基于加窗FFT的頻譜分析

1、基于加窗FFT的頻譜分析設信號為x(t)=sin(t+10兀/180)+0.5sin(3t+20兀/180)+0.5sin(5t+40幾/180)+0.4sin(7t+60兀/180)+0.3sin(9t+80兀/180)+0.2sin(11t+90兀/180),二99兀。1、分別用矩形窗、漢寧窗、哈明窗、布萊克曼窗+FFT對信號進行頻譜分析，分析各窗函數對頻譜分析的影響；2、在采樣頻率一定時，增加截斷時間長度，分析截斷時間長度對頻譜分析的影響；3、在截斷時間長度一定時，修改采樣頻率，分析采樣頻率對頻譜分析的影響；4、給出所有MATLA勰序及相關頻譜圖.1 .該信號的最高頻率fc=544.5H

2、z,Tcmax=0.02s,為了分析各窗函數對頻譜分析的影響，暫定采樣頻率fs=2048Hz=3.76f*fc,截斷時間Tp=Tcmax=0.02s,所以采樣周期T=1/fs;采樣點數N=Tp/T=40，做4096點DFT運算首先觀察各窗函數的時域和頻域波形當采樣頻率fs=2048Hz，截斷時間Tp=0.02s,即采樣點數N=40，分別用矩形窗、漢寧窗、哈明窗、布萊克曼窗截取信號，并給出相關頻譜圖1矩形窗截取100015002000hanning窗截取2500hamming囪截取blackman窗截取N從40,160,320變化2 .令采樣頻率fs=2000Hz,增加截斷時間，即采樣點數觀察頻

3、譜變化，頻率分辨率為5012.56.25矩形窗截取hanning窗截取0.50.50.5X0510001500200025001000150020002500hamming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11000150020002500hamming窗截取1000150020002500hanning窗截取1000150020002500blackman窗截取1000150020002500令采樣頻率fs=2000Hz,增加截斷時間，即采樣點數

4、N從20,80,160變化觀察頻譜變化，頻率分辨率為1002512.5矩形窗截取矩形窗截取矩形窗截取1110-5opkx0.u10500100015002000hanning窗截取1100015002000hanning窗截取hanning窗截取0.50.50100015002000hamming窗截取0100015002000blackman窗截取X0.570000.50.50.5500500500700075Q020000.5010001500hamming窗截取2000hamming窗截取1000ti150020000.5010001500blackman窗截取2000blackman窗

5、截取1000詢020000.5令采樣頻率fs=2000Hz,增加截斷時間，即采樣點數N從10,40,80變化觀察頻譜變化，頻率分辨率為2005025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101I05001000150020000.500500100015002000hamming窗截取100500100015002000hamming窗截取10.501>10500100015002000blackman窗截取15001000150020000.50«-«0500100015002000bl

6、ackman窗截取1500500OO0.5hanning窗截取hamming窗截取1500100015002000blackman窗截取0-51N*akx.1一0500100015002000由圖可見，隨著截斷時間的增加，主瓣脈寬越窄，旁瓣峰值越大，雖然頻譜泄露越來越小，但譜問干擾也越來越嚴重3 .令截斷時間Tp=0.02s,增力口采樣頻率，fs=2000Hz,fs分別等于fs,4*fs,8*fs,采樣點數為40,160,320觀察頻譜變化。頻率分辨率為50Hz觀察頻譜在全頻范圍內：hamming窗截取hamming窗截取1hamming窗截取0.505LIblackman窗截取blackma

7、n囪截取2000400060008000100002000400060008000100000.50.5)0.51.5blackman窗截取24x100.51.524x10觀察頻譜在4000Hz范圍內:矩形窗截取矩形窗截取矩形窗截取0.50.5400040000.50.50.50.50.50.5100010000.50.50.510002000300040001000200030004000100020003000£0.5100020003000hanning窗截取100020003000hanning窗截取100020003000hanning窗截取4000100020003000

8、hamming窗截取4000100020003000hamming窗截取4000100020003000hamming窗截取4000100020003000blackman窗截取400020003000blackman窗截取400020003000blackman窗截取40004000令截斷時間采樣點數為Tp=0.02s,增加采樣頻率,20,80,160觀察頻譜變化,fs=1000Hz,fs頻率分辨率為分別等于fs,4*fs,8*fs50Hz1s0.5由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20003000-hanning

9、窗截取4000-10002000300040000.51000200030004000hamming窗截取0.51UU02000300040001000200030004000hamming窗截取TOOT2000300040001hanning窗截取0.51000200030004000blackman窗截取blackman窗截取blackman窗截取令截斷時間采樣點數為Tp=0.02s,增加采樣頻率，fs=500Hz,fs10,40,80觀察頻譜變化，頻率分辨率為分別等于fs,4*fs,8*fs50Hz0.5矩形窗截取100020003000hanning窗截取矩形窗截取051000300005100020003000400020004000hanning窗截取hanning窗截取40000.510002000300040000.50.510002000300040001000200030004000觀察頻譜在1000Hz范圍內:矩形窗截取10.5匚？一0._.02004006008001000hanning窗截取矩形窗截取1sF0.5.!i002004006008001000hanning窗截取矩形窗截取0.5F°.5,002004006008001000hamming窗截取1F05.0,.02004006008001000blackman窗截取1S0.5