{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"nbsphinx": "hidden"
},
"source": [
"# Characterization of Systems in the Spectral Domain\n",
"\n",
"*This Jupyter notebook is part of a [collection of notebooks](../index.ipynb) in the bachelors module Signals and Systems, Communications Engineering, Universität Rostock. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Combination of Systems\n",
"\n",
"The representation of complex systems as combination of simpler systems is often convenient for their analysis or synthesis. This section discusses three of the most common combinations, the series and parallel connection of systems as well as feedback loops."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Concatenation\n",
"\n",
"When two linear time-invariant (LTI) systems are combined in series by connecting the output of the first system to the input of a second system this is termed as *concatenation* of two systems. Denoting the impulse responses of the two systems by $h_1(t)$ and $h_2(t)$, the output signal $y(t)$ of the second system is given as\n",
"\n",
"\\begin{equation}\n",
"y(t) = x(t) * h_1(t) * h_2(t)\n",
"\\end{equation}\n",
"\n",
"where $x(t)$ denotes the input signal of the first system. Laplace transformation of the respective signals and impulse responses, and repeated application of the convolution theorem yields\n",
"\n",
"\\begin{equation}\n",
"Y(s) = \\underbrace{H_1(s) \\cdot H_2(s)}_{H(s)} \\cdot X(s)\n",
"\\end{equation}\n",
"\n",
"It can be concluded that the concatenation of two systems can be regarded as one LTI system with the transfer function $H(s) = H_1(s) \\cdot H_2(s)$. Hence, the following structures are equivalent\n",
"\n",
"![Concatenation of two systems](concatenation.png)\n",
"\n",
"The extension to a concatenation of $N$ systems is straightforward. The overall transfer function is given by multiplication of all the individual transfer functions $H_n(s)$\n",
"\n",
"\\begin{equation}\n",
"H(s) = \\prod_{n=1}^{N} H_n(s)\n",
"\\end{equation}\n",
"\n",
"Applications of concatenated systems include for instance the modeling of wireless transmission systems and cascaded filters."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Example**\n",
"\n",
"Concatenation of LTI systems can be used to construct higher-order filters from lower-order prototypes. Such filters are known as *cascaded filters*. This is illustrated at the [example of the second-order low-pass filter](../laplace_transform/network_analysis.ipynb#Example:-Second-Order-Low-Pass-Filter) introduced before. The transfer function $H_0(s)$ of the low-pass is given as\n",
"\n",
"\\begin{equation}\n",
"H_0(s) = \\frac{1}{LC s^2 + RC s + 1}\n",
"\\end{equation}\n",
"\n",
"where $R$, $L$ and $C$ denote the values of the resistor, capacitor and inductor. Concatenation of $N$ second-order filters leads to a filter with order $2 N$. Its transfer function reads\n",
"\n",
"\\begin{equation}\n",
"H_N(s) = \\left( \\frac{1}{LC s^2 + RC s + 1} \\right)^N\n",
"\\end{equation}\n",
"\n",
"The resulting transfer function is illustrated by its [Bode plot](../systems_spectral_domain/transfer_function.ipynb#Bode-Plots) for a varying number of cascaded filters using the normalized values $L = .5$, $R = 1$, $C = .4$. First the transfer function $H_N(s)$ is defined"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\left(C L s^{2} + C R s + 1\\right)^{- N}$"
],
"text/plain": [
" -N\n",
"⎛ 2 ⎞ \n",
"⎝C⋅L⋅s + C⋅R⋅s + 1⎠ "
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%matplotlib inline\n",
"import sympy as sym\n",
"sym.init_printing()\n",
"\n",
"s = sym.symbols('s', complex=True)\n",
"w, R, L, C = sym.symbols('omega R L C', real=True)\n",
"N = sym.symbols('N', integer=True)\n",
"\n",
"H0 = 1/(L*C*s**2 + R*C*s + 1)\n",
"HN = H0**N\n",
"HN"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The bode plot for the transfer function $H_N(j \\omega)$ is shown for $N = \\{1, 2, 3\\}$ (red, green, blue line)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"application/pdf": "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\n",
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
"