{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"nbsphinx": "hidden"
},
"source": [
"# Quantization of Signals\n",
"\n",
"*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Quantization Error of a Linear Uniform Quantizer\n",
"\n",
"As illustrated in the [preceding section](linear_uniform_characteristic.ipynb), quantization results in two different types of distortions. Overload distortions are a consequence of exceeding the minimum/maximum amplitude of the quantizer. Granular distortions are a consequence of the quantization process when no clipping occurs. Various measures are used to quantify the distortions of a quantizer. We limit ourselves to the signal-to-noise ratio as commonly used measure."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"### Signal-to-Noise Ratio\n",
"\n",
"A quantizer can be evaluated by its [signal-to-noise ratio](https://en.wikipedia.org/wiki/Signal-to-noise_ratio) (SNR), which is defined as the power of the continuous amplitude signal $x[k]$ divided by the power of the quantization error $e[k]$. Under the assumption that both signals are drawn from a zero-mean wide-sense stationary (WSS) process, the average SNR is given as\n",
"\n",
"\\begin{equation}\n",
"SNR = 10 \\cdot \\log_{10} \\left( \\frac{\\sigma_x^2}{\\sigma_e^2} \\right) \\quad \\text{ in dB}\n",
"\\end{equation}\n",
"\n",
"where $\\sigma_x^2$ and $\\sigma_e^2$ denote the variances of the signals $x[k]$ and $e[k]$, respectively. The SNR quantifies the average impact of the distortions introduced by quantization. The statistical properties of the signal $x[k]$ and the quantization error $e[k]$ are required in order to evaluate the SNR of a quantizer. First, a statistical model for the quantization error is introduced."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model for the Quantization Error\n",
"\n",
"In order to derive the statistical properties of the quantization error, the probability density functions (PDFs) of the quantized signal $x_\\text{Q}[k]$ and the error $e[k]$, as well as its bivariate PDFs have to be derived. The underlying calculus is quite tedious due to the nonlinear nature of quantization. Please refer to [[Widrow](../index.ipynb#Literature)] for a detailed treatment. The resulting model is summarized in the following. We focus on the non-clipping case $x_\\text{min} \\leq x[k] < x_\\text{max}$ first, hence on granular distortions. Here the quantization error is in general bounded $|e[k]| < \\frac{Q}{2}$.\n",
"\n",
"Under the assumption that the input signal has a wide dynamic range compared to the quantization step size $Q$, the quantization error $e[k]$ can be approximated by the following statistical model\n",
"\n",
"1. The quantization error $e[k]$ is not correlated with the input signal $x[k]$\n",
"\n",
"2. The quantization error is [white](../random_signals/white_noise.ipynb)\n",
"\n",
" $$ \\Phi_{ee}(\\mathrm{e}^{\\,\\mathrm{j}\\,\\Omega}) = \\sigma_e^2 $$\n",
"\n",
"3. The probability density function (PDF) of the quantization error is given by the zero-mean [uniform distribution](../random_signals/important_distributions.ipynb#Uniform-Distribution)\n",
"\n",
" $$ p_e(\\theta) = \\frac{1}{Q} \\cdot \\text{rect} \\left( \\frac{\\theta}{Q} \\right) $$\n",
"\n",
"The variance of the quantization error is then [derived from its PDF](../random_signals/important_distributions.ipynb#Uniform-Distribution) as\n",
"\n",
"\\begin{equation}\n",
"\\sigma_e^2 = \\frac{Q^2}{12}\n",
"\\end{equation}\n",
"\n",
"Let's assume that the quantization index is represented as binary or [fixed-point number](https://en.wikipedia.org/wiki/Fixed-point_arithmetic) with $w$-bits. The common notation for the mid-tread quantizer is that $x_\\text{min}$ can be represented exactly. Half of the $2^w$ quantization indexes is used for the negative signal values, the other half for the positive ones including zero. The quantization step is then given as\n",
"\n",
"\\begin{equation}\n",
"Q = \\frac{ |x_\\text{min}|}{2^{w-1}} = \\frac{ x_\\text{max}}{2^{w-1} - 1}\n",
"\\end{equation}\n",
"\n",
"where $x_\\text{max} = |x_\\text{min}| - Q$. Introducing the quantization step, the variance of the quantization error can be expressed by the word length $w$ as\n",
"\n",
"\\begin{equation}\n",
"\\sigma_e^2 = \\frac{x^2_\\text{max}}{3 \\cdot 2^{2w}}\n",
"\\end{equation}\n",
"\n",
"The average power of the quantization error quarters per additional bit spend. Introducing the variance into the definition of the SNR yields\n",
"\n",
"\\begin{equation}\n",
"\\begin{split}\n",
"SNR &= 10 \\cdot \\log_{10} \\left( \\frac{3 \\sigma_x^2}{x^2_\\text{max}} \\right) + 10 \\cdot \\log_{10} \\left( 2^{2w} \\right) \\\\\n",
"& \\approx 10 \\cdot \\log_{10} \\left( \\frac{3 \\sigma_x^2}{x^2_\\text{max}} \\right) + 6.02 w \\quad \\text{in dB}\n",
"\\end{split}\n",
"\\end{equation}\n",
"\n",
"It now can be concluded that the SNR increases approximately by 6 dB per additional bit spend. This is often referred to as the 6 dB per bit rule of thumb for linear uniform quantization. Note, this holds only under the assumptions stated above."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Uniformly Distributed Signal\n",
"\n",
"A statistical model for the input signal $x[k]$ is required in order to calculate the average SNR of a linear uniform quantizer. For a signal that conforms to a zero-mean uniform distribution and under the assumption $x_\\text{max} \\gg Q$ its PDF is given as\n",
"\n",
"\\begin{equation}\n",
"p_x(\\theta) = \\frac{1}{2 x_\\text{max}} \\text{rect}\\left( \\frac{\\theta}{2 x_\\text{max}} \\right)\n",
"\\end{equation}\n",
"\n",
"Hence, all amplitudes between $-x_\\text{max}$ and $x_\\text{max}$ occur with the same probability. The variance of the signal is then calculated to\n",
"\n",
"\\begin{equation}\n",
"\\sigma_x^2 = \\frac{4 x_\\text{max}^2}{12}\n",
"\\end{equation}\n",
"\n",
"Introducing $\\sigma_x^2$ and $\\sigma_e^2$ into the definition of the SNR yields\n",
"\n",
"\\begin{equation}\n",
"SNR = 10 \\cdot \\log_{10} \\left( 2^{2 w} \\right) \\approx 6.02 \\, w \\quad \\text{in dB}\n",
"\\end{equation}\n",
"\n",
"The word length $w$ and resulting SNRs for some typical digital signal representations are\n",
"\n",
"| | $w$ | SNR |\n",
"|----|:----:|:----:|\n",
"| Compact Disc (CD) | 16 bit | 96 dB |\n",
"| Digital Video Disc (DVD) | 24 bit | 144 dB |\n",
"| Video Signals | 8 bit | 48 dB |\n",
"\n",
"Note that the SNR values hold only if the continuous amplitude signal conforms reasonably well to a uniform PDF and if it uses the full amplitude range of the quantizer. If the latter is not the case this can be considered by introducing the level $0 < A \\leq 1$ into above considerations, such that $x_\\text{min} \\leq \\frac{x[k]}{A} < x_\\text{max}$. The resulting variance is given as\n",
"\n",
"\\begin{equation}\n",
"\\sigma_x^2 = \\frac{4 x_\\text{max}^2 A^2}{12}\n",
"\\end{equation}\n",
"\n",
"introduced into the definition of the SNR yields\n",
"\n",
"\\begin{equation}\n",
"SNR = 10 \\cdot \\log_{10} \\left( 2^{2 w} \\right) + 20 \\cdot \\log_{10} ( A ) \\approx 6.02 \\, w + 20 \\cdot \\log_{10} ( A ) \\quad \\text{in dB}\n",
"\\end{equation}\n",
"\n",
"From this it can be concluded that a level of -6 dB is equivalent to a loss of one bit in terms of SNR of the quantized signal."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Example - Quantization of a uniformly distributed signal \n",
"\n",
"In this example the linear uniform quantization of a random signal drawn from a uniform distribution is evaluated. The amplitude range of the quantizer is $x_\\text{min} = -1$ and $x_\\text{max} = 1 - Q$."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SNR = 48.090272 in dB\n"
]
},
{
"data": {
"application/pdf": "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\n",
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
"