Showing papers in "IEEE Transactions on Audio and Electroacoustics in 1967"

The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms

Abstract: The use of the fast Fourier transform in power spectrum analysis is described. Principal advantages of this method are a reduction in the number of computations and in required core storage, and convenient application in nonstationarity tests. The method involves sectioning the record and averaging modified periodograms of the sections.

What is the fast Fourier transform

Abstract: The fast Fourier transform is a computational tool which facilitates signal analysis such as power spectrum analysis and filter simulation by means of digital computers. It is a method for efficiently computing the discrete Fourier transform of a series of data samples (referred to as a time series). In this paper, the discrete Fourier transform of a time series is defined, some of its properties are discussed, the associated fast method (fast Fourier transform) for computing this transform is derived, and some of the computational aspects of the method are presented. Examples are included to demonstrate the concepts involved.

Modern techniques of power spectrum estimation

Abstract: The paper discusses the impact of the fast Fourier transform on the spectrum of time series analysis. It is shown that the computationally fastest way to calculate mean lagged products is to begin by calculating all Fourier coefficients with a fast Fourier transform and then to fast-Fourier-retransform a sequence made up of a_{k}^{2}+b_{k}^{2} (where a_{k}+ib_{k} are the complex Fourier coefficients). Also discussed are raw and modified Fourier periodograms, bandwidth versus stability aspects, and aims and computational approaches to complex demodulation. Appendixes include a glossary, a review of complex demodulation without fast Fourier transform, and a short explanation of the fast Fourier transform.

Application of the fast Fourier transform to computation of Fourier integrals, Fourier series, and convolution integrals

Abstract: The fast Fourier transform is a computational procedure for calculating the finite Fourier transform of a time series. In this paper, the properties of the finite Fourier transform are related to commonly used integral transforms including the Fourier transform and convolution integrals. The relationship between the finite Fourier transform and Fourier series is also discussed.

Historical notes on the fast Fourier transform

Abstract: The fast Fourier transform algorithm has a long and interesting history that has only recently been appreciated. In this paper, the contributions of many investigators are described and placed in historical perspective.

A method for computing the fast Fourier transform with auxiliary memory and limited high-speed storage

Abstract: A method is given for computing the fast Fourier transform of arbitrarily large size using auxiliary memory files, such as magnetic tape or disk, for data storage. Four data files are used, two in and two out. A multivariate complex Fourier transform of n=2^{m} data points is computed in m passes of the data, and the transformed result is permuted to normal order by m - 1 additional passes. With buffered input-output, computing can be overlapped with reading and writing of data. Computing time is proportional to n \log_{2} n . The method can be used with as few as three files, but file passing for permutation is reduced by using six or eight files. With eight files, the optimum number for a radix 2 transform, the transform is computed in m passes without need for additional permutation passes. An ALGOL procedure for computing the complex Fourier transform with four, six, or eight files is listed, and timing and accuracy test results are given. This procedure allows an arbitrary number of variables, each dimension a power of 2.

Fast Fourier transform method of computing difference equations and simulating filters

Abstract: Two methods for using the fast Fourier transform to reduce the number of arithmetic operations and, therefore the time required for computing discrete, preformulated, and finite convolutions are listed and justified. Under the idealistic assumption that the impulse response of a preformulated difference equation terminates, a theorem is proved that these two methods can be modified to compute such difference equations. This theorem makes plausible the application of these methods when the impulse response does not terminate, provided that the impulse response decays to a small value. In such cases, the fast Fourier transform can be used to compute approximations to the solutions, although usually this use of the fast Fourier transform offers no reduction in the amount of time required for computing the definition of the difference equation. However, if a filtering operation is specified as a frequency response, the fast Fourier transform can be used to compute the filtering operation directly without need of formulating a difference equation, although this simplification is achieved at the cost of a moderate increase (e.g., twice) in the amount of computation time.

The channel vocoder

Abstract: The channel vocoder is described. This device achieves bandwidth compression greater than that of the bandpass compressor but less than that of the formant vocoder. To date it has been much more widely used than any other kind of vocoder. The channel vocoder exploits the insensitivity of the aural mechanism to phase, and only attempts to reproduce the short time power spectrum of the speech waveform. The spectral envelope of the speech is measured with a bank of filters and ascribed wholly to the vocal tract filter, while the excitation is estimated to be either a quasi-periodic pulse train, or noise. There are several methods of combining these extracted parameters to reconstruct the speech. Several configurations of the channel vocoder are described and the factors which affect the specification of design parameters for channel vocoders are considered.

Spectral analysis of the call of the male killer whale

Abstract: Poulter previously presented sonagram analyses of underwater sound recordings of various sea mammals, calling attention to the apparent harmonic progression of components of these signals. Other workers have questioned the presence of these harmonics in the original data and have suggested that they may instead be introduced during the analysis. In this paper we use underwater sound recordings of the male killer whale Namu, taken with equipment flat within ±2 dB to beyond 18 342 Hz, the upper limit of the analysis, to show by means of digital spectral analysis methods that a harmonic progression exists. In the signals analyzed, peaks in the estimated spectrum were observed at each integer multiple of the fundamental frequency. In view of the broad frequency response of the recording equipment and the precision of the subsequent digital analysis, we can say with confidence that these harmonics were actually present in the whaler's call. For the analysis, portions of an audio recording were converted to digital form. In the conversion, a bandpass filter was used to attenuate power below 40 Hz and above 10 kHz. Digital analysis techniques similar to those proposed by Bingham, Godfrey, and Tukey were then used. For each time span of data to be analyzed, a windowed Fourier transform was first computed, using a fast Fourier transform program. The power spectrum was next computed, as the squared modulus of the windowed transform, and a correction was made for the attenuation of high frequencies during A-to-D conversion. The autocorrelation function was estimated by computing the inverse transform of the power spectrum. A moderate amount of digital smoothing was then applied to the spectrum to reduce irregularities due to noise. The resulting smoothed spectrum is used as an estimate of the power spectral density function.

Experimental, limited vocabulary, speech recognizer

Abstract: An experimental speech recognizer is described which exhibits a high level of performance and is practical in terms of size, weight, cost, and power consumption. High recognition performance is achieved by employing the limited vocabulary approach and utilizing a simple set of parameter extractors based upon the single equivalent formant theory conceived and developed by one of the authors. Recognition logic for a vocabulary word consists of circuitry for testing the levels and movements of three parameter waveforms to determine whether they conform to the conditions of acceptability for the particular word as found from parameter data for a large number of speakers. The recognizer presently responds to the spoken digits OH through NINE with a recognition accuracy of 90 percent and an error rate of one percent on live utterances by speakers who contributed the design samples, and only slightly lower than this on other male speakers of similar speech characteristics. The recognizer occupies a volume of less than 0.8 cubic foot exclusive of microphone, indicator, and power supplies, consumes less than 30 watts, and shows promise of a very low eventual cost per word.

Survey of acoustic characteristics of bullet shock waves

Abstract: The extensive literature on characteristics of shock waves provides fundamental relationships for amplitude and length which hold over a large range of projectile size. However, the discussions are spread through many publications and employ varying notation in mathematical exposition. The frequency spectrum of the shock-wave signature has received much less attention than the wave shape, although it is important in engineering applications such as bullet detection. This paper emphasizes engineering aspects. It combines data from a number of publications first to give a qualitative description of the N wave generated by bullet passage and the geometry associated with N-wave measurement. Formulas with consistent notation for calculating N-wave amplitude, length, and frequency spectrum are given. Computed values are compared to results of experimental measurements reported in the literature and carried out at Bissett-Berman. Effects on frequency spectrum of distance and shadowing by interfering objects are illustrated. It is shown that various theoretical and experimental results are consistent and produce a body of knowledge from which the characteristics of shock waves, generated by projectiles and other supersonic bodies, can be confidently predicted mathematically and accurately measured with available equipment.

About this issue [special issue on the Fast Fourier Transform (FFT)]

Abstract: This special issue is an outgrowth of standardization activities in audio and electroacoustics. In 1960, Subcommittee 30.4 on Methods of Measurement of Noise of the IRE Audio and Electroacoustics Committee (Technical Committee 30) became concerned with the characterization and measurement of quantities having a short duration. The subject of this special issue, the Fast Fourier Transform (FFT), is a technique that substantially reduces the time required to perform Fourier analysis on a computer. The first paper, was prepared by members of the Concepts Subcommittee (formerly 30.4) as a general survey of the subject. The second paper, is the keynote paper presented by C. Bingham, Jr., at the Power Spectrum Workshop. Short contributions prepared by four of the workshop panelists follow the keynote paper. Each panelist was at liberty to submit his contribution as an informal discussion or as a formal paper. These short contributions are followed by "Historical Notes on the Fast Fourier Transform," by J.W. Cooley, P.A.W. Lewis, and P.D. Welch. The remainder of the special issue is given to five papers on applications of the Fast Fourier Transform. These papers discuss mathematical developments as well as experimental results obtained by use of the Fast Fourier Transform for the solution of engineering problems.

A loudness-level monitor for broadcasting

Abstract: A Loudness Monitor for broadcasting has been developed by CBS Laboratories under joint sponsorship with the CBS Broadcast Group and is currently undergoing field tests The Monitor uses the CBS Laboratories equal-loudness contours, the Loudness Level Summation Method described previously by Bauer and Torick, [7] and a revised ear ballistics characteristic The steady-state calibration of the Monitor is in decibels re 1 mW into 600 Ω at 1000 Hz The indications of the loudness level of program are in loudness level units (LU)

Speech processing techniques and applications

Abstract: The processing of speech involves the analysis, coding, decoding, and synthesis of speech sounds. The speech analyzer consists of normalizers, syllable and syblet segmenters, sound recognizers, sequencers, adapters, and memories which convert the speech elements into a code. The speech synthesizer converts the code to speech by reproducing prerecorded speech elements. There are many applications for the speech analyzer and synthesizer ranging from limited vocabulary to complete communication systems.

Systems for compressing the bandwith of speech

Abstract: Speech bandwidth compression is based on the present knowledge of human speech production and perception. This is the first in a series of papers reviewing the articulatory, acoustic, and network description of speech and discusses the bandpass compressor, which is a simple example of a bandwidth saving device.

Informal comments on the uses of power spectrum analysis

Abstract: Two important considerations in the use of a computer for power spectrum analysis are the availability of a set of sub-programs to perform the necessary functions and an adequate display of the output. The author relates these considerations to his experiences using a digital computer to investigate the cepstrum and other kinds of echo analysis.

Digital determination of third-octave and full-octave spectra of acoustical noise

Abstract: The spectrum of the acoustical noise produced by typical sources such as business machines is usually measured with analog filter banks. The objective of this study was to perform spectral analysis using digital rather than analog methods. The Cooley-Tukey algorithm has been used to compute the Fourier coefficients of noise samples obtained with the aid of a digital recording system described previously [4]. The resulting coefficients have been used to compute octave band and third-octave band spectra of the noise samples. The digital spectral estimates are in good agreement with analog measurements. Emphasis is placed on the filter characteristic or "window" used for the analysis, and the spectral fluctuations which occur in short (65-250 ms) samples of the noise. For one machine studied, the spectral fluctuations are larger than would be expected for samples of random noise. Spectral analysis of impulsive noise produced by a second machine (a manual, key-entry card punch) indicates that spectral fluctuations occur even when the envelope of the pressure-time pattern is observed to be repetitive.

Spectrum analysis in speech coding

Abstract: In the process of hearing, the human ear develops a short-time spectrum of its acoustic input. Information-bearing features of the signal are retained in this spectral analysis. An understanding of the process by which the human auditory system preserves perceptually significant features is valuable in developing speech-transmission techniques. An example of effort in this direction is the phase vocoder.

Guest editorial [On digital frequency analysis for audio engineers]

Abstract: One of the last places one might look for a discussion of digital frequency analysis would be in the IEEE Transactions on Audio and Electroacoustics. A paper by Cooley and Tukey (1965) described a recipe for computing Fourier coefficients of a time series that used many fewer machine operations than did the straightforward procedure. This saving in computation can amount to a factor of as much as several hundred for usefully long stretches of data. Almost simultaneously G. Sande at Princeton University developed another algorithm of the same class. He used it to calculate covariances with equally impressive saving, though not of the same magnitude. Procedures that provide reductions in complexity of this order may rightfully be called breakthroughs. After the publication of Cooley and Tukey's paper a number of earlier papers were discovered describing the essentials of the fast Fourier transform. But, as has happened often in other fields, these papers appeared too early, and solved a problem whose importance had not yet been adequately recognized. Besides making digital spectrum analysis more attractive from an economic standpoint, the fast Fourier transform (FFT) has changed the concepts of digital filtering, in that the intellectually appealing approach of filtering in the frequency domain is now very often simpler and quicker than by convolution, even though two transforms between time and frequency are employed. In the use of digital systems, the important barrier between the time- and frequency-domains has been significantly lowered. Given the on-going intensive and widespread development in digital circuit technology, this means that many new applications for digital processing will be opened up. The audio engineer who naturally thinks only in terms of analog processing might well become familiar with what the digital approach is now able to offer. He may be surprised. What lies over the horizon in digital processing is anyone's guess, but I think it will surprise us all.

A study of the field around magnetic heds of trapezoidal shape

Abstract: A trapezoidal configuration of the magnetic head which is a better approximation to the actual head shape as compared to the shapes treated so far is assumed. The Schwartz-Christoffel transformation is used to determine the magnetic field distribution around this head shape, and a field mapping equation is obtained. Examples of the field distribution around the trapezoidal as well as the finite head configurations are computed with the aid of an electronic digital computer using the mapping equation obtained. The results are compared and discussed. The digital computer program used is written in FORTRAN II, and is listed and described.

High-power solid-state amplifiers

Abstract: High-power amplifiers are needed, particularly in the area of sound reinforcement for public address and auditorium usage. Paralleling a number of amplifiers to obtain the required power level has never been a wholly satisfactory solution. This paper presents the design philosophies and goals achieved in two high-power solid-state amplifiers, rated at 150 and 330 watts, respectively. In addition, there is a discussion on unique electronic protection circuitry which these amplifiers contain, in order to protect the amplifiers and their associated equipments, in the event of system malfunction.

The transient distortion of loudspeakers and its evalution

Abstract: The paper first briefly explains the causes of a considerable distortion of transient signals by electroacoustic transducers and reviews the methods used to investigate this type of distortion. Also discussed are certain questions of perceptibility and the importance of the transient distortion. There follows a brief description of preliminary listening tests with piano tones, carried out in order to examine certain disputable statements. Preliminary conclusions are drawn for the evaluation of transient distortion from the point of the perception of transient signals in music and speech.

Digital analysis of bursts in the time domain

Abstract: A technique is described for analyzing bursts and burst-like events with a digital recording system and a general-purpose computer. The waveform of the burst is sampled by an analog-to-digital converter and stored on magnetic tape. The digitized samples are used as input data to an IBM 7094 data processing system for which a burst-analysis program has been written in the FORTRAN language. The analysis of amplitude and shape variations of a burst train is completed without manual processing of the data. This technique is used to analyze the acoustical noise produced by a card punch.

Cybernetics and speech communications: A survey of russian literature

Abstract: A critical survey of Russian publications in those fields of cybernetics that apply to speech communication is presented. In particular, reports on speech analysis, production, and perception, speech bandwidth compression, and automatic speech recognition are reviewed to indicate trends rather than technical details. The paper is supplemented with bibliographic appendixes which include references to applicable books and papers as well as information on their translation availability.

Semiautomatic speech intelligibility measurements

Abstract: A recent study towards the improvement of intelligibility testing techniques has resulted in a very efficient testing procedure based on the use of the Fairbanks Rhyme Test and a computer. The Fairbanks Rhyme Test permits the actual tests to be taken quickly and simply, and the computer provides a rapid, thorough analysis of the test data. Subsequent evaluations of several vocoders, and of the effects of electrical stimuli upon test subjects, showed this testing procedure to be quite effective. Small differences in intelligibility between systems were detected by giving a large number of tests. A diagnostic evaluation of each system was performed by the computer, which pointed out specific shortcomings of each system under test.

A new approach to speech bandwidth reduction

Abstract: Infinite peak clipping is a simple way to decrease the signal-to-noise ratio for speech transmission. Investigations of this property are reported in terms of channel capacity; the clipping operator reduces it by a factor of 4. The constant-amplitude wave suggests a possible bandwidth reduction by communication of its frequency; signal-to-noise ratios required are about 8n dB, with n the compression factor. The system includes few circuits and appears promising in commercial telephony.