基于加窗FFT的頻譜分析

1、基于加窗FFT的頻譜分析設(shè)信號(hào)為 x(t)=sin( t+10 兀/180)+0.5sin(3 t+20 兀/180)+0.5sin(5 wt+40兀 /180)+0.4sin(7 t+60 兀 /180)+0.3sin(9 t+80 兀 /180)+0.2sin(11 t+90 幾/180), = =99 tt o1、分別用矩形窗、漢寧窗、哈明窗、布萊克曼窗 +FFT對(duì)信號(hào)進(jìn)行頻譜分析，分 析各窗函數(shù)對(duì)頻譜分析的影響；2、在采樣頻率一定時(shí)，增加截?cái)鄷r(shí)間長(zhǎng)度，分析截?cái)鄷r(shí)間長(zhǎng)度對(duì)頻譜分析的影 響；3、在截?cái)鄷r(shí)間長(zhǎng)度一定時(shí)，修改采樣頻率，分析采樣頻率對(duì)頻譜分析的影響；4、給出所有MATLA勰序及相

2、關(guān)頻譜圖.1.該信號(hào)的最高頻率fc=544.5Hz,Tcmax=0.02s,為了分析各窗函數(shù)對(duì)頻譜分析的影響，暫定采樣頻率fs=2048Hz=3.76f*fc,截?cái)鄷r(shí)間Tp=Tcmax=0.02s,所以采樣周期T=1/fs;采樣點(diǎn)數(shù)N=Tp/T=40，做4096點(diǎn)DFT運(yùn)算首先觀察各窗函數(shù)的時(shí)域和頻域波形當(dāng)采樣頻率fs=2048Hz,截?cái)鄷r(shí)間Tp=0.02s,即采樣點(diǎn)數(shù)N=4Q 分別用矩形窗、漢寧窗、哈明窗、布萊克曼窗截取信號(hào)，并給出相關(guān)頻譜圖一下載可編輯矩形窗截取hanning 窗截取0.5hamming 窗截取blackman 窗截取.下載可編輯N 從 40,160,320 變化2.令采樣

3、頻率fs=2000Hz,增加截?cái)鄷r(shí)間，即采樣點(diǎn)數(shù) 觀察頻譜變化，頻率分辨率為50 12.5 6.25矩形窗截取00X 0.51000150020002500矩形窗截取矩形窗截取5001000150020002500hanning窗截取hanning 窗截 取hamming 窗截取hanning 窗截取5001000150020002500hamming 窗截取0.55001000150020002500hamming 窗截取5001000150020002500blackman窗截取blackman 窗截取blackman 窗截取1NEX令采樣頻率fs=2000Hz,增加截?cái)鄷r(shí)間，即采樣點(diǎn)數(shù)N

4、從20,80,160變化觀察 頻譜變化，頻率分辨率為100 25 12.5矩形窗截取0-5矩形窗截取5001000hanning 窗截 取0.5hamming窗截取blackman窗截取0 “， I500100015002000hanning 窗截取 10500100015002000hamming 窗截取150010001500200001hanning 窗截取矩形窗截取0-5opkxblackman 窗截取令采樣頻率fs=2000Hz,增加截?cái)鄷r(shí)間, 頻譜變化，頻率分辨率為200 50 25即采樣點(diǎn)數(shù) N從10,40,80變化觀察矩形窗截取矩形窗截取100.5050010001500200

5、0矩形窗截取500100015002000hanning窗截取0-5hanning 窗截 取hanning 窗截取10N 0.50500100015002000500100015002000hamming 窗截取hamming窗截取0.5100015002000hamming 窗截取10.505001000150020000500100015002000blackman 窗截取blackman窗截取blackman 窗截取11500500o o500100015002000由圖可見(jiàn)，隨著截?cái)鄷r(shí)間的增加，主瓣脈寬越窄，旁瓣峰值越大，雖然頻譜 泄露越來(lái)越小，但譜問(wèn)干擾也越來(lái)越嚴(yán)重3.令截?cái)鄷r(shí)間Tp

6、=0.02s,增力口采樣頻率，fs=2000Hz, fs分別等于fs,4*fs,8*fs50Hz采樣點(diǎn)數(shù)為40,160,320觀察頻譜變化。頻率分辨率為觀察頻譜在全頻圍:矩形窗截取矩形窗截取矩形窗截取 I占yhanning 窗截 取10.50.5050.50.5051000024blackman 窗截取blackman 窗截取blackman囪截取0 .0005001000150050010001500hamming 窗截取200040006000800010000hanning 窗截 取hanning囪截取6000800010000hamming 窗截取hamming 囪截取20004000

7、600010000x 10觀察頻譜在4000Hz 圍:矩形窗截取矩形窗截取矩形窗截取1110.50.50.50.50.50.5002000blackman 窗截取blackman囪截取S 0.5400020003000hanning 窗截 取2000hamming 窗截取blackman 窗截取2000hanning 窗截 取2000hanning窗 截 取2000hamming 窗截取2000hamming 窗截取令截?cái)鄷r(shí)間Tp=0.02s,增加采樣頻率，fs=1000Hz, fs 分別等于fs,4*fs,8*fs采樣點(diǎn)數(shù)為20,80,160觀察頻譜變化，頻率分辨率為 50Hz矩形窗截取矩形

8、窗截取矩形窗截取1000120000505200030003000hamming 窗截取10.505001000"由 0.5Hr . .200030004000hanning 窗截 取hamming窗截取2000-2000hanning 窗截取hanning窗 截 取"2000"1000blackman窗截取hamming 窗截取1000-4000blackman窗截取令截?cái)鄷r(shí)間Tp=0.02s,增加采樣頻率，fs=500Hz, fs 分別等于fs,4*fs,8*fs采樣點(diǎn)數(shù)為10,40,80觀察頻譜變化，頻率分辨率為50Hzhanning 窗截 取hanning 窗截取hamming 窗截取0.51000200040003000矩形窗截取05100030000510000530000.51000200030004000100020004000hanning窗 截 取200030004000hamming 窗截取20004000blackman窗截取矩形窗截取矩形窗截取00200400600800to0。°200L4