Optimization of the representation of sampled data signals on orthonormal bases

Clark, Moyett

doi:10.1109/sap.1968.267092

Cited by 2 publications

(6 citation statements)

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“…The error energy in A(Z) prior to the epoch instant T (T is the time duration of the short time segment) is the same as the energy defined by (2) prior to T [2], [lo],…”

Section: B Initial Orthogonal Basismentioning

confidence: 99%

“…An algorithm for selecting pm and ym has been developed [2] from (15) and (16) for sample data signals and can be stated in matrix form as follows:…”

Section: B Initial Orthogonal Basismentioning

confidence: 99%

“…After each iteration, p,(iT1) and ym(;+l), were used in the functions VZm, Dl,, D2m, and E for the next iteration if p m ( i~l ) and T~(~+~) caused the poles of the equation z 2 + y m " "~ + pmG+') = (J to lie inside the unit circle in the 2 domain and if they decreased the percent of error energy [2]. The iteration or optimization procedure continued until the percent of error dropped below the final threshold or until the iteration procedure exceeded 20 iterations.…”

Section: B Initial Orthogonal Basismentioning

confidence: 99%

“…If the percent of error for and Y,(~) was above the initial threshold, the training process was repeated, For the iteration procedure to be useful, it had to produce two optimum sets of 20 parameters, P,(~) and Y,(~), for each short time segment by minimizing the percent of error energy. This training procedure led to an optimum set of parameters for each speaker and integer n [2], 1131, when it was programmed on the IBM 7090 computer.…”

Section: B Initial Orthogonal Basismentioning

confidence: 99%

“…Because the functions were orthogonal, the measurement of the inner products between each word and the orthogonal functions were simplified and did not interact Let f(t) be a short time segment of any one of the spoken digits, "1" to "IO". Then with a set of 40 orthogonal basis functions [2], [lo], [ 131 is and will be discussed in Section III-C. The inner products (also called ordinates or expansion coefficients) were measured by the correlation operation defined in (1).…”

Section: A Introductionmentioning

confidence: 99%

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Word recognition by means of orthogonal functions

Clark

1970

IEEE Trans. Audio Electroacoust.

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This paper describes experiments in which word recognition is based on comparing the projections of input words on an orthogonal basis with those of a stored library of words. An initial orthogonal basis is determined from the generalized spectrum of short time segments selected from a vocabulary of ten words. The initial basis is optimized by minimizing the complementary error energy. By projecting a spoken word onto the optimum orthogonal basis, a sequence of numbers is generated to represent the word. By correlating the absolute values of the sequence with those of a stored library of words, the spoken word is identifed. The percent of correct recognition varies from 71.6 to 96.6 percent for two speakers.Techniques are developed to improve the recognition scores and to reduce the lengthy computer processing time and large storage requirement. First a master template is made for each word by averaging six templates for the particular word. For one speaker the percent of correct recognition increases to 100 percent when incoming words are compared against the master templates. For a second speaker, the recognition rates improve significantly and vary between 93 and 98 percent when the master templates are used. To further improve the recognition process, the feasibility of grouping words into several classes is demonstrated. The classifications are based on the locations of formant regions and the time durations of each spoken word,

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“…The error energy in A(Z) prior to the epoch instant T (T is the time duration of the short time segment) is the same as the energy defined by (2) prior to T [2], [lo],…”

Section: B Initial Orthogonal Basismentioning

confidence: 99%

“…An algorithm for selecting pm and ym has been developed [2] from (15) and (16) for sample data signals and can be stated in matrix form as follows:…”

Section: B Initial Orthogonal Basismentioning

confidence: 99%

Section: B Initial Orthogonal Basismentioning

confidence: 99%

Section: B Initial Orthogonal Basismentioning

confidence: 99%

Section: A Introductionmentioning

confidence: 99%

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