Showing papers in "IEEE Transactions on Audio and Electroacoustics in 1969"
TL;DR: A computational algorithm for numerically evaluating the z -transform of a sequence of N samples is discussed, based on the fact that the values of the z-transform on a circular or spiral contour can be expressed as a discrete convolution.
Abstract: A computational algorithm for numerically evaluating the z -transform of a sequence of N samples is discussed. This algorithm has been named the chirp z -transform (CZT) algorithm. Using the CZT algorithm one can efficiently evaluate the z -transform at M points in the z -plane which lie on circular or spiral contours beginning at any arbitrary point in the z -plane. The angular spacing of the points is an arbitrary constant, and M and N are arbitrary integers. The algorithm is based on the fact that the values of the z -transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N+M) \log_{2}(N+M) as opposed to being proportional to N . M for direct evaluation of the z -transform at M points.
608 citations
TL;DR: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey, and includes an efficient method for permuting the results in place.
Abstract: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey. As in their algorithm, the dimension n of the transform is factored (if possible), and n/p elementary transforms of dimension p are computed for each factor p of n . An improved method of computing a transform step corresponding to an odd factor of n is given; with this method, the number of complex multiplications for an elementary transform of dimension p is reduced from (p-1)^{2} to (p-1)^{2}/4 for odd p . The fast Fourier transform, when computed in place, requires a final permutation step to arrange the results in normal order. This algorithm includes an efficient method for permuting the results in place. The algorithm is described mathematically and illustrated by a FORTRAN subroutine.
534 citations
TL;DR: In this paper, correction factors were devised for correction of bias and computation of confidence intervals around estimates of coherence spectra computed upon Gaussian random time series using Monte Carlo methods to compute approximate sampling distributions for coherence, statistical descriptions of the bias and standard deviations were obtained.
Abstract: Correction factors were devised for correction of bias and computation of confidence intervals around estimates of coherence spectra computed upon Gaussian random time series. Using Monte Carlo methods to compute approximate sampling distributions for coherence, statistical descriptions of the bias and standard deviations were obtained. Correction factors were devised which extend the utility of coherence estimates to a value of coherence = 0. Previously coherence = 0.4 was a lower limit.
185 citations
IBM1
TL;DR: In this paper, the finite Fourier transform of a finite sequence is defined and its elementary properties are developed, and the convolution and term-by-term product operations are defined and their equivalent operations in transform space.
Abstract: The finite Fourier transform of a finite sequence is defined and its elementary properties are developed. The convolution and term-by-term product operations are defined and their equivalent operations in transform space are given. A discussion of the transforms of stretched and sampled functions leads to a sampling theorem for finite sequences. Finally, these results are used to give a simple derivation of the fast Fourier transform algorithm.
165 citations
IBM1
TL;DR: In this article, an analysis of the fixed-point accuracy of the power of two, fast Fourier transform algorithm is presented, which leads to approximate upper and lower bounds on the root-mean-square error.
Abstract: This paper contains an analysis of the fixed-point accuracy of the power of two, fast Fourier transform algorithm. This analysis leads to approximate upper and lower bounds on the root-mean-square error. Also included are the results of some accuracy experiments on a simulated fixed-point machine and their comparison with the error upper bound.
164 citations
TL;DR: Fast Fourier analysis (FFA) and fast Fourier synthesis (FFS) algorithms are developed for computing the discrete Fourier transform of a real series, and for synthesizing a realseries from its complex Fourier coefficients.
Abstract: Fast Fourier analysis (FFA) and fast Fourier synthesis (FFS) algorithms are developed for computing the discrete Fourier transform of a real series, and for synthesizing a real series from its complex Fourier coefficients. A FORTRAN program implementing both algorithms is given in the Appendix.
99 citations
TL;DR: A statistical model for roundoff errors is used to predict output noise-to-signal ratio when a fast Fourier transform is computed using floating point arithmetic, and it is found experimentally that if one truncates, rather than rounds, the results of floating point additions and multiplications, the output noise increases significantly.
Abstract: A statistical model for roundoff errors is used to predict output noise-to-signal ratio when a fast Fourier transform is computed using floating point arithmetic. The result, derived for the case of white input signal, is that the ratio of mean-squared output noise to mean-squared output signal varies essentially as
u = \log_{2}N where N is the number of points transformed. This predicted result is significantly lower than bounds previously derived on mean-squared output noise-to-signal ratio, which are proportional to ν2. The predictions are verified experimentally, with excellent agreement. The model applies to rounded arithmetic, and it is found experimentally that if one truncates, rather than rounds, the results of floating point additions and multiplications, the output noise increases significantly (for a given ν). Also, for truncation, a greater than linear increase with ν of the output noise-to-signal ratio is observed; the empirical results seem to be proportional to ν2, rather than to ν.
75 citations
TL;DR: A device is built that enables the sound engineer to adjust any of the six static parameters and the system automatically chooses its own dynamic properties as a function of the input program signal.
Abstract: When manual dynamic range compression is replaced by an automatic compression system, the sound engineer must still be able to choose some characteristics of the compression. An automatic system and the theory motivating its design are described. We have built a device (EMT 156) that enables the sound engineer to adjust any of the six static parameters; also, the system automatically chooses its own dynamic properties as a function of the input program signal.
71 citations
TL;DR: The problems associated with implementing the FFT algorithm in hardware and many of the design options applicable to an FFT processor are described, and a brief comparison of several machine organizations is given.
Abstract: This discussion served as an introduction to the Hardware Implementations Session of the IEEE Workshop on Fast Fourier Transform Processing. It introduces the problems associated with implementing the FFT algorithm in hardware and provides a frame of reference for characterizing specific implementations. Many of the design options applicable to an FFT processor are described, and a brief comparison of several machine organizations is given.
64 citations
TL;DR: An approach is introduced to the design of low-pass (and, by extension, bandpass) digital filters containing only zeros by directly searching for transition values of the sampled frequency response function to reduce the sidelobe level of the response.
Abstract: We introduce an approach to the design of low-pass (and, by extension, bandpass) digital filters containing only zeros. This approach is that of directly searching for transition values of the sampled frequency response function to reduce the sidelobe level of the response. It is shown that the problem is a linear program and a search algorithm is derived which makes it easier to obtain the experimental results.
59 citations
TL;DR: Two methods for FFT of one-dimensional arrays of data to be fast Fourier transformed are presented-one efficient when data storage is only slightly larger than available internal memory, and one when data is much larger.
Abstract: Occasionally, arrays of data to be fast Fourier transformed (FFT'ed) are too large to fit in internal computer memory, and must be kept on an external storage device. This situation is especially serious for one-dimensional arrays, since they cannot be factored along the natural cleavage planes, as multi-dimensional arrays can. Two methods for FFT of such data are presented-one efficient when data storage is only slightly larger than available internal memory, and one when data is much larger. A FORTRAN program based on these methods is available.
TL;DR: A list of features that serves to characterize an FFT processor was developed during a working session of the IEEE Workshop on Fast Fourier Transform Processing and a copy of the table shown in this paper was sent to companies with the request that each company specify the data relating to their machine in the form they would like it to be printed.
Abstract: A list of features that serves to characterize an FFT processor was developed during a working session of the IEEE Workshop on Fast Fourier Transform Processing. Based on this list, information was requested on all of the processors that were known to the Workshop Organizing Committee. A copy of the table shown in this paper was sent to 20 companies with the request that each company specify the data relating to their machine in the form they would like it to be printed. The table represents a compilation of the returns.
TL;DR: The fast Fourier transform is considered to owe its speed to the fact that a certain matrix, none of whose elements is zero, can be factored into matrices with very many zeros as mentioned in this paper.
Abstract: The fast Fourier transform is considered to owe its speed to the fact that a certain matrix, none of whose elements is zero, can be factored into matrices with very many zeros. This paper describes and discusses a procedure for explicitly carrying out such a factorization.
TL;DR: In this paper, the mean and variance of the two forms of estimators are calculated as well as the equivalent duration of the data window and a generalized form of the Hanning window is considered.
Abstract: Although the use of quadratically modified periodograms as spectral estimators for the Gaussian case is well established in the literature, the linearly modified form has grown in popular use even when the data involved can be reasonably presumed to be Gaussian. The mean and variance of the two forms of estimators are calculated as well as the equivalent duration of the data window. It is shown that variance is always greater or the equivalent duration of the sample data length is always less for the linear case when the results are normalized with respect to the effective bandwidth. In addition, a generalized form of the Hanning window is considered.
TL;DR: A guided tour of the fast Fourier transform,” IEEE Spectrum (to be published).
Abstract: 166 L. E. Alsop and A. A. Nowroozi, “Fast Fourier analysis,” J. Geophys. Res., vol. 71, pp. 5482-5483, November 15, 1966. €3. Andrews, “A high-speed algorithm for the computer generation of Fourier transforms,” IEEE Trans. Computers (Short Notes), vol. C-17, pp. 373.375, April 1968. J. S . Bailey, “A fast Fourier transform without multiplications,” Proc. Symp. on Computer Processing in Communications, vol. 19, MKI Symposia Ser. New York: Polytechnic Press, 1969. V. Benignus, “Estimation of the coherence spectrum and its confidence interval using the fast Fourier transform,” this issue, pp. 145-150. G. D. Bergland, “The fast Fourier transform recursive equations for arbitrary length records,” Math. Computation, vol. 21, pp, 236-238, April 1967. -9 “A fast Fourier transform algorithm using base eight iterations,” Math. Computation, vol. 22, pp. 275-279, April 1968. -, “A fast Fourier transform algorithm for realvalued series,” Commun. A C M , vol. 11, pp. 703--710, October 1968. -, “A radix-eight fast Fourier transform subroutine for real-valued series,” this issue, pp. 138144. -, “A guided tour of the fast Fourier transform,” IEEE Spectrum (to be published). “Fast Fourier transform hardware implementations. I. An overview. 11. A survey,’’ this issue,
TL;DR: The development of special aids for speech communication and speech correction of severely hard-of-hearing or totally deaf persons has been going on since the beginning of the 1920's and an attempt will be made to summarize the development and to discuss published results from experiments with different types of equipment.
Abstract: Attempts to develop special aids for speech communication and speech correction of severely hard-of-hearing or totally deaf persons have been going on since the beginning of the 1920's. For information transmission, the auditory, tactual, and visual senses have been used. These aids have in many cases been called "sensory aids for the deaf" in analogy with the "sensory aids for the blind" that make it possible for the blind to read ordinary letters, perceive obstacles, and so on. Recently, the name "speech analyzing aids" has been suggested, which seems to be more adequate, as some types of speech analyzing techniques are used in contrast to the linear amplification used in most ordinary hearing aids. In the development of "speech analyzing aids for the deaf" two problems must be considered: 1) Which elements of the speech signals ought to be automatically extracted and transmitted to the deaf subject? 2) What kind of signals and which sense modality shall be used for the transmission of the extracted speech information? Speech is learned by imitation which means that an efficient aid for speech perception also can be used for speech learning. However, in several respects it is better to treat aids for speech correction and speech perception as separate problems. Here, for the most part, only aids for speech perception will be discussed. An attempt will be made to summarize the development in this area and to discuss published results from experiments with different types of equipment. Some suggestions for future experiments will be given.
TL;DR: The development of a reading machine for the blind offers insight into current problems of computer-to-man communications and poses a technical and humanitarian challenge.
Abstract: The development of a reading machine for the blind offers insight into current problems of computer-to-man communications and poses a technical and humanitarian challenge. Approaches to the problem include compiled speech, reformed speech, and synthesis by rule. Of these methods, synthesis by rule may offer the best long-term trade-off between quality of the speech and cost and complexity of its production. Implementation of a high-performance reading machine will involve a central service facility that can generate tape recordings or provide voice responses to remote print scanners. Technical problems, especially in providing remote on-line service, seem formidable, but the organizational problems of matching central facilities to the blind user's needs may prove to be even more so.
TL;DR: This correspondence presents a mechanization of the fast Fourier transform which results in a particularly simple and compact FORTRAN program without the need for sorting the answers.
Abstract: This correspondence presents a mechanization of the fast Fourier transform which results in a particularly simple and compact FORTRAN program without the need for sorting the answers.
TL;DR: An electronic speech processor is described which provides an analog voltage output based on the difference signal between the first speech formant and the second, which was very good when the speech processor output was sampled and compared with previously recorded memory-stored data in a small digital computer.
Abstract: In the present age of scientific discovery, man has become more and more dependent on the use of electronic computers. As this powerful tool becomes more universally important in man's day-to-day existence, it becomes increasingly more annoying that he has to speak to it in its mode of communication, paper tape or punch cards; and not in his own, the spoken word. Even today in the very infancy of the computer age, the time required to do many computations is less than the time required to instruct the machine in how to do them. All this points to the need of a method of achieving machine recognition of speech. In this paper an electronic speech processor is described which provides an analog voltage output based on the difference signal between the first speech formant and the second. Machine recognition of numbers zero through nine was very good when the speech processor output was sampled and compared with previously recorded memory-stored data in a small digital computer.
TL;DR: Speech synthesis-by-rule is the generation, according to a set of predetermined rules, of the variable parameters of a speech synthesizer as functions of time from an input of segmental and suprasegmental specifications.
Abstract: A machine with unrestricted vocabulary, that is capable of converting printed text into connected speech in real time, would be extremely useful to blind people. The problems in implementing such a machine are mainly 1) character recognition, 2) conversion of the symbolic form of written language into a symbolic form of spoken language, and 3) synthesis of connected speech from the symbolic description. The character recognition must be highly accurate, although high speed is not necessary. The language in spoken form may be symbolically represented by strings of segmental phonemes, together with additional specifications at phrase and sentence or suprasegmental levels. The segmental phonemes characterize the basic speech sound elements, and the suprasegmental specifications characterize intonation, stress, and pauses. For a restricted vocabulary, a spelling to pronouncing dictionary indicating pronunciation, as well as spelling, can be used to obtain the segmental phonemes; however, for an unrestricted vocabulary in a language like English, a scheme employing a dictionary that indicates the elements of words (prefixes, suffixes, and roots), together with a set of rules for word formation, is necessary and more economical. Since suprasegmental specifications depend upon sentence structure, sentence analysis, or parsing, must be performed to identify essential groups. The construction of a speech synthesizer may be based on the terminal transfer characteristic of the human vocal tract as a whole, or it may be based on the transfer characteristics of a cascade of many sections of variable cross-section area acoustic tubes which simulate the vocal tract. Speech synthesis-by-rule is the generation, according to a set of predetermined rules, of the variable parameters of a speech synthesizer as functions of time from an input of segmental and suprasegmental specifications.
TL;DR: A general model for speech synthesis by rule is presented along with a discussion of one specific implementation of the model, and specific recommendations as to areas of speech synthesis and speech production requiring further study are made.
Abstract: A general model for speech synthesis by rule is presented along with a discussion of one specific implementation of the model. The conversion from discrete input signals to continuous synthesizer control signals is performed by the synthesis strategy. The details of the synthesis strategy, including linguistic preprocessing of the input and separate but interdependent segmental and suprasegmental models, are described. An experimental evaluation of the specific model is included, along with specific recommendations as to areas of speech synthesis and speech production requiring further study.
TL;DR: In this paper, a reading aid for the blind which is intended to give the blind direct access to ordinary printed material is described. But this reading aid is not suitable for blind individuals.
Abstract: Progress is described on a reading aid for the blind which is intended to give the blind direct access to ordinary printed material. Operation principles and construction of the device are described. Recent reading performance of a subject on typed reading material is presented.
TL;DR: In this paper, a Monte Carlo study was performed, computing coherences and confidence intervals upon non-Gaussian time series using both a rectangular distribution and a x2 distribution with one degree of freedom.
Abstract: Previous work on computation of coherence estimates between two time series and the confidence intervals about these estimates has always assumed that the time series have a Gaussian probability density function. Here a Monte Carlo study was performed, computing coherences and confidence intervals upon non-Gaussian time series. Using both a rectangular distribution and a x2distribution with one degree of freedom, the results appear to justify the notion that the assumption of a Gaussian distribution has a fairly small importance in the computation of the above statistics.
TL;DR: A fast Fourier transform (FFT) algorithm is presented for an unstructured, parallel ensemble of computing elements with global control that makes efficient use of a fixed-size memory and minimizes data transmission between computing elements.
Abstract: A fast Fourier transform (FFT) algorithm is presented for an unstructured, parallel ensemble of computing elements with global control. The procedure makes efficient use of a fixed-size memory and minimizes data transmission between computing elements. Included are some practical considerations of the trade-offs between element utilization and gain of computing speed via parallelism.
TL;DR: A discrete analog of the narrow-band heterodyne correlator is presented and modified such as to lead to an efficient technique for wide-band FM where several time-compressed references are required.
Abstract: The fast Fourier transform is employed in the design of replica correlation algorithms for application in narrow-band and wide-band active FM sonar. A discrete analog of the narrow-band heterodyne correlator is presented and modified such as to lead to an efficient technique for wide-band FM where several time-compressed references are required.
TL;DR: The problem of acoustic transmission of speech sounds to the deaf is discussed along with the related educational problems and some methods of speech analysis which have been developed as prototypes of new speech aids are presented.
Abstract: The problem of acoustic transmission of speech sounds to the deaf is discussed along with the related educational problems. Some methods of speech analysis which have been developed as prototypes of new speech aids are presented. Two types of new aids are covered: 1) tactual aids to speech communication, and 2) visual aids for monitoring of speech in speech training or to supplement speech reception.
TL;DR: Simulation of the process indicates that the speech formant dominant in intensity "captures" the multiplication of the instantaneous frequency of a speech signal, and a scaling distortion of the spectral envelope cannot be restored by instantaneous frequency division of the broad-band signal.
Abstract: Multiplication of the instantaneous frequency of a speech signal is studied by computer simulation. Interest centers on a simple means for compressing and expanding the time dimension of the signal, and for scaling the envelope of its short-time spectrum. Simulation of the process indicates that the speech formant dominant in intensity "captures" the multiplication. In the multiplied signal, the frequency of the dominant formant is multiplied, but the frequency spacings between the dominant formant and other formants remain the same as in the original signal. Stretching the time scale of the multiplied signal by the appropriate factor restores the dominant formant to its correct frequency position, but no other formant is correctly restored. By the same result, a scaling distortion of the spectral envelope (for example, as in speech produced in a He-O atmosphere)cannot be restored by instantaneous frequency division of the broad-band signal. A two-format model of the speech signal is used to analyze instantaneous frequency multiplication. Calculations on the model are consistent with spectra obtained from the computer-processed real speech.
TL;DR: The class of digital filters which have an impulse response of finite duration and are implemented by means of circular convolutions performed using the discrete Fourier transform is considered and a least upper bound is obtained for the maximum possible output of a circular convolution for the general case of complex input sequences.
Abstract: When implementing a digital filter, it is important to utilize in the design a bound or estimate of the largest output value which will be obtained. Such a bound is particularly useful when fixed point arithmetic is to be used since it assists in determining register lengths necessary to prevent overflow. In this paper we consider the class of digital filters which have an impulse response of finite duration and are implemented by means of circular convolutions performed using the discrete Fourier transform. A least upper bound is obtained for the maximum possible output of a circular convolution for the general case of complex input sequences. For the case of real input sequences, a lower bound on the least upper bound is obtained. The use of these results in the implementation of this class of digital filters is discussed.
IBM1
TL;DR: The history of the fast Fourier transform of Cooley and Tukey, as well as experience with general-purpose optimization programs, suggests that publication alone does not result in wide use of a new and vastly more efficient computational technique.
Abstract: The history of the fast Fourier transform of Cooley and Tukey, as well as experience with general-purpose optimization programs, suggests that publication alone does not result in wide use of a new and vastly more efficient computational technique. Recounting his role as entrepreneur and missionary in connection with the fast Fourier transform, the author emphasizes these difficulties and notes the need for mechanisms for easing the cross-utilization of valuable new techniques.
TL;DR: In this article, a Honeywell DDP-516 computer is used with an interactive program to study an acoustic-oscillator model of the vocal cords, which includes a simulated vocal tract.
Abstract: A Honeywell DDP-516 computer is used with an interactive program to study an acoustic-oscillator model of the vocal cords. The program includes a simulated vocal tract. Iterative solutions are obtained to difference equations which describe the acoustic volume velocity through the cords and the sound pressure output at the mouth. The results can be printed, displayed on a scope, or D/A converted for auditory assessment. A fast Fourier transform provides spectral analysis of the synthesized signals. Parameters that the experimenter can specify from the console include, 1) subglottal pressure, 2) vocal cord tension, 3) vocal tract shape, 4) air density and 5) sound velocity. Results show that tract configuration, and hence acoustic load on the cords, substantially influences fundamental frequency of voicing. Fundamental frequency is also found to be a monotonic function of sub-glottal pressure and cord tension, other factors being constant. Increasing air density tends to reduce fundamental frequency, while changes in sound velocity affect it negligibly.