Bernard Gold

A digital frequency synthesizer

A digital frequency synthesizer has been designed and constructed based on generating digital samples of \exp [j(2^{\pi}nk/N)] at time nT . The real and imaginary parts of this exponential form samples of quadrature sinusoids where the frequency index k is allowed to vary (-N/4) \leq K . The digital samples drive digital to analog converters followed by low-pass interpolating filters to produce analog sinusoids. The method is superior to digital difference equations with poles on the unit circle since the noise or numerical inaccuracy remains bounded. The digital technique used consists of factoring the exponential into two table look-ups from an efficiently organized small READ-ONLY memory table and performing a complex multiply to produce the real and imaginary components. A small array multiplier efficiently organized performs the multiplications. The technique lends itself to the production of phase coherent or phase controlled sinusoids because of the indexing arrangement used. In addition finer frequency steps than the READ-ONLY memory allows are available by expanding the indexing register at no increase in inaccuracy.

Parallel processing techniques for estimating pitch periods of speech in the time domain.

A computational algorithm for estimating pitch periods of speech in the time domain is presented, and two recent modifications of the algorithm are discussed in detail. The algorithm and its modifications have been found to be relatively accurate and efficient in tests on real and synthetic speech.

Digital filter design techniques in the frequency domain

Digital filtering is the process of spectrum shaping using digital components as the basic elements. Increasing speed and decreasing size and cost of digital components make it likely that digital filtering, already used extensively in the computer simulation of analog filters, will perform, in real-time devices, the functions which are now performed almost exclusively by analog components. In this paper, using the z-transform calculus, several digital filter design techniques are reviewed, and new ones are presented. One technique can be used to design a digital filter whose impulse response is like that of a given analog filter; other techniques are suitable for the design of a digital filter meeting frequency response criteria. Another technique yields digital filters with linear phase, specified frequency response, and controlled impulse response duration. The effect of digital arithmetic on the behavior of digital filters is also considered.

An approach to the approximation problem for nonrecursive digital filters

A direct design procedure for nonrecursive digital filters, based primarily on the frequency-response characteristic of the desired filters, is presented. An optimization technique is used to minimize the maximum deviation of the synthesized filter from the ideal filter over some frequence range. Using this frequency-sampling technique, a wide variety of low-pass and bandpass filters have been designed, as well as several wide-band differentiators. Some experimental results on truncation of the filter coefficients are also presented. A brief discussion of the technique of nonuniform sampling is also included.

Digital speech networks

Digital techniques, already widely used for transmission of data, are now being introduced in the field of voice communications. By appreciating some of the long-range implications of this trend we can help point the way towards appropriate usage of this developing technology for improved customer service. This paper focuses on the voice problem and the possibilities offered by complete digitization of the voice signal immediately following the microphone. Included in the discussion are a summary of the properties of the speech signal and its potentialities for efficient transmission, a survey of the existing voice digitization algorithms, some examples of voice digitization implementations, and a brief treatment of voice packetization. There are some comments, near the end of the paper, on the possibility of digitized-voice inputting to, and outputting from, computers in an integrated telephone-computer network.

A note on digital filter synthesis

It is commonly assumed that digital filters with both poles and zeros in the complex z-plane can be synthesized using only recursive techniques while filters with zeros alone can be synthesized by either direct convolution or via the discrete Fourier transform (DFT). In this letter it is shown that no such restrictions hold and that both types of filters (those with zeros alone or those with both poles and zeros) can be synthesized using any of the three methods, namely, recursion, DFT, or direct convolution.

The channel vocoder

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.

A direct search procedure for designing finite duration impulse response filters

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.

Analysis of digital and analog formant synthesizers

A digital formant is a resonant network based on the dynamics of a second-order linear difference equation. A serial chain of digital formants can approximate the vocal tract during vowel production. In this paper, the digital formant is defined and its properties discussed, using z-transform notation. The results of detailed frequency response computations of both digital and conventional analog formant synthesizers are then presented. These results indicate that the digital system without higher pole correction is a closer approximation than the analog system with higher pole correction. Finally, a set of measurements on the signal and noise properties of the digital system is described. Synthetic vowels generated for different signal-to-noise ratios help specify the required register lengths for the digital realization. A comparison between theory and experiment is presented.

Effects of quantization noise in digital filters

If a discrete time linear system, hereafter called a digital filter, is programmed on a digital computer or realized with digital elements, computational errors due to finite word length are unavoidable. These errors may be subdivided into three classes, namely, the error caused by discretization of the system parameters, the error caused by analog to digital conversion of the input analog signal, and the error caused by roundoff of the results which are needed in further computations. The first type of error results in a fixed deviation in system parameters and is akin to a slightly wrong value of (say) an inductance in an analog filter. We shall not treat this problem here; it has been treated in some detail by Kaiser. The other two sources of error are more complicated but if reasonable simplifying assumptions are made they can be treated by the techniques of linear system noise theory. It is our aim to set up a model of a digital filter which includes these two latter sources of error and, through analysis of the model, to relate the desired system performance to the required length of computer registers.