microphones-solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Microphones\n",
    "\n",
    "[return to main page](index.ipynb)\n",
    "\n",
    "## Preparations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T13:09:00.246930Z",
     "iopub.status.busy": "2020-11-26T13:09:00.246519Z",
     "iopub.status.idle": "2020-11-26T13:09:00.531469Z",
     "shell.execute_reply": "2020-11-26T13:09:00.531885Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sounddevice as sd  # for playback\n",
    "import soundfile as sf  # for reading a soundfile\n",
    "\n",
    "# remove \"inline\" to get a separate plotting window:\n",
    "%matplotlib inline  \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Microphone Types\n",
    "\n",
    "### Pressure Microphone\n",
    "\n",
    "A pressure microphone measures the sound pressure $P(\\mathbf x, \\omega)$ where $\\mathbf x$ is the position of the microphone. The microphone signal is hence given as\n",
    "\n",
    "$$\n",
    "M(\\mathbf x, \\omega) = P(\\mathbf x, \\omega)\n",
    "$$\n",
    "\n",
    "### Pressure-Gradient Microphone\n",
    "\n",
    "This type of microphone measures the gradient of the sound pressure along a specific direction, which is define by the orientation of the membrane inside the microphone. The so-called directional gradient along the direction defined by the surface normal $\\mathbf n_m$ onto the membrane is given as\n",
    "\n",
    "$$ M(\\mathbf x, \\omega) = \\frac{\\partial}{\\partial \\mathbf n_m} P(\\mathbf x, \\omega)\n",
    "    = \\mathbf n_m \\cdot \\nabla P(\\mathbf x, \\omega)\n",
    "$$\n",
    "\n",
    "*Exercise*: Calculate the pressure gradient of a point source with its sound pressure given as \n",
    "\n",
    "$$P_{ps}(\\mathbf x | \\mathbf x_s, \\omega) = \\frac{\\mathrm{exp}\\left(-j\\frac{\\omega}{c} |\\mathbf x-\\mathbf x_{\\mathrm s}| \\right)}{4\\pi|\\mathbf x-\\mathbf x_{\\mathrm s}|} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "*\n",
    "For the gradient, we need the derivative with respect to each component of $\\mathbf x$. Using the chain rule of differentiation, we can write for $x$:\n",
    "\n",
    "$$\n",
    "  \\frac{\\partial}{\\partial x} P(\\mathbf x | \\mathbf x_s, \\omega) = \n",
    "      \\frac{\\partial}{\\partial x}\n",
    "      \\frac{\\mathrm{exp}\\left(-j\\frac{\\omega}{c} |\\mathbf x-\\mathbf x_{\\mathrm s}| \\right)}{4\\pi|\\mathbf x-\\mathbf x_{\\mathrm s}|} =     \n",
    "  \\left(\\frac{\\partial (|\\mathbf x - \\mathbf x_s|)}{\\partial x}\\right) \\cdot\n",
    "  \\left(\\frac{\\partial }{\\partial (|\\mathbf x -\\mathbf  x_s|)} \n",
    "  \\frac{\\mathrm{exp}\\left(-j\\frac{\\omega}{c} |\\mathbf x-\\mathbf x_{\\mathrm s}| \\right)}{4\\pi|\\mathbf x-\\mathbf x_{\\mathrm s}|}\n",
    "  \\right)\n",
    "$$\n",
    "\n",
    "The first derivative yields:\n",
    "$$ \n",
    "    \\left(\\frac{\\partial (|\\mathbf x - \\mathbf x_s|}{\\partial x}\\right) = \n",
    "    \\left(\\frac{\\partial (\\sqrt{(x-x_s)^2 + (y-y_s)^2 + (z-z_s)^2}}{\\partial x}\\right) =\n",
    "    \\frac{x-x_s}{\\sqrt{(x-x_s)^2 + (y-y_s)^2 + (z-z_s)^2}} =\n",
    "    \\frac{x-x_s}{|\\mathbf x - \\mathbf x_s|}\n",
    "$$\n",
    "\n",
    "The second derivative with $u = |\\mathbf x - \\mathbf x_s|$ yields:\n",
    "\n",
    "$$ \n",
    "  \\frac{\\partial }{\\partial u} \n",
    "  \\frac{\\mathrm{exp}\\left(-j\\frac{\\omega}{c} u \\right)}{4\\pi u} =\n",
    "  \\left(-j\\frac{\\omega}{c} - \\frac{1}{u} \\right) \\frac{\\mathrm{exp}\\left(-j\\frac{\\omega}{c} u \\right)}{4\\pi u}\n",
    "$$\n",
    "\n",
    "Repeating the procedure for $y$ and $z$ and evaulating the scalar product with $\\mathbf n_m$ results in\n",
    "\n",
    "$$\n",
    "\\frac{\\partial}{\\partial \\mathbf n_m} P_{ps}(\\mathbf x | \\mathbf x_s, \\omega) =\n",
    "    \\left(j\\frac{\\omega}{c} + \\frac{1}{|\\mathbf x- \\mathbf x_s|} \\right) \n",
    "    \\frac{(\\mathbf x_s - \\mathbf x) \\cdot \\mathbf n_m}{|\\mathbf x- \\mathbf x_s|} \n",
    "    \\frac{\\mathrm{exp}\\left(-j\\frac{\\omega}{c} |\\mathbf x_{\\mathrm s} - \\mathbf x| \\right)}{4\\pi|\\mathbf x-\\mathbf x_{\\mathrm s}|}\n",
    "$$\n",
    "*\n",
    "</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Exercise*: Can to tell anything about the behaviour of the microphone for low/high temporal frequencies and close/far distances between the microphone and the point source?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "*\n",
    "For \n",
    "*\n",
    "</font>\n",
    "\n",
    "### Combining Pressure and Pressure-Gradient Microphones\n",
    "\n",
    "There is also the possibility to combine both prior types to\n",
    "\n",
    "$$\n",
    "M(\\mathbf x, \\omega) = a(\\omega)\\,P(\\mathbf x, \\omega) + b(\\omega)\\,\\frac{\\partial}{\\partial \\mathbf n_m} P(\\mathbf x, \\omega)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Technical Parameters\n",
    "\n",
    "### The Far-Field Directivity\n",
    "\n",
    "#### Definition\n",
    "\n",
    "For the far-field directivity the microphone signal caused by a point source is normalised by the sound pressure of that point source. \n",
    "\n",
    "$$\n",
    "M_0(\\phi_s, \\theta_s, \\omega) = \\lim_{|\\mathbf x_s|\\rightarrow \\infty} \\frac{M_{ps}(\\mathbf x| \\mathbf x_s, \\omega)}{P_{ps}(\\mathbf x | \\mathbf x_s, \\omega)}\n",
    "$$\n",
    "\n",
    "where the point source is assumed to be at an infinite distance. The far-field directivity is hence depending on the direction of arrival defined by the two the angles $\\phi_s$ and $\\theta_s$ in spherical coordinates. In general, the directivity is frequency-dependent. In most cases, the directivity of the microphone is rotationally symmetric with respect to the microphone orientation $\\mathbf n_m $ so that M_0 depends only of the angle between $\\mathbf n_m$ and $\\mathbf x_s$ called $\\Theta$.\n",
    "\n",
    "*Exercise*: Calculate the Far-Field-Directivity of Pressure Microphone."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "\n",
    "$$\n",
    "M_0(\\Theta) = 1\n",
    "$$\n",
    "\n",
    "</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Exercise*: Calculate the Far-Field-Directivity of Pressure-Gradient Microphone."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "\n",
    "$$\n",
    " M_0(\\Theta) = \n",
    "    \\lim_{|\\mathbf x_s|\\rightarrow \\infty} \n",
    "    \\left(j\\frac{\\omega}{c} + \\frac{1}{|\\mathbf x - \\mathbf x_s|} \\right) \n",
    "    \\frac{(\\mathbf x_s - \\mathbf x) \\cdot \\mathbf n_m}{|\\mathbf x- \\mathbf x_s|} = \n",
    "    j\\frac{\\omega}{c} \\frac{\\mathbf x_s}{|\\mathbf x_s|} \\cdot \\mathbf n_m =\n",
    "    j\\frac{\\omega}{c} \\cos( \\Theta )\n",
    "$$\n",
    "</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is common practice, to compensate the frequency dependence of the far-field directivity of pressure gradient microphones, so that the frequency dependent term (high-pass characteristic) vanishes. \n",
    "\n",
    "#### First-Order Directivity Patterns\n",
    "\n",
    "First-order directivities subsume patterns with\n",
    "\n",
    "$$\n",
    "  M_0(\\phi_s, \\theta_s) = M_0(\\Theta) = a + (1-a) \\cos( \\Theta )\n",
    "$$\n",
    "\n",
    "They hence linearly combine the directivity patterns of a pressure and a pressure-gradient microphone. Let's plot some directivity patterns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T13:09:00.570120Z",
     "iopub.status.busy": "2020-11-26T13:09:00.555420Z",
     "iopub.status.idle": "2020-11-26T13:09:00.737311Z",
     "shell.execute_reply": "2020-11-26T13:09:00.737691Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a = ...\n",
    "# 1 - omnidirectional\n",
    "# 0.75 - wide cardioid\n",
    "# 0.5 - cardioid\n",
    "# 0.366 - super cardioid\n",
    "# 0.25 - hyper cardioid\n",
    "# 0 - figure of eight\n",
    "a = np.array([1, 0.75, 0.5, 0.3666, 0.25, 0]).reshape(-1,1);\n",
    "\n",
    "theta = np.linspace(0,2*np.pi, 361)\n",
    "theta = theta.reshape(1,-1)\n",
    "theta = np.array([1, -1, 1, -1, 1, -1]).reshape(-1,1) * theta\n",
    "\n",
    "A = np.abs(a + (1 - a)*np.cos(theta))\n",
    "\n",
    "# plotting\n",
    "ax = plt.subplot(111, projection='polar')\n",
    "plt.plot(theta.T, A.T, linewidth=3)\n",
    "ax.set_rmax(1.0)\n",
    "ax.grid(True)\n",
    "ax.legend(['omni', 'wide card.', 'card.', 'super card.', 'hyper card.', 'fig. of 8'], \n",
    "    bbox_to_anchor=(0., 1.02, 1., .102), loc=3, ncol=2, mode=\"expand\", borderaxespad=0.)\n",
    "ax.set_title(\"A line plot on a polar axis\", va='bottom')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Exercise*: Compare the directivity patterns! Can you observe any relation between the width of the front lobe (around 0$^\\circ$) and width of the back lobe (around 180$^\\circ$) ? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Exercise*: Compare the effect of different patterns with regard to the supression of noise coming from a different direction than the target sound."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T13:09:00.741825Z",
     "iopub.status.busy": "2020-11-26T13:09:00.741386Z",
     "iopub.status.idle": "2020-11-26T13:09:17.238820Z",
     "shell.execute_reply": "2020-11-26T13:09:17.238379Z"
    }
   },
   "outputs": [],
   "source": [
    "# target and masker\n",
    "[x_target, fs] = sf.read('data/xmas.wav')  # target sound\n",
    "x_noise = 0.25*np.random.randn(len(x_target))  # gaussian noise as masker\n",
    "# play around with the directions!\n",
    "theta_target = 0  # in degree\n",
    "theta_noise = 90  # in degree\n",
    "# interate over all patterns\n",
    "for aa in a:\n",
    "    A_target = np.abs(aa + (1-aa)*np.cos(theta_target*np.pi/180))\n",
    "    A_noise = np.abs(aa + (1-aa)*np.cos(theta_noise*np.pi/180))\n",
    "    x_mix = A_target*x_target + A_noise*x_noise\n",
    "    sd.play(x_mix, fs, blocking=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Short Demo\n",
    "\n",
    "One Loudspeaker is placed in front of a microphone, another loudspeaker is placed somewhere else. The first loudspeaker emits speech, while the second emits noise. We will compare the recorded signals for two different microphone capsules: one omnidirectional, one hyper-cardiod."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T13:09:17.242409Z",
     "iopub.status.busy": "2020-11-26T13:09:17.241963Z",
     "iopub.status.idle": "2020-11-26T13:09:20.114364Z",
     "shell.execute_reply": "2020-11-26T13:09:20.114800Z"
    }
   },
   "outputs": [],
   "source": [
    "[x_target, fs] = sf.read('data/xmas.wav')  # target sound\n",
    "x_noise = np.random.randn(len(x_target))  # gaussian noise as masker\n",
    "x_mix = np.column_stack((0.2*x_target,0.1*x_noise))  # two-channel signal\n",
    "\n",
    "# play and record simultaneously (change microphones in between)\n",
    "x_rec_omni = sd.playrec(x_mix, samplerate=fs, channels=1, output_mapping=[1,2], blocking=True)\n",
    "# x_rec_card = sd.playrec(x_mix, samplerate=fs, channels=1, output_mapping=[1,2], blocking=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's listen to the recorded signals!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-11-26T13:09:20.118312Z",
     "iopub.status.busy": "2020-11-26T13:09:20.117557Z",
     "iopub.status.idle": "2020-11-26T13:09:22.849742Z",
     "shell.execute_reply": "2020-11-26T13:09:22.849331Z"
    }
   },
   "outputs": [],
   "source": [
    "x_rec_omni = x_rec_omni/np.max(np.abs(x_rec_omni))\n",
    "# x_rec_card = x_rec_card/np.max(np.abs(x_rec_card))\n",
    "\n",
    "sd.play(0.05*x_rec_omni, samplerate=fs, blocking=True)\n",
    "# sd.play(0.05*x_rec_card, samplerate=fs, blocking=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Directivity Factor\n",
    "\n",
    "The directivity factor describes the ratio between the squared directivity for the frontal direction, i.e. $\\Theta = 0$, and the mean squared directivity. For the rotationally symmetric directivity this reads\n",
    "\n",
    "$$\n",
    "  \\gamma(\\omega) = \\frac{M_0^2(0^\\circ)}{\\frac{1}{2}\\int_0^\\pi M_0^2(\\Theta)\\, \\sin(\\Theta) \\, \\mathrm d \\Theta}\n",
    "$$\n",
    "\n",
    "*Exercise*: Calculate the directivity-index for a general first-order directivity pattern $M_0(\\Theta) = a + (1-a) \\cos( \\Theta)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "*\n",
    "For the directivity-index, we need the integral in the denominator\n",
    "$$\n",
    "\\int_0^\\pi (a+(a-1)\\cos(\\Theta))^2 \\sin(\\theta)\\, \\mathrm d \\Theta =\n",
    "\\int_0^\\pi \\left( a^2 + 2a(a-1)\\cos(\\Theta) + (a-1)^2\\cos^2(\\Theta)\\right) \\sin(\\Theta) \\, \\mathrm d \\Theta\n",
    "$$\n",
    "\n",
    "Substitute $u = \\cos(\\Theta)$ which yields $\\mathrm du = - \\mathrm \\sin(\\Theta) \\mathrm d \\Theta$. This results in the equivalent integral\n",
    "\n",
    "$$\n",
    "\\int_{-1}^{1} \\left( a^2 + 2a(a-1)u + (a-1)^2 u^2\\right) \\, \\mathrm d u = 2\\left[a^2 + \\frac{1}{3}(a-1)^2 \\right]\n",
    "$$\n",
    "\n",
    "The final directivity-factor reads\n",
    "\n",
    "$$\n",
    "  \\gamma(a, \\omega) = \\frac{1}{a^2 + \\frac{1}{3}(a-1)^2}\n",
    "$$\n",
    "*\n",
    "</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exercise: For which $a$ does $\\gamma(a, \\omega)$ reach a maximum? To which directivity pattern does the value correspond?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "*\n",
    "A local extremum is possibly reached if the first derivative is zero .\n",
    "$$\n",
    "  \\frac{\\partial}{\\partial a} \\gamma(a, \\omega) = \\frac{2a+\\frac{2}{3}(a-1)}{(a^2 + \\frac{1}{3}(a-1)^2)^2} = 0\n",
    "$$\n",
    "Multiplying both side with the denominator yields\n",
    "$$ \n",
    "  2a+\\frac{2}{3}(a-1) = 0 \\Rightarrow a = \\frac{1}{4}\n",
    "$$\n",
    "This value corresponds to a hyper-cardiod pattern\n",
    "*\n",
    "</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solutions\n",
    "\n",
    "If you had problems solving some of the exercises, don't despair!\n",
    "Have a look at the [example solutions](microphones-solutions.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p xmlns:dct=\"http://purl.org/dc/terms/\">\n",
    "  <a rel=\"license\"\n",
    "     href=\"http://creativecommons.org/publicdomain/zero/1.0/\">\n",
    "    <img src=\"http://i.creativecommons.org/p/zero/1.0/88x31.png\" style=\"border-style: none;\" alt=\"CC0\" />\n",
    "  </a>\n",
    "  <br />\n",
    "  To the extent possible under law,\n",
    "  <span rel=\"dct:publisher\" resource=\"[_:publisher]\">the person who associated CC0</span>\n",
    "  with this work has waived all copyright and related or neighboring\n",
    "  rights to this work.\n",
    "</p>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "mystiasp",
   "language": "python",
   "name": "mystiasp"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}