基于加窗FFT的频谱分析

1、基于加窗FFT的频谱分析设 信号为 x(t)=sin( t+10 兀 /180)+0.5sin(3 t+20 兀 /180)+0.5sin(5 t+40 几 /180)+0.4sin(7 t+60 兀 /180)+0.3sin(9 t+80 兀 /180)+0.2sin(11 t+90 兀 /180), 二99 兀。1、分别用矩形窗、汉宁窗、哈明窗、布莱克曼窗 +FFT对信号进行频谱分析，分 析各窗函数对频谱分析的影响；2、在采样频率一定时，增加截断时间长度，分析截断时间长度对频谱分析的影 响；3、在截断时间长度一定时，修改采样频率，分析采样频率对频谱分析的影响；4、给出所有MATLA勰序及相

2、关频谱图.1 .该信号的最高频率fc=544.5Hz,Tcmax=0.02s,为了分析各窗函数对频谱分析的影响，暂定采样频率fs=2048Hz=3.76f*fc, 截断时间Tp二Tcmax=0.02s,所以采样周期T=1/fs;采样点数N=Tp/T=40，做4096点DFT运算首先观察各窗函数的时域和频域波形当采样频率fs=2048Hz,截断时间Tp=0.02s,即采样点数N=4Q分别用矩形窗、 汉宁窗、哈明窗、布莱克曼窗截取信号，并给出相关频谱图1矩形窗截取100015002000hanning 窗截取2500hamming 囱截取blackman 窗截取N 从 40,160,320 变化2

3、 .令采样频率fs=2000Hz,增加截断时间，即采样点数 观察频谱变化，频率分辨率为50 12.5 6.25矩形窗截取hanning 窗截 取0.50.50.5X 0.510001500200025001000150020002500hamming 窗截取1000150020002500blackman 窗截取14山|1000150020002500矩形窗截取hanning 窗截 取hamming 窗截取blackman 窗截取矩形窗截取1 1000150020002500hamming 窗截取1000150020002500hanning窗截取1000150020002500blackma

4、n窗截取1000150020002500令采样频率fs=2000Hz,增加截断时间，即采样点数N从20,80,160变化观察 频谱变化，频率分辨率为100 25 12.5矩形窗截取矩形窗截取矩形窗截取1110-5TW opkx0. u10500100015002000hanning 窗截 取1100015002000hanning 窗截取hanning 窗截取0.50.50100015002000hamming窗截取0100015002000blackman窗截取X 0.520000.50.50.55005005007000,1500,20000.5010001500hamming 窗截取20

5、00hamming 窗截取1000t i 150020000.5010001500blackman 窗截取2000blackman 窗截取1000询020000.5500 row令采样频率fs=2000Hz,增加截断时间，即采样点数N从10,40,80变化观察频谱变化，频率分辨率为200 50 25矩形窗截取取 截 窗 形 矩矩形窗截取0.50-5hanning 窗截 取100500100015002000hanning 窗截取101 I05001000150020000.50 0500100015002000hamming窗截取1 00500100015002000hamming 窗截取10

6、.50 1>10500100015002000blackman窗截取1 5001000150020000.50 «-«0500100015002000blackman 窗截取1500 500 O O m4tkx0.5hanning 窗截取hamming 窗截取15001000150020000-5 1N*akxblackman 窗截取.1 一0500100015002000由图可见，随着截断时间的增加，主瓣脉宽越窄，旁瓣峰值越大，虽然频谱 泄露越来越小，但谱问干扰也越来越严重3 .令截断时间Tp=0.02s,增力口采样频率，fs=2000Hz, fs分别等于fs,4*

7、fs,8*fs , 采样点数为40,160,320观察频谱变化。频率分辨率为 50Hz观察频谱在全频范围内：hamming窗截取hamming 窗截取1hamming 窗截取0.50.5LIblackman 窗截取blackman囱截取2000400060008000100002000400060008000100000.50.5)0.51.5blackman 窗截取24x 100.51.524x 10观察频谱在4000Hz范围内:矩形窗截取矩形窗截取矩形窗截取0.50.5400040000.50.50.50.50.50.5100010000.50.50.5100020003000400010

8、00200030004000100020003000S 0.5100020003000hanning 窗截 取100020003000hanning 窗截 取100020003000hanning窗 截 取4000100020003000hamming 窗截取4000100020003000hamming 窗截取4000100020003000hamming 窗截取4000100020003000blackman 窗截取400020003000blackman 窗截取400020003000blackman窗截取40004000令截断时间采样点数为Tp=0.02s,增加采样频率,20,80,1

9、60观察频谱变化,fs=1000Hz, fs 频率分辨率为分别等于fs,4*fs,8*fs 50Hz1S 0.5s 0.50.5矩形窗截取1矩形窗截取矩形窗截取0.50.5-1000200030004000hanning 窗截 取T00020003000-hanning 窗截取4000-10002000300040000.51000200030004000hamming窗截取0.510002000300040001000200030004000hamming 窗截取TO002000300040001hanning 窗截取0.51000200030004000blackman窗截取blackma

10、n 窗截取blackman窗截取令截断时间采样点数为Tp=0.02s,增加采样频率，fs=500Hz, fs10,40,80观察频谱变化，频率分辨率为分别等于fs,4*fs,8*fs 50Hz0.5矩形窗截取100020003000hanning 窗截 取矩形窗截取053000051000200030004000100020004000hanning 窗截取hanning 窗截取40000.510002000300040000.50.510002000300040001000200030004000观察频谱在1000Hz范围内:矩形窗截取10.5匚？一0 ._.02004006008001000hanning 窗截 取矩形窗截取1sF 0.5.! i00200400600800to0ohanning 窗截 取矩形窗截取0.52004006008001000F 0.5,002004006008001000hamming 窗截取1F 0.5.0,.02004006008001000blackman 窗截取1S 0.5,FU 1 /