{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Цифровая обработка сигналов - Лекция 1\n",
    "# Тема: Сигналы - аналоговые, дискретные, цифровые\n",
    "\n",
    "## Введение\n",
    "\n",
    "Перед вами обучающий материал по основам **цифровой обработки сигналов** с использованием средств языка программирования Python. Предполагается, что читатель имеет базовые знания из области высшей математики, а также владеет языком Python и хотя бы поверхностно знает различные python-библиотеки - numpy/scipy, matplotlib и другие. \n",
    "\n",
    "- [Python](https://www.python.org) - official website\n",
    "- [Numpy](https://numpy.org) - the fundamental package for scientific computing with Python\n",
    "- [Scipy](https://scipy.org) - fundamental algorithms for scientific computing in Python\n",
    "- [Matlplotlib](https://matplotlib.org) - visualization with Python\n",
    "\n",
    "Для пользователей MATLAB / GNU Octave освоение материала с точки зрения программного кода не составит труда, поскольку основные функции и их атрибуты во многом идентичны и схожи с методами из python-библиотек.\n",
    "\n",
    "\n",
    "## Сигналы\n",
    "\n",
    "*Сигналом* называется физический процесс, параметры которого изменяются в соответствии с передаваемым сообщением. Cигнал является материальным носителем информации. По способу представления сигналы разделяются на две группы – *случайные* и *детерминированные*. Их описывают математической моделью или функцией, характеризующей изменение параметров сигнала.  \n",
    "\n",
    "*Случайным* сигналом называют функцию времени, значения которой заранее неизвестны и могут быть предсказаны лишь с некоторой *вероятностью*. К основным характеристикам случайных сигналов относятся:\n",
    "\n",
    "* закон распределения (относительное время пребывания значения сигнала в определенном интервале),\n",
    "* спектральное распределение мощности.\n",
    "\n",
    "*Детерминированные* сигналы описываются аналитической функцией (задаются аналитически), и их поведение полностью известно в любой момент времени. Детерминированные сигналы в свою очередь бывают *периодическими* и *непериодическими*. Непериодические сигналы, как правило, ограничены во времени. \n",
    "\n",
    "*Периодический* сигнал - это сигнал, который повторяется во времени с определенным периодом, то есть для которого выполняется условие:\n",
    "\n",
    "$$ s(t) = s(t+kT) \\tag{1.1}$$\n",
    "\n",
    "где *k* – любое целое число, *T* – период повторения.\n",
    "\n",
    "Пример *периодического* сигнала – гармоническое колебание, описываемое следующим выражением:\n",
    "\n",
    "$$ s(t) = A \\cdot cos(\\frac{2\\pi\\cdot t}{T} +\\phi) \\tag{1.2}$$\n",
    "\n",
    "где *A* – амплитуда колебания, $ \\phi $ – начальная фаза. \n",
    "\n",
    "Известно, что любой сложный периодический сигнал может быть представлен в виде суммы гармонических колебаний с частотами, кратными основной частоте $ \\omega = 2\\pi/T $. \n",
    "\n",
    "### Цифровые сигналы\n",
    "\n",
    "Все сигналы можно разделить на четыре группы: \n",
    "* аналоговые, \n",
    "* дискретные, \n",
    "* квантованные,\n",
    "* цифровые.\n",
    "\n",
    "**Аналоговый** сигнал – описывается непрерывной функцией времени. Аналоговый сигнал обеспечивает передачу данных путем непрерывного изменения во времени амплитуды, частоты или фазы. Практически все физические процессы описываются непрерывными функциями времени, поэтому представляют собой аналоговые сигналы. Для аналогового сигнала область значений и определения описывается *непрерывным множеством*. \n",
    "\n",
    "Для **дискретного** сигнала свойственно прерывистое (дискретное) изменение сигнала во времени. То есть изменения в сигнале происходят скачкообразно через некоторые промежутки времени, называемые интервалом дискретизации – Δt или Td. Дискретизация *аналогового сигнала* состоит в том, что сигнал представляется в виде последовательности значений, взятых в дискретные моменты времени, которые называются *отсчётами* (сэмплами). \n",
    "\n",
    "Для правильного восстановления аналогового сигнала из цифрового без искажений и потерь используется теорема отсчетов, известная как **теорема Котельникова (Найквиста-Шеннона)**. \n",
    "\n",
    "> Любой непрерывный сигнал с ограниченным спектром может быть восстановлен однозначно и без потерь по своим дискретным отсчетам, взятым с частотой строго больше удвоенной верхней частоты спектра непрерывного сигнала.\n",
    "\n",
    "Формула теоремы Котельникова:  \n",
    "\n",
    "$$ F_s = \\frac{1}{T_s} > 2F_a \\tag{1.3}$$\n",
    "\n",
    "где\n",
    "* F<sub>s</sub> - частота дискретизации сигнала,\n",
    "* F<sub>a</sub> - верхняя частота спектра аналогового сигнала.\n",
    "\n",
    "Такое определение относится к функциям времени, которые состоят из частот от нуля до $F_a$.\n",
    "\n",
    "В реальных задачах в радиотехнике спектр сигнала может лежать в любом диапазоне частот и начинаться и заканчиваться на любой частоте, в связи с этим определение Теоремы Котельникова правильно рассматривать относительно ширины спектра такого сигнала:\n",
    "\n",
    "> Любой непрерывный сигнал с ограниченным спектром может быть восстановлен однозначно и без потерь по своим дискретным отсчетам, взятым с частотой строго больше удвоенной ширины полосы частот, занимаемой спектром непрерывного сигнала. \n",
    "\n",
    "$$ F_s = \\frac{1}{T_s} > 2\\Delta f \\tag{1.4}$$ \n",
    "\n",
    "где $\\Delta f$ - ширина спектра непрерывного сигнала.\n",
    "\n",
    "**Квантованные** сигналы принимают ряд конечных значений из диапазона непрерывных или дискретных величин. Как правило, сигналы квантуются по уровню, то есть по амплитуде.\n",
    "\n",
    "**Цифровые** сигналы получаются из аналоговых с помощью операций **дискретизации** и **квантования** по уровню. Значениям цифрового сигнала присваивается кодовое слово или набор символов (зачастую двоичных). \n",
    "\n",
    "Устройства, осуществляющие дискретизацию по времени и квантование по уровню, называются **аналого-цифровыми преобразователями (АЦП)**.\n",
    "Устройства, переводящие цифровой сигнал в аналоговый называются **цифро-аналоговыми преобразователями (ЦАП)**. \n",
    "____\n",
    "Для работы с сигналами в **Python** потребуется ряд предварительных действий.  \n",
    "Необходимо импортировать библиотеку *numpy* для оперативного и качественного выполнения математических действий, а также графические средства отображения из библиотеки *matplotlib*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.fftpack import fft\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Напомним, что магическая функция `%matplotlib inline` позволяет отображать графики без вызова метода `plt.show()`\n",
    "\n",
    "На приведенном ниже примере представлены сигналы в аналоговой, дискретной и квантованной форме.\n",
    "\n",
    "**Шаг 1**: создать ряд временных значений:\n",
    "Функция `np.linspace(start, stop, num)` задает вектор в диапазоне [start, stop], а *num* - количество точек в диапазоне.\n",
    "\n",
    "**Шаг 2**: создать сигнал произвольной формы:\n",
    "С помощью функции `np.sin()` задаём сигнал из набора гармонических воздействий. Для простоты амплитуды всех компонент равны 1, а смещение по фазе нулевое.\n",
    "\n",
    "**Шаг 3** Отрисовка графиков.\n",
    "Методы matplotlib задают различный стиль отображения:\n",
    "* `plot()` - стандартный график, выводит сигнал в аналоговой форме,\n",
    "* `stem()` - график в виде отсчетов, выводит сигнал в дискретной форме,\n",
    "* `step()` - график в виде уровней, выводит сигнал в квантованной форме.\n",
    "\n",
    "Для уменьшения количества кода создана вспомогательная функция `plt_sel(s, *args, **kwargs)`, которая выбирает стиль отображения графика. Аргументы `*args` передают значения по осям ординат и абсцисс, `**kwargs` используется для передачи параметров в метод `stem()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1280x320 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 40\n",
    "# time vector\n",
    "t = np.linspace(0, 1, n, endpoint=True)\n",
    "# sine wave\n",
    "x = np.sin(np.pi*t) + np.sin(2*np.pi*t) + np.sin(3*np.pi*t) + np.sin(5*np.pi*t)\n",
    "\n",
    "# Select: plot, stem, bar\n",
    "def plt_sel(s, *args, **kwargs):\n",
    "    if s == 0:\n",
    "        return plt.plot(*args)\n",
    "    if s == 1:\n",
    "        return plt.stem(*args, **kwargs)\n",
    "    if s == 2:\n",
    "        return plt.step(*args)\n",
    "\n",
    "# Subplot titles\n",
    "t_titles = ['Аналоговый', 'Дискретный', 'Квантованный']\n",
    "\n",
    "# Plot figures\n",
    "fig = plt.figure(figsize=(16, 4), dpi=80)\n",
    "for i in range(3):\n",
    "    plt.subplot(1, 3, i+1)\n",
    "    plt.title(t_titles[i]) \n",
    "    plt_sel(i, t, x, use_line_collection=True)\n",
    "    plt.xlim([0, 1])\n",
    "    plt.yticks(np.linspace(np.floor(np.min(x)), np.ceil(np.max(x)), 9))\n",
    "    plt.grid(True)\n",
    "    \n",
    "    # change plot view\n",
    "    ax = plt.gca()\n",
    "    ax.spines['right'].set_color('none')\n",
    "    ax.spines['top'].set_color('none')\n",
    "    ax.spines['bottom'].set_position(('data',0))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Если шаг квантования и дискретизации выбраны неправильно, преобразование сигнала из аналоговой формы в дискретную будет происходить с искажениями. Покажем на примере неграмотный выбор шага дискретизации и шага квантования.\n",
    "\n",
    "Зададим график синуса. Длина сигнала `n = 64` отсчетов, на которых укладывается один период гармонического сигнала. Установим шаг квантования таким образом, чтобы иметь выборку из `d = 3, 5, 8 и 32` отсчетов."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 960x480 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 64\n",
    "# time vector\n",
    "t = np.linspace(0, 1, n, endpoint=True)\n",
    "# sine wave\n",
    "ds = np.sin(2*np.pi*t)\n",
    "\n",
    "# discrete step\n",
    "step_lst = np.array([3, 5, 8, 32])\n",
    "\n",
    "#plot figure\n",
    "fig = plt.figure(figsize=(12, 6), dpi=80)\n",
    "for i in range(4):\n",
    "    tt = np.linspace(0, 1, step_lst[i], endpoint=True)\n",
    "    \n",
    "    plt.subplot(2, 2, i+1)\n",
    "    plt.title('Number of points = {}'.format(step_lst[i]))\n",
    "    plt.plot(t, ds, '-', linewidth=2.0)\n",
    "    plt.plot(tt, np.sin(2*np.pi*tt), '--o', linewidth=1.5, markersize=8)\n",
    "    plt.step(tt, np.sin(2*np.pi*tt), linewidth=1.5)\n",
    "    plt.grid()\n",
    "    plt.xlim([0, 1])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как видно, наихудшая форма сигнала получилась при большом значении шага дискретизации, то есть большом расстоянии между соседними отсчетами цифрового сигнала. \n",
    "Чем меньше расстояние между соседними отсчетами (меньше шаг дискретизации и больше число точек последовательности), тем лучше дискретный сигнал повторяет форму аналогового сигнала.\n",
    "____"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Дискретные последовательности\n",
    "\n",
    "**Дискретной последовательностью** называется математическая модель дискретного сигнала, представляющая собой решетчатую функцию: x(nT) = x(n), где *T* – интервал дискретизации, *n* = 0, 1, 2, ..., N-1 - отсчёты или сэмплы. \n",
    "\n",
    "Пример конечной дискретной последовательности `x(nT) = {2, 1, -2, 0, 2, 3, 1, 0}`. Данная последовательность выглядит, как показано на рисунке:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1280x320 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Digital signal\n",
    "xt = np.array([2, 1, -2, 0, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n",
    "# Time vector\n",
    "t = np.linspace(0, xt.size-1, xt.size, endpoint=True)\n",
    "\n",
    "# Plot figure\n",
    "fig = plt.figure(figsize=(16, 4), dpi=80)\n",
    "plt.title('Digital signal') \n",
    "plt.stem(t, xt, linefmt='C3', markerfmt='D', use_line_collection=True)\n",
    "plt.xticks(t)\n",
    "plt.xlim([np.min(t)-0.2, np.max(t)+0.2])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Дельта-функция\n",
    "\n",
    "**Единичный импульс** – простейшая дискретная последовательность. Это дискретная δ-функция δ(nT) *Дирака*, которая равна единице при n = 0 и нулю при всех остальных значениях n.\n",
    "\n",
    "Дискретная δ-функция, смещенная во времени на **m** тактовых интервалов, записывается следующим образом: `δ(nT-mT)`.\n",
    "\n",
    "### Единичный скачок\n",
    "\n",
    "Единичный скачок или **функция Хевисайда** – еще один вид простых и важных дискретных последовательностей. Он принимает нулевые значения в отрицательной области времени и единичные значения в положительной. \n",
    "\n",
    "Математически функция единичного скачка записывается как: \n",
    "\n",
    "$$ \\sigma(nT) = \\delta(nT) + \\delta(nT - T) + \\delta(nT – 2T) + \\cdots \\tag{1.5}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 960x240 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 6\n",
    "# time vector\n",
    "t = np.linspace(-n, n-1, 2*n)\n",
    "\n",
    "# Delta function\n",
    "xd = np.zeros(2*n)\n",
    "xd[n] = 1\n",
    "\n",
    "# Heaviside function\n",
    "xh = np.heaviside(t, 1)\n",
    "\n",
    "# Combine them together\n",
    "xs = [xh, xd]\n",
    "\n",
    "# Plot results\n",
    "fig = plt.figure(figsize=(12, 3), dpi=80)\n",
    "for i, sig in enumerate(xs):\n",
    "    plt.subplot(1, 2, i+1)\n",
    "    plt.stem(t, sig, linefmt='C3', markerfmt='D', use_line_collection=True)\n",
    "    plt.ylabel('Amplitude')\n",
    "    plt.xlabel('Samples')\n",
    "    plt.xticks(t)\n",
    "    plt.xlim([np.min(t)+1, np.max(t)])\n",
    "    plt.grid(True)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Дискретный единичный скачок `σ(n)` и дискретная δ-функция `δ(n)` связаны между собой следующими соотношениями:\n",
    "\n",
    "$$ \\delta(nT) = \\sigma(nT) - \\sigma(nT-T) \\tag{1.6}$$\n",
    "\n",
    "$$ \\sigma(nT) = \\sum_{k=0}^{+\\infty}\\delta(nT-kT) ) \\tag{1.7}$$\n",
    "\n",
    "Произвольная дискретная последовательность может быть записана в виде взвешенной суммы дельта-функций:\n",
    "\n",
    "$$ x(nT) = \\sum_{k=0}^{+\\infty}x(kT)\\cdot\\delta(nT-kT) ) \\tag{1.8}$$\n",
    "\n",
    "Последовательность x(nT) называется периодической, если она удовлетворяет условию $ x(nT) = x(nT+mNT) $, где \n",
    "- m и N – целые числа, m = 0, 1, 2, ..., NT \n",
    "- *NT* – период дискретной последовательности. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Z-преобразование\n",
    "\n",
    "Дискретные последовательности очень удобно описывать с помощью **Z-формы** или Z-преобразований. \n",
    "\n",
    "*Z-преобразование* – аналог преобразования Лапласа в дискретной форме. Для дискретной последовательности x(nT) одностороннее Z-преобразование  определяется следующим рядом:\n",
    "\n",
    "$$ X(z) = Z |x(nT)| = \\sum_{n=0}^{\\infty}x(nT)z^{-n} ) \\tag{1.9}$$\n",
    "\n",
    "где $z = Re(z) + j \\cdot Im(z)$ - комплексная функция, X(z) - это Z-форма последовательности x(nT).\n",
    "\n",
    "Z-преобразование связано с преобразованием Лапласа через формулу:\n",
    "\n",
    "$$ z = e^{sT} \\tag{1.10}$$\n",
    "\n",
    "### Свойства Z-преобразования\n",
    "\n",
    "1. **Линейность**\n",
    "\n",
    "Если последовательность x(nT) можно представить в виде линейной комбинации\n",
    "$$ x(nT) = a \\cdot x_1(nT) + b \\cdot x_2(nT) \\tag{1.11}$$\n",
    "\n",
    "то $$ X(z) = a \\cdot X_1(z) + b\\cdot X_2(z) \\tag{1.12}$$\n",
    "\n",
    "Иными словами, Z-преобразование суммы сигналов равно сумме z-образов этих сигналов.\n",
    "\n",
    "2. **Задержка (сдвиг по времени)**\n",
    "\n",
    "$$ Z[x(nT-mT)] = z^{-m} \\cdot X(z) \\tag{1.13}$$\n",
    "\n",
    "Задержка входного сигнала на m вносит добавочный множитель $z^{-m}$. \n",
    "\n",
    "3. **Свертка**\n",
    "\n",
    "Для последовательности y(nT) свертка двух последовательностей равна:  \n",
    "\n",
    "$$ y(nT) = \\sum_{m=0}^{\\infty}x_{1}(mT) \\cdot x_{2}(nT-mT) \\tag{1.14}$$\n",
    "\n",
    "или  \n",
    "\n",
    "$$ y(nT) = \\sum_{m=0}^{\\infty}x_{2}(mT) \\cdot x_{1}(nT-mT) \\tag{1.15}$$  \n",
    "\n",
    "А для Z-формы:\n",
    "\n",
    "$$ Y(z) = X_{1}(z) \\cdot X_{2}(z) \\tag{1.16}$$  \n",
    "\n",
    "Z-преобразование свёртки сигналов равно произведению их Z-образов.\n",
    "\n",
    "____\n",
    "\n",
    "Если входной сигнал x(nT) представить в виде взвешенной суммы δ-функций, то Z-форма принимает вид  \n",
    "\n",
    "$$ X(z) = \\sum_{k=0}^{\\infty}x(kT) \\cdot z^{-k} \\tag{1.17}$$  \n",
    "\n",
    "\n",
    "### Примеры\n",
    "\n",
    "1. Записать Z-форму для последовательности `x(nT) = {1,2,3,4,5}` \n",
    "\n",
    "$X(z) = 1 + 2z^{-1} + 3z^{-2} + 4z^{-3} + 5z^{-4}$.  \n",
    "\n",
    "2. Записать Z-форму для последовательности в виде единичного скачка $ \\sigma(nT) $.\n",
    "\n",
    "$X(z) = 1 + z^{-1} + z^{-2} + z^{-3} + z^{-4} + ... = \\frac{1}{(1-z^{-1})}$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 960x320 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Digital signal\n",
    "xt = np.arange(30)\n",
    "\n",
    "# Plot figure\n",
    "fig = plt.figure(figsize=(12, 4), dpi=80)\n",
    "plt.title('Digital signal') \n",
    "plt.stem(xt, linefmt='C2', markerfmt='D', use_line_collection=True)\n",
    "plt.ylabel('Amplitude')\n",
    "plt.xlabel('Samples')\n",
    "plt.xticks(xt)\n",
    "plt.xlim([np.min(xt)-0.2, np.max(xt)+0.2])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В следующих главах мы познакомимся с различными формами сигналов, а также с операциями над ними: фильтрация, свёртка, преобразования в частотную область и обратно."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}