{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "这一章开始,我们将从频域分析离散时间信号和系统.\n", "\n", "# DTFT变换\n", "\n", "序列$x[n]$的离散时间傅里叶变换(DTFT)$X(e^{j\\\\omega})$\n", "\n", "$$\n", "X\\left(e^{j \\omega}\\right)=\\sum_{n=-\\infty}^{\\infty} x[n] e^{-j \\omega n}\n", "$$\n", "\n", "通常$X(e^{j\\\\omega})$是实变量$\\\\omega$的一个复函数,可以写成\n", "\n", "$$\n", "X\\left(e^{j \\omega}\\right)=X_{r e}\\left(e^{j \\omega}\\right)+j X_{im}\\left(e^{j \\omega}\\right)\n", "$$\n", "\n", "其中$X_{r e}\\\\left(e^{j \\\\omega}\\\\right)$和$X_{im}\\\\left( e^{j \\\\omega}\\\\right)$分别是$X(e^{j\\\\omega})$的实部和虚部,它们都是$\\\\omega$的实函数.$X(e^{j\\\\omega})$也可以表示为\n", "\n", "$$\n", "X\\left(e^{j \\omega}\\right)=\\left\\vert X\\left(e^{j \\omega}\\right)\\right\\vert e^{j \\theta(\\omega)}\n", "$$\n", "\n", "其中,\n", "\n", "$$\n", "\\theta(\\omega)=\\arg \\left\\{X\\left(e^{j \\omega}\\right)\\right\\}\n", "$$\n", "\n", "$\\\\left\\\\vert X\\\\left(e^{j \\\\omega}\\\\right)\\\\right\\\\vert$称为幅度函数,$\\\\theta(\\\\omega)$称为相位函数,这两个函数都是$\\\\omega$的实函数.\n", "\n", "\n", "当DTFT变换形式如下类似如下时,可以通过freqz计算DTFT变换\n", "\n", "$$\n", "X\\left(e^{\\jmath \\omega}\\right)=\\frac{p_{0}+p_{1} e^{-j \\omega}+\\cdots+p_{M} e^{-j \\omega M}}{d_{0}+d_{1} e^{-j \\omega}+\\cdots+d_{N} e^{-j \\omega N}}\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Image Part')" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy import signal\n", "\n", "# 离散时间傅里叶变换\n", "w = np.arange(-4*np.pi,4*np.pi,8*np.pi/511)\n", "num = np.array([2,1])\n", "den = np.array([1,-0.6])\n", "\n", "ws, h = signal.freqz(num,a=den,whole=True)\n", "# 离散时间傅里叶变换的实部和虚部\n", "plt.subplot(121)\n", "plt.plot(ws,np.real(h))\n", "plt.title('Real Part')\n", "plt.subplot(122)\n", "plt.plot(ws,np.imag(h))\n", "plt.title('Image Part')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Phase Spectrum')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# 离散时间傅里叶变换的幅度谱和相位谱\n", "plt.subplot(121)\n", "plt.plot(ws,np.abs(h))\n", "plt.title('Amplitude Spectrum')\n", "plt.subplot(122)\n", "plt.plot(ws,np.angle(h))\n", "plt.title('Phase Spectrum')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 离散时间傅里叶变换的收敛性\n", "\n", "### 指数序列\n", "\n", "指数序列定义为\n", "\n", "$$\n", "x[n] = A \\alpha ^n \\mu[n]\n", "$$\n", "\n", "其中,$A$和$\\\\alpha$是任意的实数或者复数,表示为\n", "\n", "$$\n", "\\alpha = e^{\\sigma_0+j\\omega_0} \\quad A = |A|e^{j\\phi}\n", "$$\n", "\n", "其离散时间傅里叶变换为\n", "\n", "$$\n", "\t\\begin{split}\n", "\t\tX(e^{j\\omega})&=|A|e^{j\\phi}\\sum_{n=-\\infty}^{\\infty} \\alpha^n \\mu[n] e^{-j\\omega n} = |A|e^{j\\phi}\\sum_{n=0}^{\\infty} \\alpha^n e^{-j\\omega n} \\\\\n", "\t\tX(e^{j\\omega})&= \\frac{|A|e^{j\\phi}}{1-\\alpha e^{-j\\omega}}\n", "\t\t\\end{split}\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# 产生一个指数序列:sigma=-0.5,w0=0.15,phi=0.2,|A|=10\n", "N = 100\n", "n = np.arange(N) # 定义序号\n", "w0=0.15\n", "phi=0.5\n", "A=2\n", "sigma=-0.5 # try some value of sigma >0\n", "en = A*np.exp(sigma*n+1j*(2*np.pi*n*w0+phi))\n", "\n", "ws, h = signal.freqz(en,whole=True)\n", "# 离散时间傅里叶变换的实部和虚部\n", "plt.subplot(121)\n", "plt.plot(ws,np.real(h))\n", "plt.title('Real Part')\n", "plt.subplot(122)\n", "plt.plot(ws,np.imag(h))\n", "plt.title('Image Part')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sinc序列与矩形窗频谱\n", "\n", "$$\n", " h_{LP}[n] = \\frac{\\sin \\omega_c n}{\\omega_c n} \\longleftrightarrow H_{LP}(e^{j\\omega}) = \\begin{cases}\n", "\t\t1, & \\quad 0\\leq |\\omega| \\leq \\omega_c\\\\\n", "\t\t0, & \\quad \\omega_c \\leq |\\omega| \\leq \\pi\n", "\t\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/lyu/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in true_divide\n", " \n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Sinc函数和矩形窗\n", "N = 2000 # increase N, then the spectrum converge to window function\n", "Nc = np.int(N/2)\n", "\n", "n = np.arange(N) # 定义序号\n", "w0=0.6\n", "phi=np.pi\n", "sinc = np.sin(w0*(n-N/2))/np.pi/(n-N/2)\n", "sinc[Nc]=w0/np.pi\n", "sinc = sinc*np.exp(1j*phi*n)\n", "\n", "ws, h = signal.freqz(sinc,whole=True)\n", "# 离散时间傅里叶变换的实部和虚部\n", "plt.subplot(121)\n", "plt.plot(ws,np.abs(h))\n", "plt.title('Amplitude')\n", "plt.subplot(122)\n", "plt.plot(ws,np.angle(h))\n", "plt.title('Phase')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 常数序列\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Sinc函数和矩形窗\n", "N = 20 # increase N, \n", "Nc = np.int(N/2)\n", "\n", "n = np.arange(N) # 定义序号\n", "w0=0.6\n", "phi=np.pi\n", "x = np.ones([N,])/N\n", "\n", "ws, h = signal.freqz(x,whole=True)\n", "# 离散时间傅里叶变换的实部和虚部\n", "plt.subplot(121)\n", "plt.plot(ws,np.real(h))\n", "plt.title('Real part')\n", "plt.subplot(122)\n", "plt.plot(ws,np.imag(h))\n", "plt.title('Image part')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 离散时间傅里叶变换的性质\n", "\n", "\n", "### 时移定理" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "num = np.array([1,2,3,4,5,6,7,8,9])\n", "ws, h1 = signal.freqz(num,whole=True)\n", "D = 10\n", "ws, h2 = signal.freqz(np.concatenate((np.zeros([D,]),num),axis=0),whole=True)\n", "plt.subplot(221)\n", "plt.plot(ws,np.abs(h1))\n", "plt.subplot(222)\n", "plt.plot(ws,np.abs(h2))\n", "plt.subplot(223)\n", "plt.plot(ws,np.angle(h1))\n", "plt.subplot(224)\n", "plt.plot(ws,np.angle(h2))\n", "# 幅度谱不变,相位谱变化" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 频移定理\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "num = np.array([1,3,5,7,9,11,13,15,17])\n", "n = np.arange(len(num))\n", "w0 = 0.4*np.pi # 尝试改变这个大小,然后观察显示的图形, 并结合理论分析\n", "num1 = np.exp(1j*w0*n)*num\n", "ws, h1 = signal.freqz(num,whole=True)\n", "ws, h2 = signal.freqz(num1,whole=True)\n", "\n", "plt.subplot(221)\n", "plt.plot(ws,np.abs(h1))\n", "plt.subplot(222)\n", "plt.plot(ws,np.abs(h2))\n", "plt.subplot(223)\n", "plt.plot(ws,np.angle(h1))\n", "plt.subplot(224)\n", "plt.plot(ws,np.angle(h2))\n", "# 幅度谱和相位谱平移" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### 卷积定理\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# 时域卷积,频域相乘\n", "num1 = np.array([1,3,5,7,9,11,13,15,17])\n", "num2 = np.array([1,-2,3,-2,1])\n", "\n", "y = signal.convolve(num1,num2)\n", "ws, h1 = signal.freqz(num1,whole=True)\n", "ws, h2 = signal.freqz(num2,whole=True)\n", "ws, h3 = signal.freqz(y,whole=True)\n", "\n", "hp = h1*h2\n", "\n", "\n", "plt.subplot(221)\n", "plt.plot(ws,np.abs(h3))\n", "plt.subplot(222)\n", "plt.plot(ws,np.abs(hp))\n", "plt.subplot(223)\n", "plt.plot(ws,np.angle(h3))\n", "plt.subplot(224)\n", "plt.plot(ws,np.angle(hp))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 调制定理\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# 时域乘积,频域卷积\n", "num1 = np.array([1,3,5,7,9,11,13,15,17])\n", "num2 = np.array([1,-1,1,-1,1,-1,1,-1,1])\n", "\n", "y = num1*num2\n", "ws, h1 = signal.freqz(num1,whole=True)\n", "ws, h2 = signal.freqz(num2,whole=True)\n", "ws, h3 = signal.freqz(y,whole=True)\n", "\n", "# hp = signal.convolve(h1,h2)\n", "# hp = hp[:(len(ws))]/len(ws)\n", "\n", "plt.subplot(131)\n", "plt.plot(ws,np.abs(h1))\n", "plt.subplot(132)\n", "plt.plot(ws,np.abs(h2))\n", "plt.subplot(133)\n", "plt.plot(ws,np.abs(h3))\n", "# plt.subplot(224)\n", "# plt.plot(ws,np.angle(hp))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### 翻转定理" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# 时域翻转,频域翻转\n", "num1 = np.array([1,3,5,7,9])\n", "w0 = 5\n", "num1 = num1*np.exp(np.arange(len(num1))*1j*w0)\n", "num2 = np.flipud(num1)\n", "\n", "\n", "ws, h1 = signal.freqz(num1,whole=True)\n", "ws, h2 = signal.freqz(num2,whole=True)\n", "\n", "\n", "plt.subplot(221)\n", "plt.plot(ws,np.abs(h1))\n", "plt.subplot(222)\n", "plt.plot(ws,np.abs(h2))\n", "plt.subplot(223)\n", "plt.plot(ws,np.angle(h1))\n", "plt.subplot(224)\n", "plt.plot(ws,np.angle(h2))\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Raw Cell Format", "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 }