/pdf/a-new-approach-to-linear-filtering-and-prediction-problems-1f1lkk9j5b.pdf

A New Approach to Linear Filtering and Prediction Problems

A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented. The objective of the field is to describe how the spectral content of a signal changes in time and to develop the physical and mathematical ideas needed to understand what a time-varying spectrum is. The basic gal is to devise a distribution that represents the energy or intensity of a signal simultaneously in time and frequency. Although the basic notions have been developing steadily over the last 40 years, there have recently been significant advances. This review is intended to be understandable to the nonspecialist with emphasis on the diversity of concepts and motivations that have gone into the formation of the field. >

/pdf/time-frequency-distributions-a-review-3lxbcw4fg4.pdf

Time-frequency distributions-a review

This paper discusses the effects of frequency offset on the performance of orthogonal frequency division multiplexing (OFDM) digital communications. The main problem with frequency offset is that it introduces interference among the multiplicity of carriers in the OFDM signal. It is shown, and confirmed by simulation, that to maintain signal-to-interference ratios of 20 dB or greater for the OFDM carriers, offset is limited to 4% or less of the intercarrier spacing. Next, the paper describes a technique to estimate frequency offset using a repeated data symbol. A maximum likelihood estimation (MLE) algorithm is derived and its performance computed and compared with simulation results. Since the intercarrier interference energy and signal energy both contribute coherently to the estimate, the algorithm generates extremely accurate estimates even when the offset is far too great to demodulate the data values. Also, the estimation error depends only on total symbol energy so it is insensitive to channel spreading and frequency selective fading. A strategy is described for initial acquisition in the event of uncertainty in the initial offset that exceeds 1/2 the carrier spacing, the limit of the MLE algorithm. >

A technique for orthogonal frequency division multiplexing frequency offset correction

A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems encountered in time-varying signal processing are provided. >

Linear and quadratic time-frequency signal representations

The theory of the diffraction grating pair is developed by expanding the frequency dependence of the phase shift as far as the quadratic frequency term. The analogy between pulse compression and Fresnel diffraction is treated. The effect of the cubic phase term is discussed for ultrashort pulses having appreciable fractional bandwidth.

Optical pulse compression with diffraction gratings

A new radar technique has been developed that provides a solution for the conflicting requirements of simultaneous long-range and high-resolution performance in radar systems. This technique, called Chirp at Bell Telephone Laboratories, recognizes that resolution depends on the transmitted pulse bandwidth. A long high-duty-factor transmitted pulse, with suitable modulation (linear frequency modulation in the case of Chirp), which covers a frequency interval many times the inherent bandwidth of the envelope, is employed. The receiver is designed to make optimum use of the additional signal bandwidth. This paper contains many of the important analytical methods required for the design of a Chirp radar system. The details of two signal generation methods are considered and the resulting signal waveforms and power spectra are calculated. The required receiver characteristics are derived and the receiver output waveforms are presented. The time-bandwidth product is introduced and related to the effective increase in the performance of Chirp systems. The concept of a matched filler is presented and used as a reference standard in receiver design. The effect of amplitude and phase distortion is analyzed by the method of paired echoes. One consequence of the signal design is the presence of time side lobes on the receiver output pulse analogous to the spatial side lobes in antenna theory. A method to reduce the time side lobes by weighting the pulse energy spectrum is explained in terms of paired echoes. The weighting process is described, and calculated pulse envelopes, weighting network characteristics and dele-???

The theory and design of chirp radars

This paper concerns digital single-sideband modulators with analog inputs and outputs. A group of 12 modulators is treated as a single system, with analog-to-digital converters at 12 input ports and a digital-to-analog converter at a single output port. Tradeoffs are obtained between computational parameters. Substitution of digital counterparts for the phase shifters and product modulators in 12 analog Hartley modulators gives a simple program. However, operation in real time requires quite a large number of multiplications per second. A similar digitalization of 12 Weaver modulators requires even more multiplications. However, the 12 Weaver modulators can be transformed as a system, to reduce the multiplication rate for the Hartley system by a factor 4 . The cost is an increase in scratch pad storage and a more complex program.

On digital single-sideband modulators

This paper bears on the problem of splitting a signal into two parts of like amplitudes but different phases. Constant phase differences are utilized in such circuits as Hartley single sideband modulators. The networks considered here are pairs of constant-resistance phase-shifting networks connected in parallel at one end. The first part of the paper shows how to compute the best approximation to a constant phase difference obtainable over a prescribed frequency range with a network of prescribed complexity. The latter part shows how to design networks producing the best approximation.

Realization of a constant phase difference

This paper is an informal history of the birth and growth of network synthesis and filter theory, as it was developed for RLC circuits. It includes events, experiences, and anecdotes which are not all well documented but may make interesting reading. Other papers in this issue are histories of other aspects of circuit theory; for the most part descended from the RLC theory.

A history of network synthesis and filter theory for circuits composed of resistors, inductors, and capacitors

A general method is developed for finding functions of frequency which approximate assigned gain or phase characteristics, within the special class of functions which can he realized exactly as the gain or phase of finite networks of linear lumped elements. The method is based upon manipulations of two Tchebycheff polynomial series, one of which represents the assigned characteristic, and the other the approximating network function, The wide range of applicability is illustrated with a number of examples.

Sidney Darlington

Papers

The theory and design of chirp radars

On digital single-sideband modulators

Realization of a constant phase difference

A history of network synthesis and filter theory for circuits composed of resistors, inductors, and capacitors

Network synthesis using Tchebycheff polynomial series