{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 正弦信号采样的混叠现象\n", "\n", "以下程序用Python语言编写。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "对于两个频率分别为$f_1$和$f_2$的正弦信号,\n", "\n", "$$\n", "x_1(t) = \\sin(2\\pi f_1 t)\n", "$$\n", "\n", "$$\n", "x_2(t) = \\sin(2\\pi f_2 t)\n", "$$\n", "\n", "分别以相同的频率$f_s$进行采样,得到两个序列$x_1[n]$和 $x_2[n]$。\n", "\n", "那么,当$f_1 + f_2 = k*f_s, \\ k\\in \\mathbb{Z}$时,满足\n", "\n", "$$\n", "x_1[n] = x_2[n]\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib.pyplot import *\n", "from numpy import *" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fs = 1.3 # 采样频率为 3Hz\n", "\n", "f1 = 0.5 # 产生频率为 10Hz 的正弦信号\n", "f2 = f1 + fs # 取 k = 1\n", "\n", "dT = 0.001\n", "t = arange(0,2*pi,dT)\n", "\n", "figure(figsize=(10,5))\n", "plot(t,sin(2*pi*f1*t),'-r')\n", "plot(t,sin(2*pi*f2*t),'-m')\n", "\n", "dT = 1/fs\n", "ts = arange(0,2*pi,dT)\n", "plot(ts,sin(2*pi*f1*ts),'bs')\n", "\n", "legend({'Sin with f_1','Sin with f_2','Samples'})\n", "show()" ] }, { "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }