{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pachete necesare pentru folosirea acestui Notebook\n",
    "\n",
    "Vom folosi [numpy](https://numpy.org/), [matplotlib](https://matplotlib.org/), și [sounddevice](https://python-sounddevice.readthedocs.io/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sounddevice as sd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generarea unui semnal sinusoidal\n",
    "\n",
    "Întâi trebuie să definim parametrii sinusoidei continuue:\n",
    "\n",
    "* orizontul de timp ($t$)\n",
    "* frecvența semnalului original ($f_0$)\n",
    "* amplitudinea ($A$)\n",
    "* faza ($\\varphi$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_of_view = 1     # s\n",
    "frequency = 2        # Hz\n",
    "amplitude = 1\n",
    "phase = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Iar apoi parametrii de măsurare, sinusoida discretizată:\n",
    "* frecvența de eșantionare ($f_s$)\n",
    "* perioada de eșantionare ($t_s$)\n",
    "* numărul de eșantionare ($n$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampling_rate = 12    # Hz\n",
    "sampling_period = 1./sampling_rate  # s\n",
    "n_samples = time_of_view/sampling_period"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cu datele de mai sus putem genera orizontul de timp cu momentele de interes pentru semnalul continuu și cel discretizat ($t$, respectiv $nt_s$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "atime = np.linspace (0, time_of_view, int(10e5 + 1)) # s.\n",
    "time = np.linspace (0, time_of_view, int(n_samples + 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Observație*: orizontul de timp continuu (analog) este de fapt un orizont de timp discret ($nt_s$) foarte dens ($n=10^5$ eșantione).\n",
    "\n",
    "Cu aceste date putem crea o funcție sinus ce generează sinusoidele parametrizate conform variabilelor de mai sus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sine (amplitude, frequency, time, phase):\n",
    "    return amplitude * np.sin (2 * np.pi * frequency * time + phase)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sinusoidă continuă\n",
    "Pentru a obține o sinusoidă \"continuă\" putem apela funcția ```sine```:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fce38ed6e20>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "asignal = sine(amplitude, frequency, atime, phase)\n",
    "\n",
    "plt.grid(True)\n",
    "plt.plot (atime, asignal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sinusoidă discretizată\n",
    "Discretizarea se obține apelând aceiași funcție ```sine``` dar cu parametrii discreți și folosind ```stem``` pentru a obține cele $n$ eșantioane:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "signal = sine(amplitude, frequency, time, phase)\n",
    "\n",
    "plt.grid(True)\n",
    "plt.stem (time, signal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Producerea și audiția unui ton\n",
    "\n",
    "Pentru a produce o sinusoidă ce poate fi percepută de urechea umană trebuie să creștem frecvența și amplitudinea acesteia.\n",
    "\n",
    "În exemplul de mai jos generăm o sinusoidă de frecvență $f_0=440\\text{Hz}$ și amplitudine $10.000$ pe care o discretizăm cu frecvența de eșantionare $f_s=44.100\\text{Hz}$ pe un orizont de timp de $2\\text{s}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_of_view = 2     # s\n",
    "frequency = 440      # Hz\n",
    "amplitude = 10000\n",
    "phase = 0\n",
    "\n",
    "sampling_rate = 44100\n",
    "sampling_period = 1./sampling_rate  # s\n",
    "n_samples = time_of_view/sampling_period\n",
    "time = np.linspace (0, time_of_view, int(n_samples + 1))\n",
    "\n",
    "tone = sine(amplitude, frequency, time, phase)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aceast ton îl vom discretiza cu o frecvență de eșantionare $f_s$ conform ```sampling_rate``` și îl vom transforma în formatul WAV prin conversia eșantioanelor la întregi pe 16-biți:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sd.default.samplerate = sampling_rate\n",
    "wav_wave = np.array(tone, dtype=np.int16)\n",
    "sd.play(wav_wave, blocking=True)\n",
    "sd.stop()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sarcini\n",
    "\n",
    "1. [8p] Scrieți tonurile pentru notele muzicale Do, Re, Mi, Fa, Sol, La, Si, Do.\n",
    "\n",
    "2. [8p] Compuneți un cântec simplu clasic (ex. Frère Jacques) într-un singur semnal.\n",
    "\n",
    "3. [4p] Citiți o partitură la intrare (folosind [LilyPond](https://lilypond.org/) sau formatul propriu) și produceți semnalul ce conține melodia la ieșire prin compunerea tonurilor asociate notelor automat."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}