DFT.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "# 複素数の出力の調整\n",
    "np.set_printoptions(formatter={'complexfloat':' {0.real:4.2f}{0.imag:+4.2f}i'.format})\n",
    "\n",
    "# 個数\n",
    "N = 6\n",
    "\n",
    "# 入力\n",
    "f = np.sin(np.arange(N))\n",
    "\n",
    "# 回転子\n",
    "w  = np.exp(- 2 * np.pi / N * 1j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.18+0.00i  -0.28-3.00i  0.12-0.12i  0.13+0.00i  0.12+0.12i  -0.28+3.00i]\n"
     ]
    }
   ],
   "source": [
    "# 1 : for loop\n",
    "F = np.zeros(N, dtype=complex)\n",
    "\n",
    "for k in range(N):\n",
    "    for n in range(N):\n",
    "        F[k] += f[n] * w **(n * k)\n",
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.18+0.00i  -0.28-3.00i  0.12-0.12i  0.13+0.00i  0.12+0.12i  -0.28+3.00i]\n"
     ]
    }
   ],
   "source": [
    "# 2 : Matrix(1)\n",
    "# 変換行列\n",
    "W = np.zeros([N,N], dtype=complex)\n",
    "\n",
    "for n in range(N):\n",
    "    for k in range(N):\n",
    "        W[n, k] = w **( n * k)\n",
    "        \n",
    "F = W @ f\n",
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.18+0.00i  -0.28-3.00i  0.12-0.12i  0.13+0.00i  0.12+0.12i  -0.28+3.00i]\n"
     ]
    }
   ],
   "source": [
    "# 3 : Matrix(2)\n",
    "k = np.tile(np.arange(N),[N,1])\n",
    "n = k.T\n",
    "W = w**(n*k)\n",
    "\n",
    "F = W @ f\n",
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.18+0.00i  -0.28-3.00i  0.12-0.12i  0.13-0.00i  0.12+0.12i  -0.28+3.00i]\n"
     ]
    }
   ],
   "source": [
    "print(np.fft.fft(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}