Suboptimum Filter Research Articles

A systematic technique for designing approximately linear phase recursive digital filters

A systematic method is introduced for designing approximately linear phase low-pass recursive digital filters. The filter structures under consideration are the conventional cascade form realization and the parallel connection of two allpass filters (lattice wave digital filters). Given the amplitude specifications, the filter parameters as well as the slope of the linear phase response are optimized in such a way that the maximum phase deviation from this linear phase is minimized in the passband. The filters are designed such that either the maximum amplitude value in the transition hand is less than or equal to the passband maximum or the amplitude response is monotonically decreasing in this band. The design scheme consists of two basic steps. The first step involves finding, in a simpler manner, a good suboptimum filter. In the second step, this filter is then used as an initial filter for further optimization that is carried out by the second algorithm of Dutta and Vidyasagar. Several examples are included illustrating the efficiency of the proposed design scheme. They also show the superiority of the resulting recursive filters over their linear phase finite-impulse response equivalents, especially in narrow-band cases.

Use of a linear filter to pulse timing and amplitude from PPM‐PAM multiplexed pulse

AbstractThe proposed PPM‐PAM modulation that can change pulse timing and pulse amplitude independently has the advantage that analog and digital information can be transmitted in mixed mode. Receiving filter characteristics used in the detection of pulse timing and amplitude are investigated for PPM‐PAM multiplexed transmission. Separation of timing and amplitude information for the isolated pulse is possible by combining the linear filter with the signal zero crossing detector. Here error performance is compared for the isolated pulse by using the optimum and suboptimum filters. Then, using the effect of pulse interference at the filter output, the minimum pulse interval required for information detection and the amount of error increase are calculated. More‐over, by calculating pulse detection error probability, the pulse detection limit and amount of error in signal detection are investigated. As a result of investigations it has been estimated that PPM‐PAM multiplexed transmission can be realized by using suboptimum filters because it can reduce pulse interference and attain better error performance. It has been assumed here that pulse transmission through optical fiber and calculations are based on Gaussian shaped pulses with white and f2 noise.

Experimental results for optimum coded digital PPM with Ge APD receiver and Gaussian noise approximated theory

Practical and theory results are presented for an optical (λ = 1.523 μm) digital PPM system using a suboptimum filtered Ge APD receiver. These original results show that an optimum coding level and APD gain exists for received FWHM Gaussian pulse widths of 11.3 and 35 ns. These optima compare well with those predicted by a suboptimum filter, APD model using Gaussian approximated noise statistics.

A case for upward continuation as a standard separation filter for potential‐field maps

Separation filtering is incomplete even under the ideal synthetic condition of known power spectra of the regional and residual fields. I have designed some Wiener filters, which minimize the inevitable separation error, from previous statistical source models of Naidu, and Spector and Grant. This formulation includes the classic separation filters of Strakhov and of Elkins as Wiener filters. A proposed generalization of Wiener filters, denoted as uniformly suboptimum filters, quantitatively supports the statement that a wide span of separation problems may be solved adequately using some convenient, small standard filter family. A uniform random‐source model without assumed vertical correlations invokes upward continuation filters. In addition to this role as a Wiener filter, the upward continuation operator is given by elementary functions in both space and wavenumber domains, is numerically stable, and is also physically comprehensible when applied to real, nonrandom anomalies. In view of these distinguishing features, I propose to use the upward continuation operator to build a convenient, standard family of separation filters.

An experimental comparison of optimum and sub-optimum filters' effectiveness in the generalized correlator

Various optimum and sub-optimum filters have been added to the basic cross-correlator in order to enhance its detection and estimation capabilities in the presence of noise. These pre-detection filters include the Hannan-Thomson, the Eckart, the Smoothed Coherence Transform, some least-squares, and two optimum filters recently derived by the authors. Here, a quantitative comparison of all six filters has been conducted by extensive simulation for various input signal to noise ratios and signal and noise bandwidths. The results define the actual enhancement in time delay detection and estimation when using the optimum filters and the amount of performance degradation from the optimum for the other filters. The rank ordering of the filters is carried out. Histograms of the time delay estimates, their mean, variance and probability of detection are presented. Wherever available, comparison of analytical predictions with the experimental results is noted.

Probability Densities and Characteristic Functions for Fluctuating Targets

Probability density functions and characteristic functions for the projected area of a tumbling target object are derived together with the densities and characteristic functions for the corresponding signal-plus-noise voltage output of an infrared sensor. Several cases are considered in which the signal pulse arrival time is either known or unknown, a matched filter or a suboptimum filter is used; the signal pulse shape is either Gaussian or is unspecified; and the target orientation angles are either uniformly or nonuniformly distributed.

The Use of Intrinsic Components in an ECG Filter

The problem of filtering artifact from QRST complexes of ECG records has been approached by the use of a digital, time-varying filter. The optimum form of this filter assuming uncorrelated, zero-mean, additive noise is presented and shown to be equivalent to estimating the coefficients of an intrinsic component expansion of the complex. Results are reported showing that QRST complexes in limb leads of normals may be accurately represented by only eight terms of the intrinsic component expansion. A suboptimum filter is presented and results reported which show that an order of magnitude reduction of the 0.05 to 100 Hz artifact energy in the filtered complex can be achieved.

Optimum Pre- and Postfiltering of Sampled Signals with Application to Pulse Modulation and Data Compression Systems

The following classical problem is solved and the results are applied to minimize the mean-square error e of communication and data compression systems: stationary random input signal x(t) is prefiltered, corrupted by noise n(t) , sampled every T seconds, and finally postfiltered to yield output \hat{x}(t) . Let the desired output z(t) = a(t) \bigotimes x(t) where a(t) is any real function of t and \bigotimes denotes convolution. Determine the linear timeinvariant pre- and postfilters which jointly minimize \epsilon = E\{\frac{1}{T}\int^{T}_{0}[z(t) - \hat{x}(t)]^{2}dt\} subject to power constraint P = E\{[k(t) \bigotimes f(t) \bigotimes x(t)]^{2}\} .'' Operator E{\dot} denotes expected value, k(t) is a real function of t , and f(t) is the prefilter impulse response. Appropriate choice of T , P,k(t) , and n(t) makes the solution applicable to amplitude, angle, pulse-amplitude (PAM), pulse-code (PCM), and differential pulsecode (DPCM) modulation systems, and data compression systems. In this analysis no restrictions are placed on the input-signal spectrum, the noise spectrum, or the passbands of the filters; furthermore, the cross correlation between signal and noise is taken into consideration. Necessary and sufficient conditions are obtained for the jointly optimum pre- and postfilters. The performance obtainable using these optimum filters is compared with that obtainable using suboptimum filters. One suboptimum filtering scheme is derived which yields virtually the same performance as optimum filters and has the practical advantage that the filter transfer characteristics are independent of noise n(t) in many cases of interest. In applying the results to PCM, DPCM, and data compression systems, the filters, sampling rate, and quantizer are jointly optimized. The performance obtainable for various filtering schemes and various communication systems is compared with the optimum attainable as calculated from information theory.