New classes of nonrecursive linear digital filters are proposed as alternatives to conventional methods for digital signal processing devices. In fact, the traditional approach, where signal samples are represented by 8-15 bit words, can be very expensive to implement due to the complexity of multibit multipliers and adders. Filter structures consisting of a transversal filter with tap coefficients restricted to - 1, 0, or + 1 and cascaded with simple recursive sections are proposed. Using a mean square error criterion, dynamic programming methods to select optimum sets of coefficient values for the taps are presented and evaluated. It is shown that these structures lend themselves to very simple hardware implementations and offer a valid alternative to the conventional filtering approach. Designs for several example filters are presented, and their implementation complexity is examined.

FIR filters with powers-of-two coefficients are attractive for cost-effective implementations. The performance of one such structure, the difference routing digital filter [8], is discussed. Using an SNR criterion, an optimal algorithm to select the value of the filter coefficients is presented. Results indicate that a 2-3 dB improvement in the SNR can be obtained with this new approach. In addition, the study gives some insight into the relationship between the filter sampling rate, the number of coefficients, and the size of the coefficient alphabet. In particular, it is seen that a tradeoff between the filter sampling rate and the size of the coefficient alphabet exists.

There is a growing need for people to browse through files of images such as satellite or medical photos, to determine which ones warrant further examination. Users located at some distance from the image archive often must use slow transmission links such as telephone lines. If an image is scanned out line-by-line, top-to-bottom, the user must often wait too long to determine whether the image is of any use. Using the Progressive Transmission Method, however, images are encoded so that during transmission the entire display shows a rough version of the image in 'fat pixels'. If the user wishes to see more detail, additional data is sent and used to refine these pixels, until the exact original image is seen. We report here on extensions of this method to the rich color imagery found in remote-sensing applications. A significant advance is the elimination of unworkably large look-up tables by using a single simple algorithm for performing the required encoding and decoding operations. The method is conceptualized in a 'transmission cone' context which assists a user in interacting with the system. The user can roam over large images, zoom to various levels of resolution, and cause specified subregions of interest in the image to fill in to full resolution, at a tremendous saving in time.

PAM data transmission receivers accomplishing maximum likelihood sequence detection (MLSD) usually require a matched filter prefilter, a sampler at the symbol rate, and a Viterbi algorithm detector. When the channel is unknown or slowly changing, one must use an adaptive matched filter prefilter. We examine an alternative optimum receiver whose optimality is independent of the matched filter prefilter and which is applicable when the channel is effectively band-limited. The sampler in the proposed receiver operates at a rate faster than the data symbol rate, enabling one to replace the matched filter by a fixed low-pass filter and still ensure that the maximum likelihood detector is supplied with a set of sufficient statistics. It is shown that the matched filter is incorporated within a modified Viterbi detector without increasing the number of states in the algorithm, although the Viterbi detector must perform computations at approximately twice the usual rate. Simulations support the optimality of the new receiver and quantitatively indicate the degradation in performance experienced by some adaptive receivers previously proposed.

Channels (i.e., operators) are studied that produce time warping, or delay modulation, in signals passing through them, and many interesting properties of these channels are developed. It is shown that a first-in first-out (FIFO) assumption for such channels is compelling on physical grounds and vastly simplifies ensuing analysis. Two descriptions of the channel, the "send-delay" and "receive-delay" functions, are compared, and it is shown that one is precisely the shape needed to equalize or unwarp signals warped by the other. A series expansion for time-warped signals is developed, and the unitary nature of the warp operators is exploited to generate rich sets of orthonormal signals. The random time-warp channel is then analyzed, and certain statistics such as the autocorrelation function of the output signals are developed, along with conditions on their stationarity. Finally, optimum linear filters for extracting a signal from a noisy and time-warped version are derived and compared with some previous results.

The problem of designing optimum pulseshapes for data transmission over randomly selected channels is examined using a meansquared error criterion. Earlier work has focused principally on SSB or VSB systems in the presence of timing and carrier phase jitter, but we extend the results here to any two-dimensional signaling scheme (including as special cases SSB, VSB, combined AM-PM, QAM, and staggered QAM) and to any type of channel dispersion. By imposing certain mild constraints on the transmitter and receiver filters, it is seen that one can solve for optimum pulses more easily than with earlier approaches, and yet the resulting system is still essentially optimum. These constraints leave design freedom only in the rolloff bands of the pulse spectra, and a major thurst of the work is to design for optimal utilization of whatever excess bandwidth is available. The approach used involves immunity to channel distortions: only the type of channel distortion to be encountered is known, and series expansions of mean-squared error are used to find sensitivity coefficients. These coefficients are then minimized by proper signal design. Closed form expressions are found for the optimum pulses, and these results are compared with previous work. A second approach, which uses as its criterion the mean-squared error averaged over all possible channel characteristics, is also discussed.

A decision-feedback equalizer (DFE) is proposed as a prefilter which limits the complexity of a maximum-likelihood sequence estimator (MLSE) implemented by the Viterbi algorithm (VA) for channels having a long impulse response. By imbedding a DFE into the structure of the MLSE, the overall impulse response of the system is truncated to a short duration. With this practical receiver, a compromise may be made between performance and complexity by properly choosing the duration of a desired impulse response. A technique is also developed to estimate the performance of the receiver numerically, taking into account the effect of incorrect decision feedback on the VA. Analysis and computer simulation over a single-pole channel show that the proposed scheme can reduce the complexity of the MLSE while retaining much of its performance advantages.

When designing pulse-amplitude modulation (PAM) systems for use over bandpass channels having restricted bandwidth, one may be led to use single-sideband (SSB) or vestigial sideband (VSB) transmission in order to maximize transmission rate. Carefully shaped pulses must be used to minimize degradation due to intersymbol interference (isi). In this paper VSB pulses are derived that have no inherent isi, and in addition have maximum immunity in a mean-squared-error (MSE) sense to timing and carrier phase errors. The results here generalize on those of Franks who treated the SSB case. The optimum VSB pulses are shown to be identical to those of Franks at the band edges, and to have vestigial roll-off characteristics of a similar discontinuous nature. It is also shown that one may allocate available bandwidth to the vestigial roll-off band band and Nyquist roll-off band in any way desired. The final performance for the optimum pulse depends only on the total bandwidth used. These results are shown to apply as well to a system employing a matched filter. The case of random timing and phase errors is also considered, and optimum pulses are again found. Several mathematical properties of the optimal pulses are given physical justification and geometric insight through error ellipses, and optimal signal shapes are plotted for various cases of special interest.

High-speed pulse amplitude modulation (PAM) data transmission systems require carefully shaped pulses having small bandwidth, and various coding schemes are used to increase transmission efficiency via spectrum shaping. Traditional hardware for the generation of such pulses, whether coded or not, is both difficult to design and expensive to implement. The binary transversal filter (BTF) has recently been studied in this context, and shown to be a promising alternative to other methods. It is inherently a binary device, however, and some coding schemes require multilevel signal outputs. Simple methods are presented in this paper that permit the use of a BTF for generating pulses such as bipolar, partial response, etc. The additional hardware required when coding is used is shown to be trivial in most cases.

Modern narrow-band pulse-amplitude modulation (PAM) and pulse-code modulation (PCM) systems require the generation of precisely shaped pulses in order to avoid intersymbol interference. It is not a simple matter to design analog filters having pulse responses with the requisite carefully positioned zeros, and this has led researchers to study other approaches. It is shown that the use of a binary transversal filter (BTF) coupled with a simple low-pass filter can generate extremely good pulses with small bandwidths. A BTF consists of a digital shift register and weighting resistor network to construct a staircase approximation to the desired pulse. The attendant circuitry is very simple, such that a highquality pulse generator can be built and adjusted with remarkable ease. The problem of pulse design using BTF's is considered in some generality, and a computational procedure is developed for adjusting the weighting network in the BTF to generate optimum pulse shapes. This method is then applied to several practical cases, and the circuitry required to generate excellent pulses is discussed. Test results on an implementation of such a generator using only five taps are presented, revealing the inherent simplicity and quality of the approach.

An interesting and long-standing problem in probability theory is surveyed, and its applications to analyzing the effects of intersymbol interference in digital transmission systems are discussed. Old and new results are presented which enable one to obtain analytical forms for the probability density function of the intersymbol interference in special eases. The probability of error is then computed and compared with some popular upper bounds.

Most receivers for multilevel pulse-code modulation (PCM) signals incorporate a sample-and-hold circuit in the analog-analog-to-digital converter. The sample-and-hold circuits cannot respond instantaneously in practice, and this paper considers the effects on system performance of their finite response time. To provide guidelines for system designers, the problem is analyzed in some generality and numerical results are obtained for a specific example. It is shown that a definite tradeoff exists between the bandwidth of the operational amplifiers in the sample-and-hold circuit and the follow time, and that system performance deteriorates rapidly if the bandwidth is reduced past a certain critical value. Unless the bandwidth is much larger than the critical value, there is a strong advantage in using follow times larger than onehalf the symbol interval. The bandwidth required for good eight-level transmission is about twice that required for binary transmission.