosa\n", "import scipy.signal\n", "\n", "path_filename_wav = os.path.join('..', 'data', 'C2', 'FMP_C2_Sampling_C-major-scale.wav')\n", "x, Fs = librosa.load(path_filename_wav, sr=8000)\n", "Fs_orig = Fs\n", "len_orig = len(x)\n", "for i in range(5):\n", " print('Sampling rate Fs = %s; Number of samples = %s' % (Fs, len(x)), flush=True)\n", " # ipd.display(ipd.Audio(data=x, rate=Fs))\n", " # Some web browsers do not support arbitray sample rates. \n", " # Therefore, the previous output may work for some web rowers. \n", " # This is a work around: \n", " x_play = scipy.signal.resample(x, len_orig)\n", " ipd.display(ipd.Audio(data=x_play, rate=Fs_orig))\n", " Fs = Fs // 2\n", " x = x[::2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sampling Theorem\n", "\n", "The **sampling theorem**, which is often associated with the names Harry Nyquist and Claude Shannon, states that a continuous-time (CT) signal that is bandlimited can be reconstructed perfectly under certain conditions. More precisely, a CT-signal $f\\in L^2(\\mathbb{R})$ is called **$\\Omega$-bandlimited** if the Fourier transform $\\hat{f}$ vanishes for $|\\omega|>\\Omega$ (i.e., $\\hat{f}(\\omega) = 0$ for $|\\omega|>\\Omega$). Let $f\\in L^2(\\mathbb{R})$ be an $\\Omega$-bandlimited function and let $x$ be the $T$-sampled version of $f$ with $T:=1/(2\\Omega)$ (i.e., $x(n)=f(nT)$, $n\\in\\mathbb{Z}$). Then $f$ can be reconstructed from $x$ by\n", "\n", "$$\n", " f(t)=\\sum_{n\\in\\mathbb{Z}}x(n)\\mathrm{sinc}\\left(\\frac{t-nT}{T}\\right)\n", " =\\sum_{n\\in\\mathbb{Z}}f\\left(\\frac{n}{2\\Omega}\\right) \\mathrm{sinc}\\left(2\\Omega t-n\\right),\n", "$$\n", "\n", "where the $\\mathrm{sinc}$-function is defined as\n", "\n", "\\begin{equation}\n", " \\mathrm{sinc}(t):=\\left\\{\\begin{array}{ll}\n", " \\frac{\\sin \\pi t}{\\pi t},&\\mbox{ if $t\\not= 0$,}\\\\\n", " 1,&\\mbox{ if $t= 0$.}\n", "\\end{array}\\right.\n", "\\end{equation}\n", "\n", "In other words, the CT-signal $f$ can be perfectly reconstructed from the DT-signal obtained by equidistant sampling if the bandlimit is no greater than half the sampling rate. This reconstruction based on the $\\mathrm{sinc}$-function has been used in the function `reconstruction_sinc`." ] }, { "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\"
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