Linear filter

Abstract: This paper describes a new approach to the design of multidimensional (M-D) finite-wordlength digital filters with specifications in the frequency and spatial domains. The approach is based on stochastic optimization and extends previous work on finite impulse response (FIR) filters in two ways: by inclusion of spatial constraints and by application to the case of infinite impulse response (IIR) filters. The formulation proposed is based on a multiple-term objective function that, in addition to magnitude constraints, also includes step response, group delay and stability constraints. Our attention to these characteristics stems from the application of such filters to video processing that we are actively pursuing. Since filter coefficients are of finite precision and since the objective function is multivariable, nondifferentiable and likely to have multiple minima, we use simulated annealing for optimization. We show numerous examples of the design of practical filters such as channel and luminance/chrominance separation filters used in the NTSC system. We demonstrate the impact of coefficient precision as well as of group delay and step response constraints on filter parameters. >

Abstract: A trellis coded modulation system comprises a source of successive 2-bit data symbols X1, X2 arranged in a frame format wherein each frame comprises a plurality of data segments each including a plurality of groups of interleaved data symbols. Each group of interleaved data symbols is separately coded by a precoder (32a) and convolution encoder (32b) to derive coded output symbols Z0, Z1, Z2, which are mapped to respective 8-level symbols for transmission together with periodically generated frame and segment sync symbols. The received signal may be filtered by a linear filter (42), e.g. a comb filter (42), to reduce co-channel interference and each group of filtered symbols is applied to a respective first Viterbi decoder (44) for estimating data bits X1, X2. Each first decoder (44) preferably comprises a reduced complexity Viterbi decoder (44) responsive to a partial representation of the state of the linear filter (42). Each group of received symbols may also be directly applied to a respective second Viterbi decoder (46) for estimating data bits X1 X2. Estimated data bits X1 X2 from the first or second decoders (44 or 46) are selected for further processing.

Abstract: In this paper, reversible subband coding of images are proposed. The high-band signals of conventional one-dimensional reversible filter banks were extrapolative prediction error signals or interpolative ones of which number of levels became four times that of the input signals. Therefore, we design reversible filter banks that generate interpolative prediction error signals of which number of levels becomes twice that of the input signals. We also design nonseparable filter banks. It is shown that the proposed methods have the better performance than the conventional reversible subband coding and that the separable method with low-pass filter has little aliasing in the reduced images.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Abstract: This paper is concerned with the linear estimation problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time-stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal linear filter is presented based on Kalman filtering technique. However, the optimal filter is time-varying, stochastic, and does not converge to a steady state in general. Then an alternative suboptimal filter with deterministic gains is developed under a new criteria. The estimator performance in terms of their error covariances is provided, and its mean square stability is established. Note that both filters have the same dimension as the original systems.