130TH ANNIVERSARY ISSUE

This is a story of passion, triumph andheartache. People, when their imagina-tion is captured by an idea, can becomeenergized and deeply involved, produc-ing remarkable results and reaching newheights that lead to the creation of land-marks in the progress of man. The FastFourier Transform (FFT) was such anidea.

Cooley and Tukey published their his-toric paper on the computation of theFourier transform in 1965. Overnight, inuniversities and laboratories around theworld, scientists and engineers begandeveloping computer programs and elec-tronic circuits to implement the FFT.

The FFT is a brilliant technique forcomputing the (discrete) Fourier trans-form quickly. By recognizing that theFourier transform of a sequence can bederived from the Fourier transforms oftwo half length sequences more economi-cally than if the whole sequence is trans-formed directly and by carrying this con-cept through to its logical conclusion ofevaluating only the direct transform of se-quences of two terms, Cooley and Tukeyshowed that the FFT required only N ×log2(N) operations while the direct formtook N2 operations. This meant that a1024 term FFT would take one hundredththe time it would have taken before. Notonly was it faster, it also could be evalu-ated in-place, requiring only half theamount of then scarce electronic memory.It is not difficult to see why the FFT cap-tured the minds and hearts of scientistsand engineers. In spite of the oft men-tioned description of scientists as au-tomatons, without touch and feel, we areall romantics at heart able to separatepoetry from prose.

Ed Sloan was an engineer working ontape recorders at Ampex in Palo Altowhen he came across the Danielson andLanczos technique for speeding up thecomputation of the Fourier transformpublished in the Franklin Journal in1942. Having failed to get Ampex inter-ested in the idea of a Fourier transforminstrument, Ed rounded up a group ofprivate investors (venture capitalistswere not yet an identified breed) in early1966, to finance his start-up company,

Thirty Years of FFT Analyzers . . .Sri Welaratna , Data Physics Corporation, San Jose, California

S&V OBSERVER

Time/Data Corporation. Ed Sloan, oftendescribed as “a certifiable genius,” withthe help of another brilliant young engi-neer named Bruce McKeever, was discov-ering larger computational efficienciesover the “Frequency Folding” techniqueof Danielson and Lanczos when theywere shown the Cooley-Tukey paper thathad been published the year before.Heartbreak, over being beaten to thegoalpost by someone else, soon gave wayto enthusiasm to build an FFT machine;and Ed and Bruce rolled out their FFTinstrument in October 1967. The Time/Data 100 consisted of two six foot racksof purpose built hardware, performed a1024 point FFT in 1 sec, and was a tre-mendous technical achievement.

Unfortunately, the equally large com-mercial success it was expected to be-come didn’t happen. Nearly thirty cus-tomers had been canvassed, all of themin medical applications, who had fund-ing approved from the National Institutefor Health when the Johnson governmentdiverted the funds to the Vietnam wareffort.

This time the heartbreak was difficultto deal with and only an accident of faterevived the fortunes of Time/Data. TheF111 fighter aircraft that sported variableswept wings was in trouble – the wingsfell off in flight! The Air Force had givenan ultimatum to General Dynamics thatno more aircraft would be accepted with-out proof of wing integrity. Faced with afield full of planes that were undeliver-able, General Dynamics was ready tomove heaven and earth in search of a so-lution. A young MIT graduate named JimGreen at General Dynamics rememberedhis grandfather testing steel rails by hoist-ing each rail in the middle, hitting eachend with a calibrated hammer and listen-ing to the ringing. His grandfather wasable to detect cracks in the rails with re-markable accuracy. Jim convinced him-self that this could be made into a scienceand called around for likely sources. Hefound Time/Data and after a weekend ofanalyzing tape recordings of aircraft wingimpact tests with Bruce McKeever, Gen-eral Dynamics discovered their measur-ing instrument. The acceleration signalsmeasured from wings with cracked pivotholes showed characteristic frequencyspectra, thus providing an unmistakablemethod of detection.

The Air Force commandeered the firstavailable Time/Data 100, bumping othersin line and the company received a tre-mendous boost in the marketplace. Soon,vibration applications would be added tothe list of uses for the FFT instrument,which had up until then, found most of

Time/Data 90 FFT Processor, November 1969.

its uses in medical applications includ-ing the Stanford sleep studies of 1967.The Time/Data 100 was followed by theTime/Data 90 which provided speedup ofthe FFT in a general purpose minicom-puter system. An improved version,based on the PDP11, was marketed as theTime/Data 1923 in 1972.

When the private investors wanted tocash out, General Radio bought Time/Data. Since the new owners probablynever understood what they had bought,they failed to provide the environment inwhich Ed Sloan, Bruce McKeever and thescores of other bright men who followedcould have realized their dreams. Brucestill drives around in a car carrying theregistration FFT. While the passion hassubsided, he has not entirely forgottenthe heady excitement of the early period.

About the same time, at the Santa Claradivision of Hewlett-Packard, an unas-suming young engineer named Ron Pot-ter set out to develop a waveform calcu-

Hewlett-Packard 5451A Fourier Analyzer, De-cember 1972.

The Fourier transform todaytouches the lives of everyone.

It does so in the form ofsuperior automobiles, aircraft,telecommunications systems,

chain saws, washing machinesand myriad other aspects of

modern life.

SOUND AND VIBRATION/JANUARY 19972

tion testing, modal analysis of mechani-cal structures and machine signatures ofrotating equipment.

Far away in Yonkers, New York ’sHarlem (fondly referred to as upper Man-hattan), Henry Bickel had started a busi-ness named Federal Scientific Corpora-tion with four professors from ColumbiaUniversity to develop long range missiledetection technology for the Defense De-partment. Federal Scientific carved out aniche for itself with the ‘Ubiquitous®’ se-ries of real-time analyzers based on time-compression techniques. Their largestsuccess was a contract to supply subma-rine detection instrumentation for thefleet of P3 Orion Aircraft. It was afterNicolet had acquired Federal Scientificand the FFT business was in full swingthat Federal made its first single channelFFT analyzer called the ‘Mini-Ubiqui-tous®’ 440A. The 440A, its progeny andits companion, the two channel 660, wereto make their mark during the secondwave of FFT analyzers.

Yet another young man, Laurie Bur-rows left the Convair Instrument Divisionof General Dynamics, which had fallenon hard times, to start a company in SanDiego with Hugh Ness and a couple ofothers. They named their company Spec-tral Dynamics after General Dynamicsand bought the rights to the tracking fil-ter that Laurie had developed while atGeneral Dynamics for use in the 880 and990 aircraft. Laurie’s tracking filter useda low cost HP oscillator in place of anexpensive precision oscillator to cut thecost to a tenth of the rival instruments.Initially, Spectral Dynamics made track-ing filters, but later they built real-timeanalyzers using the time compressiontechnology patented by Victor Andersonwho worked for the Naval Research Labin San Diego. While they did not build afirst generation FFT instrument until1975 when the SD360 was introduced,they joined the fray in full force with the

Computational Systems, Inc. Wavepak® FFTSignal Analyzer, September 1985.

Nicolet Scientific Corporation 440A Mini-Ubiq-uitous® real-time spectrum analyzer, Septem-ber 1975.

Spectral Dynamics Corporation SD360 DigitalSignal Processor, November 1975.

lator that would allow computations onwaveforms and their spectra rather like ahand held calculator could do with indi-vidual numbers.

Ron Potter had studied electronics atthe University of Illinois and taught him-self to program on the ENIAC, which had1024 words of 40 bit memory, no drumnor disk storage, but did have a CRT dis-play and a camera. He was able to plot thecubic polynomial he had derived as thestep response of a two pole amplifier andpublished one of the earliest papers onthe use of a digital computer in RadioApplications. Ron Potter is a true genius;there have been few men who have un-derstood the measurement and analysisof physical phenomena as well as he andeveryone who worked with him knew “hewalked on water.”

Correlation was gaining momentum asa technique for pulling signals out ofnoise and studying physical systems. Theevaluation of a spectrum took too muchcomputational effort to be practical andthere was a debate on as to what was bet-ter. When the Cooley-Tukey paper ap-peared, Ron understood the algorithmand its significance immediately. The cor-nerstone of his new instrument would bethe FFT. Ron Potter worked out the math-ematics, Ago Kiss worked on the hard-ware and Pete Roth joined to build theADC (Analog to Digital Converter).

In the typical product developmentstyle of HP, they assembled a simulator ina six foot rack of equipment comprisingof a PDP minicomputer, an ADC for cap-turing the signals, a CRT device for wave-form display, a paper tape reader for pro-gram input and a teletype for interactingwith the system. In those days, BillHewlett and Dave Packard personally re-viewed every new product idea. After be-ing presented with a demonstration of thewaveform calculator in gestation, it wasPackard who suggested that they sell the

simulator as the product itself. HP wasjust getting into the computer business atthat time and Ron received one of the firstprototype computers from the Cupertinodivision. It quickly replaced the rivalDigital Equipment Corporation’s PDPcomputer; the HP 5450 Fourier Analyzerwas born. Ron Potter who had made his-tory as the father of the Fourier analyzerhad briefly left the company and it wasPete Roth who was in charge when thisrevolutionary instrument/computer sys-tem was brought to market. There were anumber of other bright engineers whowrote the software and developed thehardware: Skip Ross, Steve Cline, ChuckHershkowitz and Charlie Heisman amongthem. But, if not for Al Bagley, the Fre-quency & Time Division Manager, whoacted as the inspiration and supportedPackard’s idea, the Fourier analyzer maynot have been born, at least not in thatform.

The first customer for the HP FourierAnalyzer was the Walter Reed Hospital inMaryland, where they were studying neu-ral responses of monkeys. Dave Snyder,another bright engineer who had justjoined the team, went east with Pete Rothto install and train the users. They neverimagined that eventually the productwould find its focus in noise and vibra-tion applications. There were to be manyfalse starts in a number of applicationsbefore HP would discover a market forthe FFT technology. Bob Perdriau, whojoined the digital signal analysis group atHP Santa Clara to produce the HP5453telephone test system, the first derivativeof the Fourier Analyzer, remembers theexcitement and fervor among the teammembers. The HP5453 never took off andthe politics and economics of businessleft behind a few more young men withhearts full of sorrow. Fortunately, a sig-nificant business grew around the HP-5451 Fourier Analyzer with applicationsin closed loop shaker control for vibra-

330TH ANNIVERSARY ISSUE

Data Physics Corporation DP420 FFT Analyzer,June 1989.

Scientific Atlanta SD390 Dynamic Signal Ana-lyzer, February 1993.

SD380 which commanded a significantsegment of the FFT market in the secondwave.

There was a sense of excitement in theair at all these places, the feeling thatonce a waveform was captured in digitalform and available in a computer, therewas no limit to the measurements thatcould be derived. In effect, this was auniversal instrument, making obsolete allothers. Of course, nothing is quite sosimple and the measurement of physicalprocesses demands a lot more than a digi-tizer and a computer.

The first FFT analyzers came in a sixfoot high, 19 in. wide rack with a visibleminicomputer, CRT display device, ana-log to digital converter, optional digital toanalog converter, paper tape reader, anda teletype. At Hewlett-Packard, everyproject to create a faster FFT device withdedicated hardware FFT ran into compe-tition from the ever faster computer. DaveSnyder remembers how his microcodedFFT in the 5451B made obsolete in onestroke, the 5471 hardwired FFT box. AtGenRad, Bruce McKeever acknowledgesthat having first made a dedicated hard-ware FFT system in the Time/Data 100,they quickly changed to a general com-puter system for the Time/Data 1923,though still using a speedup box for theFFT. At HP, Webb McKinney inventedband selectable Fourier analysis to yieldhigher frequency resolution from a lim-ited available memory. Zoom transform,as it later came to be called, was a signifi-cant milestone.

An unsung hero of the FFT revolution,Norm Rodgers was a quiet engineer work-ing at GenRad who one day announced tohis colleagues that he had something toshow. It was a breathtaking revelation. Hehad all by himself invented an entire pro-gramming system, inclusive of language,that would allow users to build new mea-surements extending the basic instru-ment. TSL (Time Series Language) was

born and became the backbone of manynew applications that were developedlater, including modal analysis and vibra-tion exciter control systems.

The first ten years were exciting butpainful. The market remained small andnarrow, both Hewlett-Packard and Gen-Rad found it difficult to make the busi-ness grow in the model of the rest of theirbusiness. Spectral Dynamics and Nicolethad entered the fray, competition wasbecoming fierce and attention turned toapplications. Dick Watts had worked oncorrelators at HP South Queensferry inthe UK and had moved to Santa Clara.While Dick was marketing manager forFFT products, HP tried a bold experimentto create a specialist sales and applica-tion group to promote the products. Thisachieved instant success and attractedanother band of enthusiasts who em-braced the science with the same fervor,but HP always had difficulty dealing withprimadonnas and eventually disbandedthe special sales force in order to normal-ize its instrument sales operations, break-ing the hearts of those who by then werebitten by the bug and enjoying theirCamelot.

The Second Wave. The second wave ofFFT analyzers came almost exactly at theend of the first decade. Gone were thevisible computers. The weight was downto around 70 lbs. The most noticeablechange was the lower price, instead ofcosting $50,000 to $100,000, they werenow much more accessible at $20,000 to$50,000. The HP5420, GR2508, SD360and the Nicolet 446A and 660B domi-nated the scene. Brüel & Kjær from Den-mark, the undisputed leader in acousti-cal instrumentation had held out for along time against the digital revolution,but the FFT analyzer was too large a forceto resist and when they did join the band-wagon, their offering was significant. TheB&K Type 2032 was the first to incorpo-rate a larger capture buffer in the front-

end allowing reanalysis of captured datawith selective overlap.

The biggest surprise came from an un-expected quarter, another division of HPat Loveland, CO, brought out the twochannel HP3582 at around $12,000 andin a small package, but weighing 55 lbs.The HP3582 changed the FFT analyzerbusiness overnight, selling four times asmany units as its nearest competitor; itwas a runaway success. Nicolet andRockland found the competition verytough and bowed out. Another romantic,George Fox Lang, left the ashes of Nicoletto carve out a niche informing and amus-ing us through Sound and Vibrationmagazine.

For a while HP, GenRad, B&K andSpectral Dynamics shared the spoils. Oneof the biggest casualties was the SantaClara Division of HP, which had been theMecca of digital signal analysis at HP. TheLoveland Division had packaged thezoom transform on four chips. This func-tion occupied at least four large printedcircuit assemblies in every other instru-ment. The HP3582 was a very good in-strument. Although it was short onmemory and therefore lines of resolution,it became a workhorse in the industry.What they had done was nothing morethan another milestone in the inevitablemarch of electronics towards smaller andfaster devices. This was what HP wasgood at, but to the faithful at Santa Clarait was a bitter pill. Progress had come notfrom the development of applications butminiaturization and reduction of cost.

The second decade of the FFT analyzerwas also dominated by the emergence ofthe applications into significant sciences.Four distinct areas of application of theFFT analyzer emerged.

Modal analysis, popularized by DaveBrown at the University of Cincinnati,captured the imagination of engineers.The ability to identify the modes of vibra-tion of a structure and extract individual

SIGnology SP-20 Fourier Spectrum Analyzer,January 1987.

SOUND AND VIBRATION/JANUARY 19974

Data Physics Corporation DP540 VibrationControl System, November 1994.

Data Physics Corporation DP104 FFT Analyzer,November 1996.

mode shapes from a set of frequency re-sponse functions was a remarkableachievement. The ability to display eachmode in animation made them ecstatic.The HP5423 Structural Dynamic Ana-lyzer was the first of many instrumentsdedicated to modal analysis. Unfortu-nately, HP’s search for success in the tra-ditional packaging of technology to cre-ate ever increasing markets did not leaveroom for technologies that could notyield market size. The HP5423 markedthe end of HP’s direct involvement inmodal testing applications. They choseinstead to remain a supplier of generalpurpose FFT instruments.

Four modal aficionados left to formStructural Measurement Systems led byMark Richardson. In Belgium, a Univer-sity of Leuven alumnus, Maurice Mer-geay started Leuven Measurement Sys-tems (LMS) which would eventuallydominate the field, though by then hewould have left the company, not fittinginto the politics within. Dave Formenti,one of the four founders of SMS remem-bers the sweet agony of labor, relentlesslypursuing modal analysis applications.Ten years after its founding, SMS was ac-quired by the Structural Test Productsdivision of GenRad where SMS failed toflourish because once again GenRadfailed to understand what they hadbought.

Digital vibration control, though it didnot have as much ‘sizzle,’ emerged as asignificant application. A shaker could becontrolled to reproduce a vibration envi-ronment in the laboratory with remark-able accuracy. Random vibration experi-enced in a vehicle on the road, shockexperienced in dropping something onthe floor or the periodic vibration pro-duced by an engine speeding up – allcould be simulated in the laboratory sav-ing tremendous man hours of productqualification. The first applications ap-peared as software add-ons to the GR1921and the HP5451 but by 1980 dedicatedvibration controllers had taken over withthe HP5427, GR2511 and the SD1700 se-ries dominating this burgeoning busi-ness.

The growth of digital vibration control,which had brought large improvementsin accuracy and speed over the analogsystems with banks of parallel filters,fueled growth at Spectral Dynamics,GenRad and HP. Spectral Dynamics hadtheir own Camelot in the period follow-ing the first wave and was a haven formany committed signal analysis profes-sionals, until they were acquired by Sci-entific Atlanta. GenRad continued to sellvibration controllers long after HP andSD had left the field thus becoming thecompany with the largest installed base.

Signature analysis of rotating equip-ment was a distant third in appeal andsize of application. The three dimen-sional RPM-spectral map is a remarkablemethod of separating vibration due to

structural resonance from that due to ro-tating masses. The derived plots of ordertracks provide a means of identifying vi-bration causing mechanisms. Engine run-up and coast-down waterfall maps be-came available with the first Fourieranalyzers and have since become a stan-dard feature in the majority of analyzersthat followed.

Acoustic intensity was a new measure-ment technique in 1979. Two micro-phones spaced a few mm apart could beused to measure not only the magnitudeof sound intensity but also its direction.The FFT-based cross power spectrumcomputation between the two micro-phone signals could be used to derive thesound intensity. This technique has beensuccessfully used to identify sound-radi-ating components in internal combustionengines and other machines. B&K, withtheir superior position in acoustical ap-plications and dominance of precisionmeasurement microphone technology,

has been the best proponent of acousticintensity measurement. While the num-ber of users of this measurement tech-nique remains modest, it has, neverthe-less, become an important feature in FFTinstrumentation.

The growth of any business lies not inmaking and selling clever instruments,however fascinating the inventions maybe, but in making a contribution to thebusiness of the users who pay for them.The FFT analyzer was no exception. Itwas the growth of the applications thatmade a growth business for its suppliers.An editorial comment in the October1969 edition of Sound and Vibration byits publisher, Jack Mowry, is worth re-peating “. . . the man who recognizes yourapplications, understands what he’s sell-ing and fits his products to your needs,is going to get the order. One buys a ham-mer to pound nails, not just to have ahammer.” An astute commentary by ayoung man at the time, Jack knew whathe was talking about.

The Third Wave. The third decadebrought about the FFT analyzer on a cardto be plugged into a PC. IBM had intro-duced the PC, setting in motion a revo-lution in the way we would make mea-surements. In the beginning, many FFTanalyzers could be connected to a com-puter by an IEEE488 or RS232 interfacecable, providing connectivity betweenthe measurements and further analysisprograms. The inclusion of the measuringinstrument within the computer wouldbenefit all, and the advent of the digitalsignal processor would make this pos-sible. DSP (Digital Signal Processor)chips are remarkable; they are nearlycomplete computers, optimized for vec-tor operations and especially, the compu-tation of the FFT. The second generationDSP chips that became popular in FFTanalyzers around 1986 could perform a1024 point FFT in under 10 msec. Min-iaturization and the commensurate re-duction in cost had taken its next jump.A complete two channel FFT analyzer ap-peared on a single PC I/O card, the priceof which came down to a range of $10,000to $20,000. Even the instruments in con-ventional boxes came down to under 25lbs in weight.

CSI Wavepak®, Data Physics DP420and the SD390 PC-based analyzers tooktheir place among the traditional FFT in-struments from HP and B&K. SIGnologyintroduced a DSP solution in a separatebox attached to the computer. In additionto the normal attributes of FFT instru-ments, the PC-based analyzers were ableto provide better graphics and vastly im-proved user interfaces. As graphical userinterfaces became popular in PC applica-tions, HP and Tektronix also producedtheir own PC-based analysis systems, butwith the data capture and signal process-ing hardware in an external box con-nected to the PC. The rapid developmentof the PC in speed and capacity has

530TH ANNIVERSARY ISSUE

Sri Welaratna came across the Fourieranalyzer in 1970 while doing research atthe University of Bradford in Englandand went to work for Hewlett-Packard,first in Europe and then at Santa Clara.After a brief stint at SMS he founded DataPhysics Corporation with Dave Snyder,another alumnus of HP Santa Clara. Oneof his hobbies is collecting loose ends,loosely defined as wandering signalanalysis professionals, who lost theirmoorings in the shifting tides of corporatemergers.

brought about corresponding improve-ments in the analyzers built upon them.The formula of modifying a general pur-pose computer to make an FFT analyzerclaiming the benefits of the independentdevelopment of computer technology hadcome full circle to that of the first genera-tion.

The FFT processor card within the PCalso proved to be an ideal solution for thevibration control application. The DataPhysics DP540 debuted in 1990, redefin-ing the price/performance standards of ashaker controller. Initially used primarilyin defense applications, the price reduc-tion from the $60,000 to $100,000 rangeto the $20,000 to $50,000 range broughtthe technology within the grasp of alarger number of commercial applica-tions.

The Future. A decade later, as we cel-ebrate the 30th year of Sound and Vibra-tion magazine, the FFT analyzer is aboutto register its next quantum leap. A com-plete analyzer weighing only 1.8 oz. hasbeen introduced by Data Physics provid-ing phenomenal performance: 20 kHz tri-spectrum real-time rate, 64k max trans-form size and 100 dB dynamic range.This tiny module plugs into any type IIIPCMCIA slot in any notebook computerrunning Windows 95 and provides a full

repertoire of time, frequency and ampli-tude domain measurements. As youmight expect, the cost of the FFT analyzerhas made a corresponding leap down-ward. The entire package of notebookcomputer and FFT analyzer weighs about6 lbs, painting visions of vibration engi-neers spending the day with their light-weight instrument and then writing theirreports on the way home using the samesystem.

Those who began their careers with thefirst FFT analyzers and remember lugginghuge bays of instruments around in wag-ons and trailers would look at this latestFFT analyzer in your palm and either cryfor joy or shed tears in regret. But, nonewould fail to be amazed at what is trulya remarkable journey of technologicalaccomplishment.

Epilog. The author wishes to thank allthose who gave of their time and volun-teered information about the early days.It has been the most enjoyable task I haveundertaken in a long time, listening tocolleagues reminisce about the gloriouspast and indulging in my own nostalgia.Some of you poured your hearts out, sur-prising me with the intensity of feelingfor your work going back thirty years. Thesatisfaction of intellectual endeavor, theexhilaration of scientific discovery and

the warm glow that comes with eruditionwhen your mathematical models fit thephysics – thank you for sharing your ex-periences with me. I am sorry time andspace did not permit the inclusion of ev-ery name and event, some of them omit-ted in error. This account is highly per-sonal and it probably does not do justiceto all. Unfortunately, we cannot see his-tory except through the eyes of the his-torian. I alone am responsible for the er-rors and omissions.

Reference. Cooley, J. W., and Tukey, J.W., “An Algorithm for the Machine Cal-culation of Complex Fourier Series,”Mathematics of Computation, Vol. 19,1965.