Publications

The data recording of storm information as detected by a weather radar has been customarily made on photographic film. Research radars and an occasional U. S. Weather Bureau radar are fitted with scope cameras to record the radar plan position indicator (PPI) display. Over the past 15 years a large sample of weather radar data has been accumulated in this fashion. The photographic technique provides an easy, quick, and inexpensive way to record weather radar data. The major drawback of this technique is data reduction. Information on storm shape, size, and intensity is normally extracted from the photographic images by hand. This means that only the most interesting aspects of individual storms are analyzed and the vast majority of the collected radar data is not analyzed. A vast amount of climatological information could be obtained from the existing store of weather radar data if an automatic technique of data retrieval were available. The first part of this report describes the use of a computer-controlled programmable film reader to process weather radar PPI photographs to obtain digital maps of rainfall intensity for use in climatological studies.

Application of a type of predictive coding to the channel signals of a homomorphic vocoder has produced sizable bit rate reductions. With only slight degradation in speech quality, reduction (for the spectral envelope information) from 7800 to 4000 bits/s was achieved. A technique for obtaining the formant frequencies from the predictive coding parameters is described; this approach promises further bit rate reductions. As a byproduct of this study of predictive coding, direct and cascade form speech synthesizers are compared on the basis of differing quantization effects.

By the mid-1970's, the evolving NAS/ARTS ground environment will provide the air traffic controllers with high quality computer-processed traffic situation displays. We believe it would be useful, particularly in busy terminal areas, to display some of this data in the cockpit. Systems with this objective have been constructed and flight tested at least 3 times during the past 25 years, but these earlier systems could not benefit from: 1) a source of computer-processed data of the quality to be available from NAS/ARTS; 2) aircraft altitude information; 3) contemporary digital data link techniques; and 4) airborne equipment capable of automatically selecting and displaying only information relevant to a particular airplane. It is believed that an effective cockpit display would permit pilots, under IFR conditions, to retain some of the station-keeping and navigation functions they perform during VFR conditions and thereby improve the efficiency of terminal area operation. The goals of the proposed program are: a) to evaluate the effectiveness of this class of system in reducing pilot and controller work loads, and b) to determine its potential for expediting traffic flow in busy terminal areas. A simulated cockpit display has been developed and experienced pilots and controllers who have "flown" it have endorsed enthusiastically the desirability of evaluating this class of system in an operational environment.

Radar measurements of thin turbulent layers in the clear atmosphere have been extensively reported in the literature and have recently been summarized by Hardy and Katz (1969). The majority of the thin turbulent layer detections reported have been for layers in the lower troposphere. Using the high power radar facilities at Wallops Island, Atlas, et al (1966) have detected layers at heights up to the tropopause. In this paper, layer detections at heights above the tropopause are discussed. The detection of layers in the lower 10 km of the stratosphere is made possible by using a radar system which has approximately 10 dB more sensitivity than the Wallops Island radars for the detection of turbulent layers. The program of radar measurements of thin turbulent layers was undertaken to provide basic information about the structure of scattering layers in the upper troposphere and lower stratosphere for use in the prediction of troposcatter field strengths. The radar measurements were accompanied by radiosonde soundings. For a limited series of measurements, a U-2 aircraft was also used to probe for turbulent layers.

Simultaneous measurements were made of the backscatter cross section and the bistatic scattering cross section of rain and thin turbulent layers. The radar measurements were made at a frequency of 1.3 GHz using the Millstone Hill Radar. The bistatic scattering measurements were made using CW transmission at 7.7 GHz with a 145-km separation between transmitter and receiver. The receive station was the Westford Communication Terminal with a 60-foot antenna. The transmitter was van-mounted and used either a 6-foot antenna or a standard gain horn. Stable frequency sources were used to allow Doppler shift measurements on the bistatic scattering link. The measurements were made by fixing the pointing angles of the transmit antenna and scanning both the receive antenna and the radar to investigate the dependence of the scattered signals both on scattering angle and on the location of the scatterers. The measurements of the scattering cross section of the thin turbulent layers were made in the near forward direction, the measurements of rain at a large number of scattering angles. System sensitivities allowed the measurement of scattering from turbulent layers at a 10-km height with a thickness, Cn^2 product of 10^-13 N^2 m^1/3 and from rain with a 0.1 mm/hr. rate. Comparisons between the radar and bistatic measurements were in good agreement with the appropriate scattering theories.

This is the first report in the Quarterly Technical Summary series covering the Air Traffic Control activities at Lincoln Laboratory. The previous work on ATC was included in the General Research Quarterly Technical Summary. Because the allowable effort on ATC is comparatively small, it has been focused on only one facet of the problem; namely, on the data acquisition and communications task. The new group has started to make significant progress in several study aspects of the problem and has also obtained experimental L-band multipath data from an experimental airground test system. When additional support is received, the program will be expanded to include over-all system design studies and the investigation of radar improvements and multilateration systems, both ground- and satellite-based.

When a digital filter is implemented on a computer or with special-purpose hardware, errors and constraints due to finite word length are unavoidable. These quantization effects must be considered, both in deciding what register length is needed for a given filter implementation and in choosing between several possible implementations of the same filter design, which will be affected differently by quantization. Quantization effects in digital filters can be divided into four main categories: quantization of system coefficients, errors due to analog-digital (A-D) conversion, errors due to roundoffs in the arithmetic, and a constraint on signal level due to the requirement that overflow be prevented in the computation. The effects of these errors and constraints will vary, depending on the type of arithmetic used. Fixed point, floating point, and block floating point are three alternate types of arithmetic often employed in digital filtering. A very large portion of the computation performed in digital filtering is composed of two basic algorithms the first- or second-order, linear, constant coefficient, recursive difference equation; and computation of the discrete Fourier transform (DFT) by means of the fast Fourier transform (FFT). These algorithms serve as building blocks from which the most complicated digital filtering systems can be constructed. The effects of quantization on implementations of these basic algorithms are studied in some detail. Sensitivity formulas are presented for the effects of coefficient quantization on the poles of simple recursive filters. The mean-squared error in a computed DFT, due to coefficient quantization in the FFT, is estimated. For both recursions and the FFT, the differing effects of fixed and floating point coefficients are investigated. Statistical models for roundoff errors and A-D conversion errors, and linear system noise theory, are employed to estimate output noise variance in simple recursive filters and in the FFT. By considering the overflow constraint in conjunction with these noise analyses, output noise-to-signal ratios are derived. Noise-to-signal ratio analyses are carried out for fixed, floating, and block floating point arithmetic, and the results are compared. All the noise analyses are based on simple statistical models for roundoff errors (and A-D conversion errors). Of course, somewhat different models are applied for the different types of arithmetic. These models cannot in general be verified theoretically, and thus one must resort to experimental noise measurements to support the predictions obtained via the models. A good deal of experimental data on noise measurements is presented here, and the empirical results are generally in good agreement with the predictions based on the statistical models. The ideas developed in the study of simple recursive filters and the FFTare applied to analyze quantization effects in two more complicated types of digital filters frequency sampling and FFT filters. The frequency sampling filter is realized by means of a comb filter and a bank of second-order recursive filters; while an FFT filter implements a convolution via an FFT, a multiplication in the frequency domain, and an inverse FFT. Any finite duration impulse response filter can be realized by either of these methods. The effects of coefficient quantization, roundoff noise, and the overflow constraint are investigated for these two filter types. Through use of a specific example, realizations of the same filter design, by means of the frequency sampling and FFT methods, are compared on the basis of differing quantization effects.

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 v = log2 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 v2. 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 v). Also, for truncation, a greater than linear increase with v of the output noise-to-signal ratio is observed; the empirical results seem to be proportional to v2 rather than to v.

A statistical model for roundoff noise in floating point digital filters, proposed by Kanoko and Liu, is tested experimentally for first- and second-order digital filters. Good agreement between theory and experiment is obtained. The model is used to specify a comparison between floating point and fixed point digital filter realizations on the basis of their output noise-to-signal ratio, and curves representing this comparison are presented. One can find values of the filter parameters at which the fixed and the floating point curves will cross, for equal total register lengths.

Measurements were made of the scattering properties of thin turbulent layers at and above the tropopause. The Millstone Hill L-band radar was used to measure the backscatter cross section per unit volume of these layers as a function of time and space. An X-band forward scatter link was set up between Wallops Island, Virginia and Westford, Massachusetts to observe scattering from these layers. Although the radar could not provide observations of the common volume of the forward scatter link, for days where no clouds were observed in the vicinity of the tropopause, the radar observations of layers near the tropopause showed horizontal uniformity of height and backscatter cross section, and the radiosonde data taken near the radar and near the common volume showed similar wind and temperature structure near the tropopause, the signal strength on the forward scatter link and its dependence on scattering angle behaved in accordance with the prediction of turbulent scattering theory using the radar data as an input. The radar observations have shown that on each day measurements were made, layers were detected near and above the tropopause. Turbulent layers in the stratosphere have been detected at heights up to 22 km. These layers provide one of the mechanisms for weak, long-distance troposcatter propagation.