基于加窗FFT的频谱分析

基于加窗FFT的频谱分析

设信号为x(t)=sin(ωt+10π/180)+0.5sin(3ωt+20π/180)+0.5sin(5ωt+40π/180)+0.4sin(7ωt+60π/180)+0.3sin(9ωt+80π/180)+0.2sin(11ωt+90π/180) ，ω=99π。

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MATLAB程序及相关频谱图.

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=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

矩形窗时域210.80.610.40.50.200.40.200.40.20hanning窗时域10.80.6hamming窗时域10.80.6blackman窗时域1.50010203040010203040010203040010203040矩形窗频域50403020100-102520151050-5-100200040006000-150hanning窗频域2520151050-5-10200040006000-150hamming窗频域20151050-5-10200040006000-150blackman窗时域200040006000

当采样频率fs=2048Hz,截断时间Tp=0.02s,即采样点数N=40，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

矩形窗截取10.5005001000hanning窗截取15002000250010.5005001000hamming窗截取15002000250010.5005001000blackman窗截取15002000250010.5005001000150020002500

2.令采样频率fs=2000Hz,增加截断时间，即采样点数N从40,160,320变化观察频谱变化,频率分辨率为 50 12.5 6.25

矩形窗截取11矩形窗截取1矩形窗截取Xk[4*N]0.50.5Xk[8*N]05001000150020002500Xk[N]0.50050010001500200025000005001000150020002500hanning窗截取11hanning窗截取1hanning窗截取Xk[4*N]0.50.5Xk[8*N]05001000150020002500Xk[N]0.50050010001500200025000005001000150020002500hamming窗截取11hamming窗截取1hamming窗截取Xk[4*N]0.50.5Xk[8*N]05001000150020002500Xk[N]0.50050010001500200025000005001000150020002500blackman窗截取11blackman窗截取1blackman窗截取Xk[4*N]0.50.5Xk[8*N]05001000150020002500Xk[N]0.50050010001500200025000005001000150020002500

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11矩形窗截取1矩形窗截取Xk[4*N]0.50.5Xk[8*N]05001000hanning窗截取15002000Xk[N]0.5005001000hanning窗截取150020000005001000hanning窗截取15002000111Xk[4*N]0.50.5Xk[8*N]05001000hamming窗截取15002000Xk[N]0.5005001000hamming窗截取150020000005001000hamming窗截取15002000111Xk[4*N]0.50.5Xk[8*N]05001000blackman窗截取15002000Xk[N]0.5005001000blackman窗截取150020000005001000blackman窗截取15002000111Xk[4*N]0.50.5Xk[8*N]0500100015002000Xk[N]0.500500100015002000000500100015002000

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11矩形窗截取1矩形窗截取Xk[4*N]0.50.5Xk[8*N]05001000hanning窗截取15002000Xk[N]0.5005001000hanning窗截取150020000005001000hanning窗截取15002000111Xk[4*N]0.50.5Xk[8*N]05001000hamming窗截取15002000Xk[N]0.5005001000hamming窗截取150020000005001000hamming窗截取15002000111Xk[4*N]0.50.5Xk[8*N]05001000blackman窗截取15002000Xk[N]0.5005001000blackman窗截取150020000005001000blackman窗截取15002000111Xk[4*N]0.50.5Xk[8*N]0500100015002000Xk[N]0.500500100015002000000500100015002000

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，但谱间干扰也越来越严重

3.令截断时间Tp=0.02s,增加采样频率，fs=2000Hz, fs分别等于fs,4*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：

矩形窗截取11矩形窗截取1矩形窗截取Fs[4*fs]0.500.50Fs[8*fs]0200040006000800010000Fs[fs]0.500500100015002000250000.51hanning窗截取1.5x 1024hanning窗截取11hanning窗截取1Fs[4*fs]0.50.5Fs[8*fs]Fs[fs]0.5005001000150020002500hamming窗截取1]sf[s0.5F005001000150020002500blackman窗截取1]sf[s0.5F005001000150020002500观察频谱在4000Hz范围内：

矩形窗截取1]sf[s0.5F001000200030004000hanning窗截取1]sf[s0.5F001000200030004000hamming窗截取1]sf[s0.5F001000200030004000blackman窗截取1]sf[s0.5F001000200030004000

00200040006000800010000hamming窗截取1]sf*4[0.5sF00200040006000800010000blackman窗截取1]sf*4[0.5sF00200040006000800010000矩形窗截取1]sf*4[0.5sF001000200030004000hanning窗截取1]sf*4[0.5sF001000200030004000hamming窗截取1]sf*4[0.5sF001000200030004000blackman窗截取1]sf*4[0.5sF001000200030004000000.511.52x 104hamming窗截取1]sf*8[0.5sF000.511.52x 104blackman窗截取1]sf*8[0.5sF000.511.52x 104

矩形窗截取1]sf*8[0.5sF001000200030004000hanning窗截取1]sf*8[0.5sF001000200030004000hamming窗截取1]sf*8[0.5sF001000200030004000blackman窗截取1]sf*8[0.5sF001000200030004000

令截断时间Tp=0.02s,增加采样频率，fs=1000Hz, fs分别等于fs,4*fs,8*fs，采样点数为20,80,160观察频谱变化，频率分辨率为50Hz

矩形窗截取11矩形窗截取1矩形窗截取Fs[4*fs]0.50.5Fs[8*fs]010002000hanning窗截取30004000Fs[fs]0.50010002000hanning窗截取3000400000010002000hanning窗截取30004000111Fs[4*fs]0.50.5Fs[8*fs]010002000hamming窗截取30004000Fs[fs]0.50010002000hamming窗截取3000400000010002000hamming窗截取30004000111Fs[4*fs]0.50.5Fs[8*fs]010002000blackman窗截取30004000Fs[fs]0.50010002000blackman窗截取3000400000010002000blackman窗截取30004000111Fs[4*fs]0.50.5Fs[8*fs]01000200030004000Fs[fs]0.50010002000300040000001000200030004000

令截断时间Tp=0.02s,增加采样频率，fs=500Hz, fs分别等于fs,4*fs,8*fs，采样点数为10,40,80观察频谱变化，频率分辨率为50Hz

矩形窗截取11矩形窗截取1矩形窗截取Fs[4*fs]0.50.5Fs[8*fs]010002000hanning窗截取30004000Fs[fs]0.50010002000hanning窗截取3000400000010002000hanning窗截取30004000111Fs[4*fs]0.50.5Fs[8*fs]010002000hamming窗截取30004000Fs[fs]0.50010002000hamming窗截取3000400000010002000hamming窗截取30004000111Fs[4*fs]0.50.5Fs[8*fs]010002000blackman窗截取30004000Fs[fs]0.50010002000blackman窗截取3000400000010002000blackman窗截取30004000111Fs[4*fs]0.50.5Fs[8*fs]01000200030004000Fs[fs]0.50010002000300040000001000200030004000

观察频谱在1000Hz范围内：

矩形窗截取11矩形窗截取1矩形窗截取Fs[4*fs]0.50.5Fs[8*fs]Fs[fs]0.5002004006008001000hanning窗截取1]sf[s0.5F002004006008001000hamming窗截取1]sf[s0.5F002004006008001000blackman窗截取1]sf[s0.5F002004006008001000

002004006008001000hanning窗截取1]sf*4[0.5sF002004006008001000hamming窗截取1]sf*4[0.5sF002004006008001000blackman窗截取1]sf*4[0.5sF002004006008001000002004006008001000hanning窗截取1]sf*8[0.5sF002004006008001000hamming窗截取1]sf*8[0.5sF002004006008001000blackman窗截取1]sf*8[0.5sF002004006008001000

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