{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## 2015/4/14 回答同學之疑問\n", "\n", "問題：y[n]=(x[n])^n 比較delay前後之差別" ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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eWFXfX+RzddTnUcm1wM8lOXH0L+xLgI/1OM/SShLgXcDuqnpb3/MAJPmpJMeNPj8SOAO4\nvs+ZqurPq2pzVT2W4Y/an+k72kmOSnLs6POjgecAvV6xVFV3AHuTPH501zbg5h5HOtDZwAdX22DR\n57gvBI4Brhhd3vLOBT/fQSX5jSR7gVOBjyf5RB9zVNUPgf2/xLQb+Ke+r5IASPJB4IvA45PsTXJO\n3zMBzwR+B/jVsUulzux5pkcCnxmd474KuKyqPt3zTAdahtNxxwOfH/t7+peq+mTPMwG8Cnh/khuB\nJwN/1fM8wI//cdsGfGTV7fwFHElqi0uXSVJjDLckNcZwS1JjDLckNcZwS1JjDLckNcZwS1JjDLck\nNeb/AL5Cq+HQ1lIHAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "n=np.arange(6)\n", "x=np.array([0,1,2,3,4,0])\n", "plt.figure(1)\n", "plt.stem(n,x)\n", "plt.xlim((-2,7))\n", "plt.ylim((0,10))\n", "plt.title('x[n]')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##第一種情形\n", "###先將 x delay " ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n=np.arange(6)\n", "x_n_minus_n0=np.array([0,0,1,2,3,4,])\n", "plt.figure(1)\n", "plt.stem(n,x_n_minus_n0)\n", "plt.xlim((-2,7))\n", "plt.ylim((0,10))\n", "plt.title('x[n-n0]')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "再送入系統" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0 1 2 3 4 5]\n", "[ 1 0 1 8 81 1024]\n" ] } ], "source": [ "w=x_n_minus_n0**n\n", "#plt.stem(n,y)\n", "print n\n", "print w" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 第二種情形\n", "###先送入 x 再將 y delay " ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n\n", "[0 1 2 3 4 5]\n", "x\n", "[0 1 2 3 4 0]\n", "x_n_minus_n0\n", "[0 0 1 2 3 4]\n", "w\n", "[ 1 0 1 8 81 1024]\n", "y\n", "[ 1 1 4 27 256 0]\n", "y_n_minus_n0\n", "[ 0 1 1 4 27 256 0]\n" ] } ], "source": [ "y=x**n\n", "y_n_minus_n0=np.insert(y,0,0)\n", "print 'n'\n", "print n\n", "print 'x'\n", "print x\n", "print 'x_n_minus_n0'\n", "print x_n_minus_n0\n", "print 'w'\n", "print w\n", "print 'y'\n", "print y\n", "print 'y_n_minus_n0'\n", "print y_n_minus_n0\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "結論：\n", "w[n] ==> 第3個時間點為8，是x[2]的3次方\n", "y[n-1] ==> 第3個時間點為4，是x[2]的2次方\n", "或許能回答你的問題" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }