{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ZADANIE 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) Wykonaj poniższy skrypt i przeanalizuj go:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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c/0vsOCZ3NEmSJEn9HPmuhNtvh64u4uSTmdTWxJSJLUxqa7J4q2IionitzXwP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\niIiIyCBT8S0iIiIiIiIyyP4XKiYRBTl4eVsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1051d95c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "from pylab import *\n",
    "from numpy import *\n",
    "from scipy import *\n",
    "from ipywidgets import *\n",
    "import math as mt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "A = 1\n",
    "# Amplituda sygnału\n",
    "\n",
    "LP = 1 \n",
    "# Liczba analizowanych pełnych przebiegów sygnału (okresów)\n",
    "w = 40           \n",
    "# czśstotliwość probkowania [Hz] sygnału \n",
    "#(jak często w ciągu sekundy pobieramy informacje o wartości sygnału)\n",
    "\n",
    "f = 2.0           \n",
    "# Czestotliwosc sygnalu [Hz]\n",
    "\n",
    "T = 1.0/f        \n",
    "# Okres sygnalu [s] (jak długo trwa jeden przebieg sinusa)\n",
    "\n",
    "TW = 1.0/w        \n",
    "# Okres probkowania [s] (co ile sekund pobieramy próbkę)\n",
    "\n",
    "t = np.arange(0, LP*T, TW)\n",
    "# generujemy momenty, w których pobieramy próbki\n",
    "\n",
    "n = len(t)\n",
    "    \n",
    "FUNC = lambda t : A*sin(2*pi*t*f)    \n",
    "# def. funkcji (tutaj sinus)\n",
    "\n",
    "signal = FUNC(t)                 \n",
    "# funkcja sprobkowana\n",
    "\n",
    "fig = plt.figure(figsize=(15, 6), dpi=80)   \n",
    "ax = fig.add_subplot(121)\n",
    "## --- POMOCNICZY SYGNAL\n",
    "base_t = np.arange(0, LP*T, 1.0/200.0)\n",
    "base_signal = FUNC(base_t)\n",
    "ax.plot(base_t, base_signal, linestyle='-', color='red')\n",
    "ax.set_ylim([min(base_signal), max(base_signal)])\n",
    "## --- \n",
    "ax.plot(t, signal, 'o')\n",
    "\n",
    "signal1 = fft(signal)\n",
    "# sygnal w dziedzinie czestotliwosci \n",
    "signal1 = abs(signal1)        \n",
    "# modul sygnalu\n",
    "\n",
    "freqs = range(int(n))\n",
    "\n",
    "\n",
    "ax = fig.add_subplot(122)\n",
    "ymax = max(signal1)\n",
    "if (ymax > 3.0):\n",
    "    ax.set_ylim([0.0,ymax])\n",
    "else:\n",
    "    ax.set_ylim([0.0,3.0])\n",
    "stem(freqs, signal1, '-*')\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "UWAGA: do dalszych ćwiczeń warto powyższy skrypt przekształcić na funkcję o wielu argumentach, typu: amplituda, częstotliwość próbkowania, liczba przebiegów. Oczywiście dla wygody, należy nadać wartości domyślne argumentom funkcji."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Zdefiniuj funckję\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "UWAGA DLA CHĘTNYCH: można wykorzystać 'interact', dzięki któremu można zmieniac parametry danej funkcji i na bieżąco obserwować zmiany. Poniższy kod przedstawia sposób wykorzystania interact:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from ipykernel.pylab.backend_inline import flush_figures\n",
    "\n",
    "def prosta(a=2, b=0):\n",
    "    x = linspace(-5, 5, 100, endpoint=False) # punkty na osi OX [s]\n",
    "    f = lambda x : a*x + b\n",
    "    y = f(x)   \n",
    "    \n",
    "    fig = plt.figure(figsize=(6, 3), dpi=80)\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.set_xlim(-5, 5)\n",
    "    ax.set_ylim(-5, 5)\n",
    "    ax.plot(x, y)\n",
    "    flush_figures()\n",
    "    \n",
    "interact(prosta, a=(-5,5,0.5), b=(-5,5,0.5))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Zmień częstotliwość próbkowania na 50Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# w=50"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Punkty na osi OX spektrum są teraz kolejnymi liczbami naturalnymi, a nie częstotliwościami w Hz. Popraw skrypt (funkcje), tak aby oś OX spektrum była w Hz (podpowiedź: oś OX rozpoczyna się od 0Hz, a kończy się na (prawie!)  Hz, gdzie  jest częstotliwością próbkowania). Następnie: Upewnij się, że spektrum dla 1Hz-owego sinusa i pięciu (LP=5) analizowanych przebiegów wygląda teraz prawidłowo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# popraw oś OX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d) Podpisz osie obu wykresów, używając funkcji xlabel() i ylabel(). Pamiętaj o jednostkach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Podpisz osie wykresów"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "f) Porównaj spektrum funkcji $sin(2*pi*f*t)$, $2*sin(2*pi*f*t)$ i $3*sin(2*pi*f*t)$. Jak zmienia się wartość na osi OY na wykresie spektrum?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=1, A=1, LP=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=1, A=2, LP=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# f=1, A=3, LP=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "g) Ile punktów jest na wykresach przy częstotliwości próbkowania 50Hz, T=1s? Zwiększ dwukrotnie liczbę próbek poprzez zwiększenie częstotliwości próbkowania. Następnie: dla $sin(2*pi*f*t)$ porównaj wartość na osi OY spektrum uzyskane w tym oraz poprzednim punkcie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=1, w=50, LP=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=1, w=100, LP=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "h) Na podstawie wyników uzyskanych w dwóch poprzednich punktach przeskaluj oś OY spektrum tak, aby wskazywała wartości amplitud badanych sygnałów. Sprawdź wyniki dla kilku wybranych funkcji."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# popraw oś OY"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Zadanie 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) Wygeneruj spektrum dla funkcji sinus o częstotliwościach 5Hz i 21Hz, dla czestotliwości próbkowania 20Hz i 20 (LP=20) analizowanych przebiegów. Czy rozpoznajesz te funkcje patrząc na ich spróbkowane wykresy? Odczytaj w drugim przypadku uzyskaną częstotliwość z FFT. Dlaczego uzyskano taki wynik?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=5, w=20, LP=20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=21, w=20, LP=20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zwróć uwagę, że spektrum jest symetryczne (poza pierwszym elementem)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Przy w=100Hz, przeanalizuj widma sygnałów:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "i) $sin(2*pi*t*f)$, $f=10Hz$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=10, w=100, A=1, LP=10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ii) $sin(2*pi*t*f)$, $f=20Hz$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=20, w=100, A=1, LP=10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "iii) $sin(2*pi*t*f)$, $f=30Hz$ (tutaj słupki nie będą wyglądać idealnie; dlaczego?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=30, w=100, A=1, LP=10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "iv) $sin(2*pi*t*f)$, $f=40Hz$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=40, w=100, A=1, LP=10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Przy F=50Hz, w=100Hz, wygeneruj spektrum dla $sin(2*pi*f*t)$. Zwróć uwagę na skalę wykresów."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# f=50, w=100, A=1, LP=10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Jak się nazywa twierdzenie, którego konsekwencją jest takie zachowanie się spektrum?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Zadanie 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poniższe przypadki skłądają się z złożonych sygnałów. Trzeba teraz będzie zmodyfikować trochę FUNC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) $sin(2*pi*t*f) + 2*sin(4*pi*t*f)$, T=1s, w=20Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Wyrysuj sygnał"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "c) Wygenerujemy trochę szumu. Wychodząc z funkcji sin(2*pi*t*f), dodamy do niej 100 losowych sinusów. Wygenerujemy dla nich losowo amplitudy (z [0.02, 0.08], częstotliwosci: [5.0, 10.0] oraz modyfikacje fazy[0 + 2*pi]. Inne parametry: w=20Hz, T=1s. Czy dla powyższych paramerów losowania, jesteś w stanie odnaleźć bazowy przebieg (sin(2*pi*t))? Czy jesteś w stanie zlokalizować szum?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d) $0.5 + 2*sin(2*pi*t*f)$, T=1s, w=20Hz. Czy amplituda zerowego prążka jest prawidłowa? Dlaczego? (Podpowiedź: zwróć jeszcze raz uwagę na “symetrię” spektrum)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Wyrysuj sygnał\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "e) $sin(2*pi*t*f)$ oraz $sin(2*pi*t*f + pi/4)$ dla T=1s, w=20Hz. Czy informacja o fazie zniknęła? Poszukaj śladów tej informacji w tablicy, będącej wynikiem operacji fft(signal). (funkcja angle(sygnal, deg=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# faza = 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# faza = pi/4\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Zadanie 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oblicz wynik ifft(fft(x)), gdzie x=random.random(10). Czy jakaś informacja została stracona?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# wygeneruj wektor x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# oblicz fft z x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# oblicz ifft"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#porownaj x z ifft(fft(x)), wystarczy print"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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