{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "fd6fde37",
   "metadata": {},
   "source": [
    "## What are the key parameters for a Pulsar Observation?\n",
    "\n",
    "### Pulsar Target:\n",
    "Spsr:  Strength of the radio signal from the pulsar in Janskys (Watts per square meter per Hz) \n",
    "\n",
    "P: Pulse Period in seconds\n",
    "\n",
    "W: Pulse width in seconds\n",
    "\n",
    "### Telescope:\n",
    "Tsys: System Temperature, a measure of the background noise level of the telescope Kelvin (K)\n",
    "\n",
    "Gain: proportional to the size (collecting area) of the telescope dish and the performance of the amplifier (K per Jansky)\n",
    "\n",
    "Npol: Number of polerisations obsereved (generally 2)\n",
    "\n",
    "Bw:  Bandwidth of the receiver in MHz\n",
    "\n",
    "### Variable parameters:\n",
    "Tint: Integration time or duration of the observation in seconds\n",
    "\n",
    "S/N: Signal to noise ratio, how much of a signal do we need for a detection\n",
    "\n",
    "### These parameters are related by the radiometer equation:\n",
    "\n",
    "## Tint = ((Tsys*(S/N))/(G*Spsr*(Npol*BW)-2))(w/(P-W))2\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c6c8c93b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# To begin, we import some libraries that we will need later.\n",
    "from __future__ import print_function\n",
    "\n",
    "# The numpy library will allow us to do FFTs\n",
    "import numpy as np\n",
    "#import scipy\n",
    "#from astropy import coordinates as coord\n",
    "#from astropy import units as u\n",
    "#from astropy import constants as const\n",
    "#from astropy import time as astrotime\n",
    "# pi is a useful value!\n",
    "#from math import pi\n",
    "\n",
    "# The pyplot module from matplotlib will allow us to plot things.\n",
    "from  matplotlib import pyplot as plt\n",
    "import matplotlib\n",
    "from matplotlib.font_manager import FontProperties\n",
    "\n",
    "# This will tell matplotlib that we want to include the plots on our notebook, rather than in a new window.\n",
    "%matplotlib inline\n",
    "\n",
    "# Here you can control the font for the plots.\n",
    "font = {'family' : 'serif',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 12}\n",
    "matplotlib.rc('font', **font)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9efc1f8c",
   "metadata": {},
   "source": [
    "\n",
    "Now a routine to calculate the integration time using the radiometer equation \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "65c5558c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def PulsarTint(SysTemp,TGain,TPol,TBw,SNR,Period,Pw,Pflux):\n",
    "    Tint = 0  \n",
    "    if Pw == 0 :\n",
    "        Pw=Period/10  # If no W10 pulse width assume 10% value\n",
    "    a=SNR*SysTemp\n",
    "    b=TGain*Pflux*((TPol*TBw)**0.5)\n",
    "    c= (Pw/(Period-Pw))**0.5\n",
    "    Tint=(a/b*c)**2\n",
    "    return int(np.ceil(Tint))    # Round up value to whole seconds\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "864f68ba",
   "metadata": {},
   "source": [
    "\n",
    "Now we will provide the Kuntunse / Ghana values for the Tint Calculation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "82f6f8b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "Tsys=125\n",
    "Npol=2\n",
    "Gain=0.17\n",
    "BandW=75\n",
    "SNR=10\n",
    "\n",
    "PulsarAFlux=201\n",
    "PulsarAPeriod=89.328\n",
    "PulsarAWidth=1.4\n",
    "\n",
    "PulsarBFlux=26.5 \n",
    "PulsarBPeriod=714.52 \n",
    "PulsarBWidth=6.6\n",
    "\n",
    "values=(5)\n",
    "TintA1 = np.zeros(values)  # Tint times for pulsar A - base case (Kuntunse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b14ba427",
   "metadata": {},
   "source": [
    "\n",
    "### Now calculate the integration times for different Signal to Noise ratios\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f148123",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}