《论文（设计）基于时, 频域数字坐标重叠技术的信号处理研究.doc》由会员分享，可在线阅读，更多相关《论文（设计）基于时, 频域数字坐标重叠技术的信号处理研究.doc（6页珍藏版）》请在三一办公上搜索。
1、h基于时、频域数字坐标重叠技术的信号处理研究梁建武1，何志斌21（中南大学 信息科学与工程学院，湖南 长沙 410075）2（中南大学 信息科学与工程学院，湖南 长沙 410075）E-mail ：Liangjw摘要：文章通过快速傅里叶变换(FFT)对原始信号时域转换频域过程及其相互的特性作了深入的研究，并分析了折叠频率、最大分辨频率、采样频率特性及其关系,在此基础上提出了采用比例系数来换算数字坐标的算法,使时、频域数字坐标重叠。在这种数字化重叠坐标中,计算机对滤除或提取某一频率带来很大方便和直观。仿真实验表明该方法对信号处理具体的实现提供了简单实用的方案,给当前信号处理的研究提供了一个新的思
2、路。关键词：时域；FFT；频域；坐标重叠；信号处理中图分类号： 文献标识码：文章编号：Study on Digital Signal Processing Based on the Time-Domainand Frequency Domain Technology Coordinate Overlapping Research LIANG Jian-wu 1，HE Zi-bin 21（College of Information Science and Engineering, Central South University, Changsha 410075, China)2（Colleg
3、e of Information Science and Engineering, Central South University, Changsha 410075, China)Abstract: This article studies on original signal from Time-Domain to Frequency-Domain conversion process and their characteristics through FFT. Thenit analysis the characteristics of the folding frequency, th
4、e greatest frequency resolution and the sampling frequency and their relations ,It puts forwarda algorithm through Conversion factor proportional to the number of coordinates. So, the Time-Domain and Frequency-Domain digital coordinates overlap. Computer let it easy to filter or extract a certain fr
5、equency in this process. The simulation shows that the method of signal processing provides a simple and practical realization of specific programs, which provides a new way of thinking to the current signal processing. Key words: Time-Domain;FFT; Frequency-Domain; Coordinate overlapping; Signal Pro
6、cessing1引 言人类对自然界的认识和改造过程都离不开对自然界中的信息的获取.所谓信息,是指存在于客观世界的一种事物形象,是关于事物运动规律的知识1.一般泛指消息、情报、指令、数据、信号等有关周围环境的知识.可以说,我们是生活在信息的海洋之中,因此获取信息的活动是人类最基本的活动之一.在我们的周围存在着为数众多的信号.这些众多的信号中,有的是含有有用信息的信号,有的只是应当除掉的噪音.所谓信号处理,就是要把记录在某种媒体上的信号进行处理,以便抽取出有用信息的过程,它是对信号进行提取、变换、分析、综合等处理过程的统称2.我们可以用信号的频谱来描述信号.要说明的是,我们通常视信号频谱为信号的一
7、种间接描述,而将其数学描述和波形描述视为是对信号的直接描述.因为频谱与信号有一一对应关系,所以从频谱就可以知道对应信号的特点,而信号特点正是我们在描述信号时所需要表现出来的.因此,说频谱是对信号的描述也是成立的3.人类对信号处理有着悠久的历史.傅立叶变换是信号处理中最重要、应用最广泛的变换.目前出现了很多实现快速傅立叶变换的串行算法,如基2时间抽取算法和频率抽取算法、混合基 FFT算法、分裂基 FFT 算法(SRFFT)4，5、素因子算法（PFA）6、Winograd 傅立叶变换算法（WFTA）、实序列的FFT、多维FT 变换7等.在国外,围绕快速傅立叶变换的并行计算进行了多项研究和开发.美国
8、New Mexico大学asilios Georgitsis等人设计了2-DFFT程序可处理512*512 个点的图象、麻省理工学院计算机科学实验室超级计算技术组开发的FFTW可计算一维或多维、实数据和复数据以及任意规模的DFT.FFTW具有很好的自适应性和很快的运行速度,还包含对共享和分布式存储系统的并行变换.在我国,80 年代初快速傅立叶变换的并行算法问世.主要包括:基于IMD-MC2、SIMD-BF、SIMD-CC、MIMD-DM 四种体系结构上的FFT算法,它们都是基-2FFT 算法,但这些算法各有利弊,受体系结构影响较大.最近也有人提出基于共享存储的多机系统并行计算FFT 算法和基于
9、星型互联网络的并行快速傅立叶变换8等多种傅立叶变换的并行算法. 2时、频域特性分析 采样定律告诉我们,一个频带有限的信号,可以对它进行时域采样而不丢失任何信息,现在DFT（离散傅里叶变换）变换进一步告诉我们,对于时间有限的信号（有限长序列）,也可以对其进行频域采样,而不丢失任何信息,这正反应了傅立叶变换中时域、频域的对称关系9.但是它却有十分重要的意义,我们看到,由于时域上的采样,使我们能够采用数字技术来处理这些时域上的信号（序列）,而DFT理论使得不仅在时域,在频域也可采用数字处理技术10.快速傅里叶变换（FFT）是计算DFT的一种快速有效方法.有限长序列在数字技术中占有很重要的地位.有限长
10、序列的一个重要特点是其频域也可以离散化,即离散傅里叶变换（DFT）.因为信号序列的DFT本身就是信号频谱的采样集,所以DFT可直接用于分析信号的频谱11.频谱分析在数字信号处理中用途广泛:如通过语言信号的频谱分析实现语音通讯的频带压缩、声纳信号的频谱分析用以区分水面与水下目标.在各种测量仪器中,频谱分析用得更多,这些都需要DFT运算.虽然频谱分析和DFT运算很重要,但在很长一段时间里,由于DFT运算复杂,并没有得到真正的运用,而频谱分析仍大多采用模拟信号滤波的方法解决,直到1965年首次提出DFT运算的一种快速算法以后,情况才发生了根本变化,人们开始认识到DFT运算的一些内在规律,从而很快地发
11、展和完善了一套高速有效的运算方法快速傅里叶变换（FFT）算法,FFT的出现,使DFT的运算大大简化,运算时间缩短一二个数量级,使DFT的运算在实际中得到广泛应用12.时域信号数字化后是一系列离散点数,通过FFT变为频域离散点数,它们之间的关系可从理论和实验得到,图1是计算机仿真对正弦波（频率分别为：30、500、700、950、1000Hz）以采样频率2KHz采样,再通过FFT转换后的频域曲线.从这里可以看到,一旦采样频率（fs）确定,则最大分辨频率(fmax)确定,它们之间的关系是满足采样定律:fs=2* fmax13 .图中fs=2KHz,故最大分辨频率为1KHz.不难发现离散的原始信号（
12、实验N=1024）通过FFT变换后,频域是以原坐标中间点（N/2=512）作为对称轴的一个频域空间曲线.当信号频率增加,可明显看到谱线向中间靠近,直到最大分辨频率1000Hz重合为止.因此,称采样频率的一半为折叠频率(正好是最大分辨频率).它好像一面镜子,信号频率超过折叠频率时,对应的频谱就会被折迭回来,造成频谱混淆14. 奈奎斯特采样定理:要使实际信号采样后能够不失真还原,采样频率必须大于信号最高频率的两倍.如采样率过低,不满足采样定理,fs=2* fmax,使一个周期内的谱对原信号谱产生失真,无法恢复原信号,使得进一步的数字处理失去依据15.图1：频谱曲线图Fig.1 Spectrum c
13、urve现假设满足奈奎斯特采样定理的前提下,频谱坐标（频率的大小）是从两头（i=0和 i=N）逐渐向中间（i=N/2）增大,变化范围从0 到 最大分辨频率,一个频率坐标点对应两个点,且对称.3时、频域数字坐标重叠 为了简单化,对原始信号连续采样N=1024点（大于则分段处理）,采样频率为2KHz,时域数字坐标为X(i) i=0,1 .1023,i为时间坐标（X(i)包含实部和虚部,这里虚部置0）.通过FFT变换后变为Y(i) i=0,1 .1023,i为频率坐标（Y(i)包含实部和虚部）.要让它们重合,要进行信号运算,一般都是在对函数的自变量进行变换,或加上一个常数偏移(时移),或乘上一个常数
14、作比例系数(尺度),或改变变量的符号(反褶) 16.它们的作用效果能够从原信号的波形变化上很直观地看出.这里采用乘上一个常数作比例系数来换算数字坐标.根据上面的特性我们知道,信号频率从0到最大分辨频率的频域分布一半是从Y(0) 到Y(N/2),把这一半以折叠频率处折叠就得到另一半,即Y(N/2)到Y(N-1).那现在假设某频率为f,来确定频率坐标点i的值（i=0.1023）.根据上面的分析不难得出:这个比例系数应该为频率f/最大分辨频率fmax,原时域坐标长度缩小一半（N/2）.频率f坐标点位置(前半段）=N/2*频率f/最大分辨频率fmax = N/2*频率f/（采样频率fs/2）.公式:频
15、率f坐标点位置(前半段）: （公式1） 由对称性,频率f坐标点位置(后半段）： （公式2） 这说明在频域内一个频率点坐标对应两点,且和折叠频率对称,但这和时域大不相同.为了让他们重合,采用公式1和公式2变换就能让其重合,这是本文提出的关键算法.有了时、频域数字坐标重合算法,计算机对原始信号进行处理就变得尤为方便.为了对此公式进行验证,我们使用了一个带通滤波器,频率是40Hz-100Hz.假设有一个原始正弦波信号,其中含有三种频率（39Hz、60Hz、101Hz）,见图2上部分曲线.我们对原始信号连续采样N=1024点（采样频率为2KHz）.时域数字坐标为X(i) i=0,1 .1023，i为时
16、间坐标.通过FFT变换后形成变为Y(i)i=0,1 .1023，i为频率坐标.带通低频率为40Hz所对应的坐标点计算:i1= =20i2 = =1004带通高频率为100Hz所对应的坐标点计算：i3=51i4 =973根据频域特性把低频（100Hz）滤掉: Y(i)=0,（i=51 to 973）.然后再通过FFT反变换,就只得到只有60Hz正弦波信号了.仿真实验如图2所示.图2下部分有三根曲线,其中第一根是原始信号的频谱,显然是以折叠频率（1000Hz,数字坐标为N/2=512）为对称轴的一个分布曲线;第二根为带通滤波结果,只剩下60Hz正弦波信号了;第三跟为滤波结果曲线的频谱.显然39Hz
17、 和 101Hz处频谱没有了,只剩下了60Hz的对称频谱线.比例换算方法和仿真试验的结果相同.图2：带通滤波图Fig.2 Bandpass Filter比例系数获取时、频数字坐标的方法,使计算机对滤除或提取信号的频率段带来极大的方便,大大简化复杂的计算过程.4结论 傅立叶变换是分析信号时、频域特征最广泛的方法.本文通过对时域和频域的特性及其相互之间的关系作了深入的研究,通过理论和实验分析,提出了采用比例系数来换算数字坐标的算法,使时、频域数字坐标重叠,通过这种简单有效的数字化坐标重叠,可以大大简化计算机的复杂的傅立叶变换,对滤除或提取某一频率段带来很大方便和实效.仿真实验表明该方法对信号处理具
18、体的实现提供了简单实用的方案,该方案已应用到实际工程之中,且收到了很好的效果.References:1 Ding_yuxin,Shen_xueqin.The wavelet neural network based on energy densityJComputer Journal, 1997,(09):832-8382 Zen_shancui,Shen_hua,Yu_zhenli. FFT Based Spectrogram Analysis and Display of Signals Using Matlab J. BULLETIN OF SCIENCE AND TECHNOLOGY,
19、 2000,(04):241-2463 XUE Hui; YANG Ren-gang.PRECISE ALGORITHMS FOR HARMONIC ANALYSIS BASED ON FFT ALGORITHMJ. Proceedings of the CSEE,2002,(12):106-1104 HEIDEMAN MT.Multiplicative complexity, convolution,and the DFTM.New York: Springer-Verlag, 19885 VETTERLI M,DUHAMAEL P.Fast Fourier transform:a tuto
20、rial review and a state of the art J.Signal Processing,1990,196 KOLBA D P,PARKS T W.A prime factor FFT algotithm using high-speed convolution J.IEEE Trans Acoust Speech SignaL Processing,1977 (25)7 Ji Hu,Xia Shengping,Yu Wenxian. An Outline of the Fast Fourier Transform Algorithm.Modern technology20
21、01,8:11-138 Yu_xiumin. Outlined of Fast Fourier Transform parallel algorithm. CHINA SCIENCE AND TECHNOLOGY INFORMATION. May.2005:529 DUAN Yan li; ZHENG Rong .FFT Technique on Speech Time-Varied Spectrum Analysis. JOURNAL OF AIR FORCE ENGINEERING UNIVERSITY(NATURAL SCIENCE EDITION, 2000,(02):26-2810
22、Wan_ling,Jiao_lichen. Interval Estimation of FWNN and The Interval Learning Algorithm.J Electronic Journal. , 1998,(04)11 Li_jiequn. Detection of Ultra-wideband LFM Signal and Parameter Estimation MethodD University of Electronic Science and Technology of China,200512 Yu_fenqing.The Research and App
23、lication of Chirp multi-components Time-frequency and Parameter Estimation.DShanghai University,200513 Liu_qinyun.Uncertainty of the Time-varying Signal Analysis and Processing MethodD. Northwestern Polytechnical University,200414 Xiong_zhangliang. Key Technologies of Radar Based on Ultra-short-rang
24、e defense systems D. Nanjing University of Science,200615 Wang_shenli,Zhang_guangyi. Noise Filtering and suppresson Matching Fourier transform .J Electronic Journal, 2001(12)16 ZHU Li; HU Xue-cheng; LIN You-quan. Doppler Parameter Estimation for SAR using Match Fourier Transform J Journal of China A
25、cademy of Elecronics and Information Technology:152-161附中文参考文献：1 丁宇新,沈雪勤. 基于能量密度的小波神经网络J计算机学报, 1997,(09):832-8382 曾尚璀,沈华,俞振利.基于Matlab系统的信号FFT频谱分析与显示J. 科技通报, 2000,(04):241-2463 薛蕙,杨仁刚. 基于FFT的高精度谐波检测算法J. 中国电机工程学报, 2002,(12):106-1107 季虎,夏胜平,郁文贤.快速傅立叶变换算法概述.现代电子技术2001年第8期:11-138 于秀敏.快速傅立叶变换并行算法概述. CHINA
26、 SCIENCE AND TECHNOLOGY INFORMATION May.2005:529 段艳丽,郑荣. 语音时变频谱分析的FFT技术J. 空军工程大学学报(自然科学版) , 2000,(02):26-2810 王岭，焦李成. 区间估计的FWNN及其区间学习算法J电子学报 , 1998,(04)11 李洁群. 超宽带LFM信号检测和参数估计方法研究D电子科技大学 , 200512 于凤芹. 多分量Chirp信号的时频表示与参数估计的研究及其应用D上海大学 , 200513 刘庆云. 确定性时变信号的分析与处理方法研究D西北工业大学 , 200414 熊张亮. 基于超近程主动防护系统的雷
27、达关键技术研究D南京理工大学 , 200615 王盛利,张光义. 匹配傅里叶变换的噪声抑制与滤波J电子学报 , 2001,(12)16 朱力,胡学成,林幼权. 匹配傅里叶变换的SAR多普勒参数估计J中国电子科学研究院学报 , 2006,(02):152-161Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons.
28、 Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the worlds first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space
29、 shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologi
30、st, Ive still seen many important weather and space events, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.Its like the set for a George Lucas movie floating to
31、 the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons
32、 positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line we would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - t
33、he feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloo
34、n that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the fac
35、e of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather plays an important role in this mission. S
36、tarting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb highe
37、r than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slo
38、wly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearless Felix will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming poo
39、l that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 6
40、90 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be dep
41、loyed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachu
42、te that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the
43、 moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.17
