James C. Candy

A Use of Double Integration in Sigma Delta Modulation

Sigma delta modulation is viewed as a technique that employs integration and feedback to move quantization noise out of baseband. This technique may be iterated by placing feedback loop around feedback loop, but when three or more loops are used the circuit can latch into undesirable overloading modes. In the desired mode, a simple linear theory gives a good description of the modulation even when the quantization has only two levels. A modulator that employs double integration and two-level quantization is easy to implement and is tolerant of parameter variation. At sampling rates of 1 MHz it provides resolution equivalent to 16 bit PCM for voiceband signals. Digital filters that are suitable for converting the modulation to PCM are also described.

Decimation for Sigma Delta Modulation

Decimation is an important component of oversampled analog-to-digital conversion. It transforms the digitally modulated signal from short words occurring at high sampling rate to longer words at the Nyquist rate. Here we are concerned with the initial stage of decimation, where the word rate decreases to about four times the Nyquist rate. We show that digital filters comprising cascades of integrate-and-dump functions can match the structure of the noise from sigma delta modulation to provide decimation with negligible loss of signal-to-noise ratio. Explicit formulas evaluate particular tradeoffs between modulation rate, signal-to-noise ratio, length of digital words, and complexity of the modulating and decimating functions.

A Use of Limit Cycle Oscillations to Obtain Robust Analog-to-Digital Converters

High quality analog-to-digital conversions are obtained using simple and inexpensive circuits that require no high-precision components. Samples of the analog signal are cycled rapidly through a coarse quantizer while the roundoff error is fed back and subtracted from the input. By means of this feedback, the coarse quantizations are caused to oscillate between levels, keeping their running average representative of the input. A binary coding of the quantized values, summed over Nyquist intervals, provides a high resolution PCM output. The precision is determined by a product of the cycle rate and the spacing of the coarse quantization levels. The system is surprisingly tolerant of inaccuracies in gains and threshold settings; indeed, it has many of the desirable properties of classical feedback servomechanisms. An 8-bit limit cycling converter intended for 1-MHz signal bandwidths has been fabricated of standard components that, in total, cost less than

Using Triangularly Weighted Interpolation to Get 13-Bit PCM from a Sigma-Delta Modulator

150.

Interframe coding of videotelephone pictures

We present and analyze a method of interpolation that improves the amplitude resolution of an analog-to-digital converter. The technique requires feedback around a quantizer that operates at high speed and digital accumulation of its quantized values to provide a PCM output. We show that use of appropriate weights in the accumulation has important advantages for providing finer resoution, less spectral distortion, and white quantization noise. The theoretical discussion is supplemented by the report of a practical converter designed especially to show up the strengths and weaknesses of the technique. This converter comprises a sigma-delta modulator operating at 8 MHz and an accumulation of the 1-bit code with triangularly distributed weights. 13-bit resolution at 8 kwords/s is realized by periodically dumping the accumulation to the output. We present a practical method for overcoming a thresholding action that distorts low-amplitude input signals.

A Voiceband Codec with Digital Filtering

Television signals contain a great deal of frame-to-frame redundancy because picture areas are scanned in every frame whether they have changed or not. That portion of the signal describing stationary images need not be retransmitted in every frame if adequate memory is provided at the receiver. The signal describing moving images must be transmitted, of course, but it requires progressively less fidelity as the motion increases. Several techniques are described for obtaining efficient transmission by taking into account the similarity in the signal from frame to frame. Basic to most of these techniques is the need to separate the signal into segments that have changed significantly since the previous frame and ones that have not changed.

Double Interpolation for Digital-to-Analog Conversion

Oversampling and digital filtering have been used to design a per-channel voiceband codec with resolution that exceeds the typical transmission system requirement by more than 15 dB. This extended dynamic range will allow for the use of digital processing in the management of signal levels and system characteristics in many telecommunication applications. Digital filtering contained in the codec provides rejection of out-of-band inputs and smoothing of the analog output that is sufficient to eliminate the need for analog filtering in most telephone applications. Some analog filtering may be required only to maintain the expanded dynamic range in cases where there is a danger of large amounts of out-of-band energy on the analog input impairing the dynamic range of the modulator. The encoder portion of the oversampled codec comprises an interpolating modulator that samples at 256 kHz followed by digital filtering that produces a 16-bit PCM code at a sample rate of 8 kHz. In the decoder, digital processing is used to raise the sampling rate to 1 MHz prior to demodulation in a 17-level interpolating demodulator. The circuits in the codec are designed to be suitable for large-scale integration. Component matching tolerances required in the analog circuits are of the order of only ± 1 percent, While the digital circuits can be implemented with fewer than 5000 gates with delays on the order of 0.1 μs. In this paper the response of the codec is described mathematically and the results are confirmed by measurements of experimental breadboard models.

A Per-Channel A/D Converter Having 15-Segment µ-255 Companding

Interpolative digital-to-analog converters generate an output that has only a few analog levels. They provide fine resolution by oscillating rapidly between these levels in such a manner that the average output represents the value of the applied code. Here we describe an improved method of interpolating that results in reduced noise in the signal band. A theory of the interpolation, confirmed by experiments, demonstrates that switching between only two levels at 1.3 mHz could provide 16 bit resolution for telephone signals.

Direct-feedback coders: Design and performance with television signals

This paper describes a companded analog-to-digital (A/D) converter for voiceband signals that is simple and potentially inexpensive. The converter uses only 18 coarsely spaced analog levels. Fine resolution is obtained by oscillating between these levels at an increased speed and averaging the result over a Nyquist interval. The companding used in the converter is effectively the same as that of μ-255 pulse-code modulation (PCM). In the encoding process a one-bit code is generated at 256 000 samples/s. This 1-bit per sample signal can be transmitted and decoded directly, or a simple digital circuit will produce a 13-bit, 8-kHz linear PCM signal that can be compressed to 8-bit companded PCM format. In this paper the basic operation of the 1-bit coder is described and its performance when connected to a 1-bit decoder is illustrated. Methods for obtaining both linear and compressed PCM are then presented, and the properties of these PCM signals with respect to noise, gain tracking, and harmonic content are described. Relative insensitivity to circuit component variations, absence of analog gates, along with the need to generate only a few analog levels, make the coder especially well suited to integrated circuit realization.

Oversampling methods for data conversion

Direct-feedback coding is a refinement on the well-known differential coding method. Two filters are used at the transmitter of a direct-feedback coder; one connected in series with the input and the other in the forward path of a feedback loop that contains the quantizer. The first filter preemphasizes the signal and determines the overload characteristic of the coder; the other filter shapes the quantization noise and sets the stability of the feedback. At the receiver a filter reconstitutes the signal spectrum and deemphasizes the noise. For television the preemphasis should he a short time-constant differentiator, the deemphasis a short time integrator, and the feedback filter a long time integrator. Conventional differential coders use a single filter in the feedback path both to provide preemphasis and to shape the feedback characteristic, so the design is a compromise. Compared with direct-feedback coding they usually have less feedback gain and a larger time constant in the preemphasis and deemphasis, consequently, the contouring noise is more visible and the streaking caused by transmission error is longer. Although only application to television is considered, the methods have wider use. General formulae are given for the output noise and optimum filter characteristics; they take into account signal spectra, frequency weighting for noise, sampling rate, quantization step size, and an overload parameter. Measurements on real coders, operating on TV signals, and digital simulations confirm the results.