MAY/JUNE 2005 Copublished by the IEEE CS and the AIP 1521-9615/05/$20.00 © 2005 IEEE 71 Editor: Denis Donnelly, [email protected] EDUCATION E DUCATION dramatic poem Atalanta in Calydon were ringing in my ears. When the hounds of spring are on winter’s traces, … For winter’s rains and ruins are over, And all the season of snows and sins. But while the season of winter has ﬁ- nally passed and spring has indeed ar- rived, the second article in our fast Fourier transform series is not quite on its way in. Who knows the reason— was it “Pan by noon and Bacchus by night” that can explain? Still, the second and third sections will appear in subsequent issues. In part one of this series (“The Fast Fourier Transform for Experimental- ists,” vol. 7, no. 2, 2005, pp. 80–88), we discussed several basic properties of the fast Fourier transform (FFT). In addition to fundamental elements, we treated zero padding, aliasing, the relationship to a Fourier series, and ended with an introduction to win- dowing. What we originally planned for Part II, which is to focus on methods, grew too large for one segment, so the methods discussion will appear as two parts. In these two pieces, we will continue our discussion with a more general approach to spectrum estimation, including the periodogram, the autocorrelation function, autoregressive spectral estimation, and maximum entropy spectral estimation. In addition, we will include brief descriptions of treating convolution, filtering, and detrending. In the final installment, as we treat several applications, we will draw on a number of the ideas discussed in the first part dealing with concepts and then apply some of the methods that we’ll discuss in the next two articles. The particular applications we’ll con- sider include the spectral analysis of a bat chirp, atmospheric sea-level pres- sure differences, and perhaps even take a look at atmospheric CO 2 concentrations. S o, please forgive the unplanned delay, and as spring arrives and is underway, Part II will appear with no dismay: And time remember’d is grief forgotten, And frosts are slain and ﬂowers begotten, And in green underwood and cover Blossom by blossom the spring begins. THE F AST FOURIER TRANSFORM FOR EXPERIMENTALISTS By Denis Donnelly and Bert Rust C OMING IN FROM A WALK ON A GORGEOUS MARCH DAY, WITH THE SUN BEATING BACK THE PILES OF SNOW AND THE WATER SINGING IN THE FLOW CHANNELS, LINES FROM THE BEGINNING OF THE CHORUS IN ALGERNON SWINBURNE’S 1865 Got research? If you have an article you think would appeal to CiSE’s readers, please visit www.computer.org/ cise/deptguide.htm for information on how to submit it. www.computer.org/internet/ Stay on Track IEEE Internet Computing reports emerging tools, technologies, and applications implemented through the Internet to support a worldwide computing environment.

The Fast Fourier Transform for Experimentalists

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Page 1: The Fast Fourier Transform for Experimentalists

Editor: Denis Donnelly, [email protected]

EDUCATIONE D U C A T I O N

dramatic poem Atalanta in Calydonwere ringing in my ears.

When the hounds of spring are on win-ter’s traces,…For winter’s rains and ruins are over, And all the season of snows and sins.

But while the season of winter has fi-nally passed and spring has indeed ar-rived, the second article in our fastFourier transform series is not quite onits way in. Who knows the reason—was it “Pan by noon and Bacchus bynight” that can explain? Still, the sec-ond and third sections will appear insubsequent issues.

In part one of this series (“The FastFourier Transform for Experimental-ists,” vol. 7, no. 2, 2005, pp. 80–88),we discussed several basic propertiesof the fast Fourier transform (FFT).In addition to fundamental elements,we treated zero padding, aliasing, therelationship to a Fourier series, andended with an introduction to win-dowing. What we originally plannedfor Part II, which is to focus onmethods, grew too large for onesegment, so the methods discussionwill appear as two parts. In these twopieces, we will continue our discus-

sion with a more general approach tospectrum estimation, including theperiodogram, the autocorrelationfunction, autoregressive spectral estimation, and maximum entropyspectral estimation. In addition, wewill include brief descriptions oftreating convolution, filtering, anddetrending.

In the final installment, as we treatseveral applications, we will draw ona number of the ideas discussed in thefirst part dealing with concepts andthen apply some of the methods thatwe’ll discuss in the next two articles.The particular applications we’ll con-sider include the spectral analysis of abat chirp, atmospheric sea-level pres-sure differences, and perhaps eventake a look at atmospheric CO2concentrations.

S o, please forgive the unplanneddelay, and as spring arrives and is

underway, Part II will appear with nodismay:

And time remember’d is grief forgotten, And frosts are slain and flowers begotten, And in green underwood and cover Blossom by blossom the springbegins.

THE FAST FOURIER TRANSFORMFOR EXPERIMENTALISTSBy Denis Donnelly and Bert Rust

C OMING IN FROM A WALK ON A GORGEOUS MARCH DAY,

WITH THE SUN BEATING BACK THE PILES OF SNOW AND

THE WATER SINGING IN THE FLOW CHANNELS, LINES FROM THE

BEGINNING OF THE CHORUS IN ALGERNON SWINBURNE’S 1865

Got research?

If you have an article you thinkwould appeal to CiSE’s readers,please visit www.computer.org/cise/deptguide.htm for informationon how to submit it.

www.computer.org/internet/

Stay on TrackIEEE Internet Computing reportsemerging tools, technologies, andapplications implemented throughthe Internet to support aworldwide computingenvironment.