信號與系統(tǒng)》仿真實(shí)驗(yàn)實(shí)驗(yàn)指示書要點(diǎn)

1、1實(shí)驗(yàn)二實(shí)驗(yàn)二信號的頻譜分析信號的頻譜分析2系統(tǒng)仿真的要點(diǎn) 關(guān)于快速傅立葉變換的關(guān)于快速傅立葉變換的fft函數(shù)的函數(shù)的調(diào)用調(diào)用 頻譜分析舉例頻譜分析舉例3一一、fft函數(shù)的調(diào)用函數(shù)的調(diào)用 fft(x)DFT的的快速算法快速算法 （1） 數(shù)據(jù)長度為數(shù)據(jù)長度為N； 若若N為為2的整數(shù)次冪，則是基的整數(shù)次冪，則是基-2的的 DFT，運(yùn)算速度較快；，運(yùn)算速度較快； 若若N不為不為2的整數(shù)次冪，則運(yùn)算速的整數(shù)次冪，則運(yùn)算速 度較慢。度較慢。 （2）若數(shù)據(jù)實(shí)際長度小于）若數(shù)據(jù)實(shí)際長度小于N，則自動補(bǔ)，則自動補(bǔ) 一些零，使之長度等于一些零，使之長度等于N.4 復(fù)指數(shù)座標(biāo)復(fù)指數(shù)座標(biāo) 正變換正變換 反變換反變換

2、 其中其中NnnkNWnxkX1) 1() 1(NnnkNWkXnx1) 1() 1(NjNeW25 fft(x) 或或fft(x,N)的調(diào)用編程的調(diào)用編程00.10.20.30.40.50.60.70.80.91-20-1001020304050t=(0:1/255:1);x=exp(-0.9)*sin(2*pi*60*t);y=fft(x);ry=real(y);a=abs(y);plot(t,ry,r-,t,a,b-);grid這里是歸一化頻率6利用fft計算功率譜的函數(shù)演示fftdemo（1）產(chǎn)生信號）產(chǎn)生信號（2）調(diào)用函數(shù)計算頻率特性）調(diào)用函數(shù)計算頻率特性(fft)（3）計算功率譜）

3、計算功率譜(Pyy)（4）顯示結(jié)果）顯示結(jié)果7(1)(1)產(chǎn)生信號產(chǎn)生信號 運(yùn)行軟件Matlab, 進(jìn)入Matlab Comand Windows 運(yùn)行運(yùn)行fftdemo命令，該程序是按照一步命令，該程序是按照一步一步的斷點(diǎn)執(zhí)行的，它能一邊顯示注解，一步的斷點(diǎn)執(zhí)行的，它能一邊顯示注解，一邊給出每一步的結(jié)果，所以我們根據(jù)一邊給出每一步的結(jié)果，所以我們根據(jù)這個演示，能學(xué)會這個演示，能學(xué)會fft函數(shù)的調(diào)函數(shù)的調(diào) 用及其有關(guān)應(yīng)用技巧。用及其有關(guān)應(yīng)用技巧。8 To get started, type one of these commands: helpwin, helpdesk, or demo. F

4、or information on all of the MathWorks products, type tour. ?fftdemoclc% This example shows the use of the FFT function for spectral % analysis. A common use of FFTs is to find the frequency% components of a signal buried in a noisy time domain signal.%9 要求產(chǎn)生一個時間從0到250毫秒的，含有噪聲的，頻率為50到120Hzde 時域信號, 噪

5、聲的標(biāo)準(zhǔn)差為2。離散信號的時間間隔為1毫秒。 程序如下：t = 0:.001:.25;x = sin(2*pi*50*t) + sin(2*pi*120*t);y = x + 2*randn(size(t);plot(y(1:50), title(Noisy time domain signal), 10% First we need to create some data. Consider data sampled at% 1000 Hz. We start by forming a time axis for our data, running% from t=0 until t=.25

6、 in steps of 1 millisecond:t = 0:.001:.25;pause % Strike any key to continue.11pause % Strike any key to continue.% Next we can form a signal containing 50 Hz and 120 Hz:x = sin(2*pi*50*t) + sin(2*pi*120*t);pause % Strike any key to continue.12% and add some random noise with a standard deviation of

7、 2 to % produce a noisy signal y:y = x + 2*randn(size(t);pause % Strike any key to continue.plot(y(1:50), title(Noisy time domain signal), pause0204060-505Noisy time domain signal13（2）函數(shù)調(diào)用計算頻率特性）函數(shù)調(diào)用計算頻率特性計算計算功率譜以及顯示結(jié)果功率譜以及顯示結(jié)果 Y = fft(y,256); Pyy = Y.*conj(Y)/256; f = 1000/256*(0:127); plot(f,Pyy(1

8、:128), title(Power spectral density), .繪制頻譜之前先設(shè)定頻率軸NYYPyy/*只繪出前128點(diǎn)另一半對折14clc% Clearly, it is difficult to identify the frequency components% from looking at the original signal; thats why spectral analysis% is so popular.% Finding the discrete Fourier transform of the noisy signal y% is easy; we ju

9、st take the fast-Fourier transform (FFT) :Y = fft(y,256);pause % Strike any key to continue.15% The power spectral density, a measurement of the energy at% various frequencies, is found with:Pyy = Y.*conj(Y)/256;pause % Strike any key to continue.計算功率譜計算功率譜(Pyy)計算頻率軸計算頻率軸16Y=;y=;clc% To plot the pow

10、er spectral density, we must first form a % frequency axis:f = 1000/256*(0:127);% which we do for the first 127 points. (The remainder of the 256% points are symmetric.) We can now plot the power spectral% density:pause % Strike any key for plot.17plot(f,Pyy(1:128), title(Power spectral density), .0

11、200400600020406080Power spectral densityFrequency (Hz)（4）顯示結(jié)果）顯示結(jié)果18ZOOM plot(f(1:50),Pyy(1:50), title(Power spectral density), . echo off End 以上程序是Matlab 提供的fftdemo演示舉例，同學(xué)們跟著它執(zhí)行一遍，有助于理解和掌握。利用zoom把感興趣的部分放大顯示19% Lets zoom in and plot only up to 200 Hz:pause % Strike any key for plot.plot(f(1:50),Pyy(1:50), title(P