{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"<center>\n",
" <img src=\"./images/ac_header.png\">\n",
"</center>\n",
"\n",
"### <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https://www.tu-ilmenau.de/mt-ams/personen/schuller-gerald/\">Prof. Dr. -Ing. Gerald Schuller</a> <br> <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https://www.tu-ilmenau.de/mt-ams/lehre/msp-and-adsp-tutorials/\">Jupyter Notebook: Renato Profeta</a> \n",
"\n",
"[Applied Media Systems Group](https://www.tu-ilmenau.de/en/applied-media-systems-group/) <br>\n",
"[Technische Universität Ilmenau](https://www.tu-ilmenau.de/)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"# Psychoacoustics"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"hide_input": true
},
"outputs": [
{
"data": {
"text/html": [
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/Dp9NhFShaPM?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/Dp9NhFShaPM?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Block Diagram of a Perceptual Audio Encoder"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"slideshow": {
"slide_type": "-"
}
},
"source": [
"<center>\n",
" <img src='./images/ac_04_01_psycho1.png' width='900'>\n",
"</center>"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"scrolled": true,
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Structure of the Human Ear"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"hide_input": true
},
"outputs": [
{
"data": {
"text/html": [
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/BcVFpv1sczg?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/BcVFpv1sczg?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"slideshow": {
"slide_type": "-"
}
},
"source": [
"<center>\n",
" <img src='./images/ac_04_02_structureEar.png' width='900'>\n",
" <cite>Quelle: Ars Auditus; http://www.dasp.uni-wuppertal.de/index.php?id=57, 2010</cite>\n",
"</center>\n",
"\n",
" - eardrum – transforms sound wave into vibrations\n",
" - ossicular bones - transfer the mechanical vibrations to the cochlea\n",
" - cochlear structure - induces traveling waves along the length of the basilar membrane\n",
" - neural receptors - connected along the length of the basilar membrane\n",
" - convert these traveling into chemical and electrical signals"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Cochlea"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"<center>\n",
" <img src='./images/ac_04_03_cochlea.png' width='500'>\n",
"</center>\n",
"\n",
" - cochlea of a 5 month old fetus:\n",
" - spiral-shaped, fluid-filled structure\n",
" - contains the coiled basilar membrane\n",
" - blue arrow $\\rightarrow$ oval window\n",
" - yellos arrow $\\rightarrow$ round window\n",
" \n",
" <center>\n",
" <img src='./images/ac_04_04_cochlea2.png' width='600'>\n",
"</center>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Organ of Corti"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
" <center>\n",
" <img src='./images/ac_04_05_corti.png' width='600'>\n",
"</center>\n",
"\n",
" - organ of corti of a guinea pig\n",
" - white bar = 20 μm\n",
" \n",
" - $\\approx$ 3500 IHC and $\\approx$ 12000 OHC at humans.\n",
" - hair cells convert fluid motion into electrical impulses in auditory nerve."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"hide_input": true,
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"https://acoustics.org/pressroom/httpdocs/146th/mountain.htm\n"
]
},
{
"data": {
"text/html": [
"\n",
" <iframe\n",
" width=\"900\"\n",
" height=\"600\"\n",
" src=\"https://acoustics.org/pressroom/httpdocs/146th/mountain.htm\"\n",
" frameborder=\"0\"\n",
" allowfullscreen\n",
" ></iframe>\n",
" "
],
"text/plain": [
"<IPython.lib.display.IFrame at 0x11d67e1be08>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import IFrame\n",
"print('https://acoustics.org/pressroom/httpdocs/146th/mountain.htm')\n",
"IFrame('https://acoustics.org/pressroom/httpdocs/146th/mountain.htm', width=900, height=600)\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"hide_input": true,
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"http://147.162.36.50/cochlea/cochleapages/overview/history.htm\n"
]
},
{
"data": {
"text/html": [
"\n",
" <iframe\n",
" width=\"900\"\n",
" height=\"600\"\n",
" src=\"http://147.162.36.50/cochlea/cochleapages/overview/history.htm\"\n",
" frameborder=\"0\"\n",
" allowfullscreen\n",
" ></iframe>\n",
" "
],
"text/plain": [
"<IPython.lib.display.IFrame at 0x11d67e53188>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import IFrame\n",
"print('http://147.162.36.50/cochlea/cochleapages/overview/history.htm')\n",
"IFrame('http://147.162.36.50/cochlea/cochleapages/overview/history.htm', width=900, height=600)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"hide_input": true
},
"outputs": [
{
"data": {
"text/html": [
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/eQEaiZ2j9oc?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/eQEaiZ2j9oc?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Preprocessing of Sound in the Peripheral System"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"hide_input": true
},
"outputs": [
{
"data": {
"text/html": [
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/tj069m7BUf0?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/tj069m7BUf0?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"slideshow": {
"slide_type": "-"
}
},
"source": [
" - frequency selectivity of the basilar membrane\n",
" <center>\n",
" <br>\n",
" <img src='./images/ac_04_08_basilarMembrane.png' width='600'>\n",
" <cite>Source: http://cochlearimplanthelp.com/journey/choosing-a-cochlear-implant/electrodes-and-channels/</cite>\n",
" <br>\n",
"</center>\n",
"<br>\n",
" - traveling wave envelopes occur in response to an acoustic tone complex containing e.g. sinusoids of 400 Hz, 1600 Hz and 6400 Hz\n",
" - peak responses for each sinusoid are localized along the membrane surface, with each peak occurring at a particular distance from the oval window (cochlear \"input\")\n",
"<center>\n",
" <br>\n",
" <img src='./images/ac_04_06_preprocessing.png' width='700'>\n",
" <cite>Source: Yuli You \"Audio Coding Theory and Applications\" </cite>\n",
" <br>\n",
"</center>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"## Information Processing in the Auditory System"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"slideshow": {
"slide_type": "-"
}
},
"source": [
" - basilar membrane as a filter bank\n",
" - bank of highly overlapping bandpass filters\n",
" - the magnitude responses are asymmetric and nonlinear (level dependent)\n",
" - non-uniform bandwidth, and the bandwidths increase with increasing frequency\n",
" \n",
"<center>\n",
" <img src='./images/ac_04_07_preprocessing2.png' width='700'>\n",
"</center>\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Sound Perception"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"slideshow": {
"slide_type": "-"
}
},
"source": [
"### Frequency and Level Range of Human Hearing"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"hide_input": true
},
"outputs": [
{
"data": {
"text/html": [
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/sTGM9FhcNbw?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/sTGM9FhcNbw?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"slideshow": {
"slide_type": "-"
}
},
"source": [
"<center>\n",
" <img src='./images/ac_04_09_frequency.png' width='700'>\n",
"</center>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Threshold in Quiet or the Absolute Threshold"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - Hearing threshold of 100 persons with normal hearing for \n",
" sine tones (50% curve is the median).\n",
" <br>\n",
" <center>\n",
" <img src='./images/ac_04_10_threshold.png' width='800'>\n",
"</center>\n",
"<br>\n",
"\n",
" - Approximations:\n",
" \n",
" $$\\large\n",
" \\dfrac{L_{T_q}}{dB} = 3.64 \\left( \\frac{f}{kHz} \\right)^{-0.8} - \\exp \\left( -0.6\\left(\\dfrac{f}{kHz}-3.3\\right)^2\\right)\n",
" + 10^{-3}\\left(\\dfrac{f}{kHz}\\right)^4\n",
" $$\n",
" <br>\n",
" <center>\n",
" <img src='./images/ac_04_11_threshold2.png' width='600'>\n",
"</center>\n",
" \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Hearing Threshold and Age"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - Average pure-tone audiograms in dB Hearing Loss in (a) men and (b) women grouped by their age in decades (the parameter is age group in years). The extended high-frequency range is zoomed for clarity.\n",
" \n",
" <br>\n",
" <center>\n",
" <img src='./images/ac_04_12_threshold_age.png' width='500'>\n",
"</center>\n",
"\n",
"\n",
" - Pure-tone threshold standard deviation of all participants as a function of frequency (the parameter is age in 10-year groups). \n",
" \n",
" <br>\n",
" <center>\n",
" <img src='./images/ac_04_13_threshold_age2.png' width='500'>\n",
"</center>\n",
"\n",
"\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"hide_input": true,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"http://newt.phys.unsw.edu.au/jw/hearing.html\n"
]
},
{
"data": {
"text/html": [
"\n",
" <iframe\n",
" width=\"900\"\n",
" height=\"600\"\n",
" src=\"http://newt.phys.unsw.edu.au/jw/hearing.html\"\n",
" frameborder=\"0\"\n",
" allowfullscreen\n",
" ></iframe>\n",
" "
],
"text/plain": [
"<IPython.lib.display.IFrame at 0x2c276328f08>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import IFrame\n",
"print('http://newt.phys.unsw.edu.au/jw/hearing.html')\n",
"IFrame('http://newt.phys.unsw.edu.au/jw/hearing.html', width=900, height=600)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Loudness"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"hide_input": true
},
"outputs": [
{
"data": {
"text/html": [
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/BQPVCN1fmSQ?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/BQPVCN1fmSQ?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
" - Loudness LeveL:\n",
" - **Loudness N:** psychological concept to describe the magnitude of an <u>auditory sensation</u>, the loudness of a sound (measured in 'sone')\n",
" - **loudness level $L_N$** of a sound is measured in **'phon'**\n",
" - **$L_N$** of a sound is the sound pressure of a 1 kHz tone which is as loud as the sound\n",
" - 1 sone is equivalent to 40 phons, which is defined as the loudness level of a pure 1 kHz tone at $L_N$ 40 dB SPL.\n",
" \n",
" \n",
" - Equal-Loudness Level Contours:\n",
" - Equal loudness contours of pure tone sin a free sound field.\n",
" - The parameter is expressed in **loudness level**, $L_N$, and loudness, N. Can be observed:\n",
" - The sensitivity of the human ear -a function of frequency\n",
" - The most sensitive to sounds around 2–4 kHz\n",
" \n",
" <center>\n",
" <br>\n",
" <img src='./images/ac_04_14_loudness.png' width='500'>\n",
"</center>\n",
"\n",
" - Loudness Scale:\n",
" - aim: double the number of units on this scale means magnitude of sensation is doubled\n",
" <br>\n",
" $\\rightarrow$ relation between loudness level $L_N$ and the loudness N (rule of thumb):\n",
" $$2 \\cdot N \\hat{=} L_N + 10 phon $$\n",
" - one potential experiment:\n",
" <br>\n",
" listen to a sound with $L_{N_1}$ 1and then adjust the same sound until <br>\n",
" $N_2 = 2 \\cdot N_1$, then compare $L_{N_1}$ and $L_{N_2}$\n",
" \n",
" <center>\n",
"<img src='./images/ac_04_15_loudness_scale.png' width='600'>\n",
"</center> \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Critical Bands"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"### Frequency Grouping in Human Hearing"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"hide_input": true
},
"outputs": [
{
"data": {
"text/html": [
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/UI9Y8B9A__0?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/UI9Y8B9A__0?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
" - Different interpretations that produce the same segmentation:\n",
" - Constant distance in the Cochlea\n",
" - By using tones under the threshold in quiet, their intensity add up in a critical band and are now audible\n",
" - Tones in a critical band above the threshold in quiet: their energy adds up\n",
" - Formula for the width of the critical bands:\n",
" - for frequencies < 500 Hz: Constant 100Hz width\n",
" - for frequencies > 500 Hz: 0.2*frequency\n",
" \n",
"<center>\n",
"<img src='./images/ac_04_16_groupin.jpg' width='600'>\n",
" <cite>: Zwicker, Fastl “Psychoacoustics Facts and Models”, p.159 </cite>\n",
"</center> \n",
" \n",
" - Critical bandwidth as a function of frequency, that quantifies the cochlear filter passbands.\n",
" - Approximations for low and high frequency ranges are indicated by broken lines."
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"#### Excursus - Critical Bands and Loudness"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
" - Spectral effects -influence of bandwidth:\n",
" - bandwidth of the signals plays an important role\n",
" - sound level also influence loudness level\n",
" - $\\rightarrow$ total sound intensity (SPL) have to be constant to measure loudness as function of bandwidth\n",
" - $\\rightarrow$ critical bandwidth\n",
" \n",
"<center>\n",
"<img src='./images/ac_04_17_bandwidth.png' width='500'>\n",
"</center> "
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Bark Scale"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
" - Critical-band concept used in many models and hypothesis <br>\n",
" $\\rightarrow$ unit was defined leading to so-called critical-band rate scale\n",
" - scale ranging from 0 –24, unit \"Bark\"\n",
" - relation between z and f is important for understanding many characteristics of human ear\n",
"\n",
"<center>\n",
"<img src='./images/ac_04_18_bark.png' width='500'>\n",
"</center> \n",
"\n",
" - Critical-band concept used in many models and hypotheses <br>\n",
" $\\rightarrow$ unit was defined leading to so-called critical-band rate scale\n",
" - scale ranging from 0 –24, unit \"Bark\"(after Zwicker)\n",
" - One Bark corresponds to one critical band\n",
" - Attempt to approximate critical bands with formulas:\n",
" \n",
"Critical Bandrate *z*:\n",
"\n",
"$$\\large\n",
"\\dfrac{z}{Bark} = 13 \\arctan \\left( 0.76 \\cdot \\dfrac{f}{kHz} \\right) + 3.5 \\cdot \\arctan \\left( \\dfrac{f}{7.5kHz}\\right)^2$$\n",
"\n",
"Critical Bandwidth:\n",
"\n",
"$$\\large\n",
"\\Delta f_b = 25 + 75 \\left( 1 + 1.4 \\left( \\dfrac{f}{kHz} \\right)^2 \\right)^{0.69} $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"hide_input": false,
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Masking"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
" - data compression:\n",
" - exploitation of perception in critical bands with reference to the threshold in quiet is not enough\n",
"\n",
"\n",
" - Basic principle:\n",
" - a **test signal**, called a **maskee** is placed at the center frequency of the critical bandwidth.\n",
" - one **masking signal**, called **masker** (equal power and distance from maskee).\n",
" - If the $P_{maskee}$ is weak relative to the total power of the maskers $\\rightarrow$ the test signal is not audible $\\rightarrow$ test signal is masked\n",
" - In order for the test signal to become audible, its power has to be raised to above a certain level – **masking threshold**.\n",
" "
]
},
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"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/5Er45bT-hOE?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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"slideshow": {
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"source": [
"### Masking of Pure Tones by Noise -Broad-Band Noise"
]
},
{
"cell_type": "markdown",
"metadata": {
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"slideshow": {
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"source": [
" - Broad-band noise:\n",
" - white noise from 20 Hz 20 - 20kHz.\n",
" \n",
" <center>\n",
" <br>\n",
" <img src='./images/ac_04_19_broadnoise.png' width='600'>\n",
" <cite> Zwicker, Fastl \"Psychoacoustics - Facts and Models\", 2nd Edition, 1999. </cite>\n",
" <br>\n",
"</center>\n",
" \n",
" \n",
" - masking threshold for pure tones masked by broad band noise of different levels.\n",
" - uniform masking noise (UMN) by equalization of the 10 dB per decade slope.\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"### Masking of Pure Tones by Noise -Narrow-Band Noise"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"hide_input": true
},
"outputs": [
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"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/bHXbgLWkCUk?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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"source": [
" - narrow-band noise:\n",
" - noise with a bandwidth equal or smaller than critical bandwidth\n",
" \n",
" <center>\n",
" <br>\n",
" <img src='./images/ac_04_20_narrownoise.png' width='600'>\n",
" <cite> Zwicker, Fastl \"Psychoacoustics - Facts and Models\", 2nd Edition, 1999. </cite>\n",
" <br>\n",
"</center>\n",
" \n",
" \n",
" - threshold of pure tones masked by narrow-band noise for different centre frequencies.\n",
" - difference between maximum of masked threshold and test tone level.\n",
" \n",
" <center>\n",
" <br>\n",
" <img src='./images/ac_04_21_narrownoise2.png' width='600'>\n",
" <br>\n",
"</center>\n",
"\n",
" - dependence of masked threshold on level of narrow-band noise.\n",
" - dips at higher levels $\\rightarrow$ nonlinear effects (difference noise caused by interactions between test tone and noise) "
]
},
{
"cell_type": "markdown",
"metadata": {
"scrolled": true,
"slideshow": {
"slide_type": "-"
}
},
"source": [
"### Masking of Pure Tones by Low-Pass or High-Pass Noise"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"hide_input": true
},
"outputs": [
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"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/yEc89bIIcAY?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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"source": [
"<center>\n",
" <img src='./images/ac_04_22_LpHpnoise2.png' width='600'>\n",
"</center>"
]
},
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"cell_type": "markdown",
"metadata": {
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"source": [
"### Masking of Pure Tones by Pure Tone"
]
},
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"execution_count": 4,
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"outputs": [
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"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/W01-mvdXP_c?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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"source": [
" - pure tone:\n",
" - single frequency\n",
" \n",
" <center>\n",
" <br>\n",
" <img src='./images/ac_04_23_pureTone.png' width='600'>\n",
" <br>\n",
"</center> \n",
"\n",
" - 1 kHz masking tone with level of 80 dB.\n",
" - threshold for 'detection of anything'\n",
" \n",
" \n",
" - Difficulties:\n",
" - beats (hatching)\n",
" - masker and difference tone (stippling)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
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"source": [
"### Masking of Pure Tone by Complex Tones"
]
},
{
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"execution_count": 5,
"metadata": {
"hide_input": true
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"outputs": [
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"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/zuQzj9cYwnk?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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"source": [
" - complex tone:\n",
" - fundamental tone with its harmonics\n",
" \n",
" <center>\n",
" <br>\n",
" <img src='./images/ac_04_24_complexTone.png' width='600'>\n",
" <cite> Zwicker, Fastl \"Psychoacoustics - Facts and Models\", 2nd Edition, 1999. </cite>\n",
" <br>\n",
"</center> \n",
"\n",
"\n",
" - threshold of pure tones masked by a complex tone with 200 Hz fundamental frequency and nine harmonics.\n"
]
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"source": [
"### Tonality"
]
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"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/pyRuUEB8Bqk?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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"source": [
" - Tonality index $\\alpha$:\n",
" - noisy signal: $\\alpha =0$\n",
" - tonal signal: $\\alpha =1$\n",
" - System theory:\n",
" - Sharp spectral lines = Signal is periodic = Signal is predictable.\n",
" - Approximation: If the signal is predictable then it should be periodic.\n",
" - Therefore we can use prediction to approximate if a signal is tonal (by periodicity). \n",
" - Example:\n",
" <center>\n",
" <img src='./images/ac_04_25_tonality.png' width='600'>\n",
" <br>\n",
"</center> \n"
]
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"source": [
"### Masking - Spreading Function"
]
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"execution_count": 8,
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"outputs": [
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"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/2aGu9gCB1Ug?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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" <center>\n",
" <br>\n",
" <img src='./images/ac_04_26_spreadingF.png' width='900'>\n",
" <br>\n",
"</center> "
]
},
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"cell_type": "markdown",
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"source": [
"### Calculating the Masking Threshold"
]
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"metadata": {
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"source": [
" - Comparison of the signal level to Masking Threshold:\n",
"\n",
"$$\\large\n",
"\\dfrac{O_f(i)}{dB} = \\alpha (14.5+i) + (1+\\alpha)\\cdot \\alpha_v$$\n",
"\n",
"$$\\large\n",
"\\alpha_v = -2 - 2.05 \\arctan \\left( \\dfrac{f}{4kHz} \\right) - 0.75 \\arctan \\left( \\dfrac{f^2}{2.56 kHz^2} \\right)$$\n",
"\n",
"where $\\alpha \\dots$ Tonality index, $\\alpha_v \\dots$ Noise Coefficient\n",
"\n",
" - Approxitamtion:\n",
"\n",
"$$\\large\n",
"\\dfrac{O_f(i)}{dB} = \\alpha(14.5+i) + (1 - \\alpha)\\cdot 5.5 $$\n",
"\n",
" - Simultaneous Masking Threshold\n",
" \n",
" $$\\large\n",
" T(f) = 10^{\\frac{L_s(f)- O_f(i)}{10}}$$\n",
" \n",
" where $L_s(f) \\dots$ Sound Pressure Level, $O_f{i} \\dots$ Distance to Masking Threshold"
]
},
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},
"source": [
"### In-Band Making"
]
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"execution_count": 1,
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"slide_type": "-"
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"source": [
"%%html\n",
"<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/EX7x7LLJRKM?rel=0\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
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"source": [
" <center>\n",
" <img src='./images/ac_04_25_inBand.png' width='600'>\n",
" <cite> Zolzer, \"Digital Audio Signal Processig\" </cite>\n",
"</center> \n",
"\n"
]
},
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"source": [
"### Masking Neighboring Bands"
]
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"source": [
" - spread of masking due to the non-linearity of auditory filters\n",
" - resulting masking threshold = sum of power of neighbouring spreading functions-\n",
" - here: value at intersection of neighbouringspreading functions taken\n",
" <center>\n",
" <br>\n",
" <img src='./images/ac_04_27_maskingBands.png' width='800'>\n",
" <cite> Zolzer, \"Digital Audio Signal Processig\" </cite>\n",
" <br>\n",
"</center> \n",
"\n",
"\n",
"$$\\large\n",
"S_1 = 27 \\cdot \\dfrac{dB}{Bark}$$\n",
"\n",
"$$\\large\n",
"S_2 = 24 + 0.23 \\left( \\dfrac{f}{kHz} \\right)^{-1} - 0.2 \\cdot \\dfrac{L_s(f)}{dB} \\dfrac{dB}{Bark}$$"
]
},
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"source": [
"### Temporal Masking Effects"
]
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},
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" - Post-Masking: corresponds to decay in the effect of the masker $\\rightarrow$ expected\n",
" - Pre-Masking: appears during time before masker is switched on:\n",
" - Quick build-up time for loud maskers\n",
" - Slower build-up time for faint test sounds\n",
" - Frequency resolution $\\leftrightarrow$ Blurringing time\n",
" - Frequency resolution in the ear $\\rightarrow$ Masking in time\n",
" - Because of in-ear fast processing between quiet to loud signals, we get Pre-Echoes\n",
" - Pre-Masking: 1-5 ms\n",
" - Post-Masking: ~100ms\n",
" \n",
" <center>\n",
" <img src='./images/ac_04_28_temporal.png' width='800'>\n",
" <cite> Zwicker. Fastl \"Psychoacoustics Facts and Models\" </cite>\n",
"</center> \n",
" "
]
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