【正文】 ej2π(ux+vy)dudv(312)二維的離散傅立葉變換為：Fm,n=1Ni=0N1k=0N1f(i,k)ej2π(miN*nkN)(313)逆變換為：fi,k=m=0N1n=0N1F(m,n)ej2π(miN*nkN)(314)二維信號是可以用圖像的形式來表達(dá)的，一維的信號傅立葉變換以及圖像的傅立葉變換原理是同樣的，同樣也有快速的算法，在這里不進(jìn)行討論。這樣進(jìn)行計(jì)算之后，圖像的虛部和實(shí)部里面包含的就是中間數(shù)據(jù)了。這樣以來，通過傅立葉變換后得出的頻譜圖，也稱為功率圖。從帶有正弦干擾的信號移頻到原點(diǎn)的頻譜圖上，我們可以看得出，除了中心以外存在以某一點(diǎn)為中心，還有對稱分布的亮點(diǎn)，而這些集合就是噪音干擾產(chǎn)生的，這時(shí)候就可以非常直接的通過在該位置放置濾波器來消除干擾。在主界面中，我們可以通過調(diào)節(jié)二維脈沖的寬度和高度，還有橫向和縱向的位移來顯示經(jīng)過2DFFT變換的圖像。，將vi的前面板或程序框圖中右上角的顯示連線版打開。在程序框圖中點(diǎn)擊“右鍵→選擇vi→”。本次頻移實(shí)驗(yàn)的原理，是給一個(gè)初始信號疊加一個(gè)新的信號，從而使信號的頻率增加，頻譜發(fā)生變化，頻譜移動的規(guī)律更加清晰可觀。當(dāng)兩個(gè)信號的頻率增大時(shí)，頻譜的峰值間距越遠(yuǎn)，反之越近。但是信號往往不都是單一的，而是多種信號摻合而成的，所以我們對信號分析之前往往要經(jīng)過處理，例如對信號進(jìn)行多次采樣后平均，濾波掉噪聲信號等等。 頻域平均實(shí)驗(yàn)臺 頻域平均實(shí)驗(yàn)臺的程序框圖 奈奎斯特圖（Nyquist）頻率特性是一種復(fù)變函數(shù)，相頻特性φ(ω)和幅頻特性A(ω)也是輸入信號頻率ω的函數(shù)。 比例環(huán)節(jié)的極坐標(biāo)圖積分環(huán)節(jié)的傳遞函數(shù)為：Gs=1s (317)因此其頻率特性為：Gjω=1jω=j1ω (318)我們?nèi)≥敵鱿禂?shù)為1，輸入系數(shù)為4和0。因此這個(gè)頻率特性為：Gjω=ωn2ω2+j2ξωnω+ωn2=ωn2(ωn2ω2j2ξωnω)(ωn2ω2)2+4ξ2ωn2ω2 (324)我們?nèi)≥敵鱿禂?shù)為1，輸入系數(shù)為1。調(diào)用MATLAB的語句如下：num=[a1 a2 a3 a4]。grid on程序設(shè)定了分子分母各有4個(gè)可修改的系數(shù)。有兩種方法可以向腳本節(jié)點(diǎn)中輸入MATLAB的腳本。在制作的過程當(dāng)中，我們需要為MATLAB腳本中的變量添加一個(gè)輸入輸出的變量。 伯德圖（Bode）伯德圖是指通過對未知的系統(tǒng)輸入一系列頻率不相同的正弦信號，通過測量輸出信號的相位和幅值，能夠得到對應(yīng)不同頻率下該系統(tǒng)對輸入信號的幅值和相位的作用，因而得到系統(tǒng)的內(nèi)部結(jié)構(gòu)。我們?nèi)≥敵鱿禂?shù)為4，輸入系數(shù)為0和1。在這里應(yīng)當(dāng)注意到，積分環(huán)節(jié)和微分環(huán)節(jié)的對數(shù)坐標(biāo)圖（包括對數(shù)幅頻特性圖和對數(shù)相頻特性圖）都是關(guān)于橫坐標(biāo)對稱的。：震蕩環(huán)節(jié)的頻率特性為：Gjω=1T2ω2+j2ξTω+1=ωn2ω2+j2ξωnω+ωn2 (329)我們?nèi)≥敵鱿禂?shù)為1，輸入系數(shù)為1。如果阻尼比越大，曲線的過度頻率范圍則越寬；阻尼比越小，曲線斜率變化就會越明顯。伯德圖的程序框圖中MATLAB調(diào)用代碼如下：num=[a1 a2 a3 a4]。grid on程序同樣設(shè)計(jì)了4個(gè)可修改的分子分母系數(shù)。無論任何周期信號，只要滿足狄利克雷條件（在一個(gè)周期內(nèi)，如果有間斷點(diǎn)存在，則間斷點(diǎn)的數(shù)目贏是有限個(gè)，極大值和極小值的數(shù)目應(yīng)該是有限個(gè)，信號絕對可積）就可以分解成直流分量以及許多的正弦和余弦分量。一般說來。F(t)是個(gè)方波，他是由各級sin和cos函數(shù)所組成：fTt=a02+n=1∞(ancosnωt+bnsinnωt)(337)由于f(t)是偶函數(shù)，所以bn=0。程序框圖中頻率的設(shè)定，都是經(jīng)過多次試驗(yàn)后，得出的一個(gè)定值，在這個(gè)頻率的下面，試驗(yàn)圖形則可以顯示的最直觀，能更好分辨波形以及獲取參數(shù)。理論上來講，讓無限個(gè)諧振波形相疊加，就可以得到理想的波形了。輸入端指定將要循環(huán)的次數(shù)，該端子的數(shù)據(jù)表示類型是32位有符號的整數(shù)，如果輸入為0或者負(fù)數(shù)，則這個(gè)循環(huán)無法執(zhí)行并在輸出中顯示這個(gè)數(shù)據(jù)類型的默認(rèn)值；輸出端顯示當(dāng)前的循環(huán)次數(shù)，也同樣是32位有符號的整數(shù)，默認(rèn)從0開始，依次增加1。在選擇器標(biāo)簽中可以輸入單個(gè)值或者是數(shù)值列表和范圍。通過對虛擬儀器技術(shù)的開發(fā)與研究，解決并節(jié)省了各行各業(yè)的開支，提高的生產(chǎn)效率。這些問題是本次畢業(yè)設(shè)計(jì)中遇到的瓶頸。整合時(shí)域分析、頻域分析和信號處理三大模塊，本信號處理實(shí)驗(yàn)平臺將是一個(gè)功能十分強(qiáng)大的高校虛擬信號處理實(shí)驗(yàn)室，可以實(shí)現(xiàn)基本的信號處理有關(guān)實(shí)驗(yàn)項(xiàng)目。 Third, puter analyzes and displays the digital signal. Moreover, it can do feedback control through D/A transducer. The data acquisition system is multicenter and multiparameter structure. The main tasks of data acquisition and processing system are catching and recording signal. First, pressure signal should be transformed into electric voltage or current signal. Second, adjust signal through adjustment circuit. At last, the signal is transported into puter through data acquisition card.Interface of A/D transducer and puter are integrated in data acquisition card PIOMIO16E1 produced by National Instrument. Data acquisition card PIOMIO16E1 has 16 analog signal channels that could carry out 16singlechannel input and 8 pairs of difference input. So it could acquire several groups of signals simultaneously. In this virtual instrument system, singlechannel input is used. Sampling precision is 12 bit in A/D transducer. Then, the signal is transported into puter and goes on with next step.C Software platform of virtual instrument Data acquisition virtual instrument system mainly used in processing control, signal transportation and display acquired data. Furthermore, it could save and print files automatically. The data acquisition program was written with software LabVIEW. The system contains a main VI and 5 sub VI (In LabVIEW, a relatively independent program module that has special function is called a VI). “.” is a window of data acquisition virtual instrument system. ① idstsdemo. VI is a data acquisition VI and it is the main VI. It controls data acquisition, signal transportation and data display. Moreover, it can save and print files automatically. FIG. 1 A window of data acquisition virtual instrument system② global. VI is global parameter VI, and it defines global parameters. ③ sysinit. VI is system initiation VI, and it memorizes initial parameters.④ iocontrol. VI is I/O control VI, and it has 16 channels of input/output. ⑤ setpara. VI is parameter setting VI, and it is used to set parameters such as sampling hits, length, delaying and channels. ⑥ transducer. VI is electric amplifier VI, and it is used to setting amplifier and transducer parameters.(1) Starting acquiring Once, start data acquisition, all of the channel start acquiring data. After it starts, system can’t read data immediately and system must have a state function to test acquired signal, because acquiring would last a period of time and system should supervise data acquisition card’s state. “.”is acquiring procedure program that controls data acquisition procedure. (2) Displaying data intelligently The system could display data in graph and curve that make change trend of data more clear. Moreover, it provides various graphic widgets to magnify and deflate graph and show coordinate of special point. All of them make system’s graph function stronger.(3) Saving and printing files After acquiring data successfully, the system can create four kinds of data files, including text file, binary file, wave data file and wave graph file. (4) Setting parameter Parameters should be set before acquiring starts. It contain: I/O control parameter, acquiring process parameter, electric amplifier parameter and so on.D Communication of LabVIEW and data acquisition cardThere are two ways to realize munication between LabVIEW and data acquisition card: CIN (code interface node) and DLL (dynamic link library). In LabVIEW, CIN is a code interfacenode that connects with traditional program language C. CIN could create a template program and user addscorresponding source code in the template program that will later be piled into .lsb file under IDE environment of . Then, load the .lsb file in the CIN node of LabVIEW and user can make use of it directly. When LabVIEW run the CIN node, LabVIEW uses the executive .lsb file directly, and transmits data into the executive file and output result. A