Robert Bregovic

Design of practically perfect-reconstruction cosine-modulated filter banks: a second-order cone programming approach

Designing optimal perfect-reconstruction (PR) and near PR (NPR) cosine-modulated filter banks is essentially a constrained nonlinear minimization problem. This paper proposes two second-order cone-programming based algorithms for designing NPR and practically PR cosine-modulated filter banks with improved performance relative to several established design methods.

A systematic technique for designing linear-phase FIR prototype filters for perfect-reconstruction cosine-modulated and modified DFT filterbanks

This paper describes a systematic technique for designing prototype filters for generating perfect-reconstruction (PR) orthogonal cosine-modulated and modified discrete Fourier transform filterbanks. In the proposed design scheme, the stopband energy of the prototype filter is minimized, and the basic unknowns are the angles of a special lattice structure used for implementing the prototype filter so that the PR property is automatically satisfied independent of the angle values. This selection of the unknowns makes the overall optimization problem unconstrained. Due to the fact that there are several local optima, the design is performed in multiple steps in order to arrive at least at a very good suboptimal solution. First, for the given number of channels, the length of the channel filters, and the stopband edge of the prototype filter, the corresponding two-channel filterbank is designed based on the preoptimized data. Then, after knowing the angles for the optimized two-channel case, the prototype filter for the desired filterbank is generated by gradually increasing the number of channels and by properly using the result of the previous step as a start-up solution for the present step. The main benefit of the proposed design technique is that it enables one to effectively design prototype filters for filterbanks with very high-order analysis and synthesis filters.

A general-purpose optimization approach for designing two-channel FIR filterbanks

An efficient general-purpose optimization approach is proposed for designing two-channel finite impulse response (FIR) filterbanks. This technique can be used for optimizing two-channel FIR filterbanks in all alias-free cases proposed in the literature. The generalized problem is to minimize the maximum of the stopband energies of the two analysis filters subject to the given passband and transition band constraints and the given allowable reconstruction error. Therefore, in addition to the perfect-reconstruction filterbanks, nearly perfect-reconstruction banks can be optimized in a controlled manner. The optimization is carried out in two steps. In the first step, for the selected type of the filterbank, a good starting-point filterbank for further optimization is generated using an existing design scheme. The second step involves optimizing the filterbank with the aid of a modified Dutta-Vidyasagar (1977) algorithm. Several examples are included, illustrating the efficiency and the flexibility of the proposed approach.

An efficient approach for designing nearly perfect-reconstruction cosine-modulated and modified DFT filter banks

Efficient two-step algorithms are described for optimizing the stopband response of the prototype filter for cosine-modulated and modified DFT filter banks either in the minimax or in the least-mean-square sense subject to the maximum allowable aliasing and amplitude errors. The first step involves finding a good start-up solution using a simple technique. This solution is improved in the second step by using nonlinear optimization. Several examples are included illustrating the flexibility of the proposed approach for making compromises between the required filter lengths and the aliasing and amplitude errors. These examples show that by allowing very small amplitude and aliasing errors, the stopband performance of the resulting filter bank is significantly improved compared to the corresponding perfect-reconstruction filter bank. Alternatively, the filter orders and, consequently, the overall delay can be significantly reduced to achieve practically the same performance.

An efficient approach for designing nearly perfect-reconstruction low-delay cosine-modulated filter banks

A systematic multi-step approach is described for optimizing the stopband response of the prototype filter for low-delay critically sampled cosine-modulated filter banks in the least-mean-square sense subject to the maximum allowable aliasing and amplitude errors. In this approach, filter banks having several channels are designed by starting with a filter bank with a small number of channels. Then, the number of channels is gradually increased and a new prototype filter is optimized using the modified version of the prototype filter of the previous step as a good start-up solution. Several examples are included illustrating the flexibility of the proposed approach for making compromises between the required filter orders, the required filter bank delays, and the aliasing and amplitude errors. These examples show that by allowing very small amplitude and aliasing errors, the stopband performance of the resulting filter bank is significantly improved compared to the corresponding perfect-reconstruction filter bank. Alternatively, the filter bank delay and the order of the prototype filter can be significantly reduced while still achieving practically the same filter bank performance.

A Generalized Window Approach for Designing Transmultiplexers

This paper proposes a computational, very efficient, approach for designing a novel family of M-channel maximally decimated nearly perfect-reconstruction cosine-modulated transmultiplexers. This approach is referred to as the generalized windowing method for transmultiplexers because after knowing the transmission channel a proper weighted sum of the inter-channel and inter-symbol interferences can be properly taken into account in the optimization of the window function, unlike in other existing windowing techniques. The proposed approach has also the following two advantages. First, independent of the number of subchannels and the common order of the subchannel filters, the number of unknowns is only four. Second, the overall optimization procedure is made considerably fast by estimating the above-mentioned sum in terms of two novel measures, namely, the signal to inter-symbol and the signal to inter-channel interferences, which are very easy to evaluate. Furthermore, when the transmission channel is not considered in the design, a table is provided, which contains the parameters for designing the prototype filter directly by using the windowing method without any time-consuming optimization. When comparing the resulting transmultiplexers with the corresponding perfect-reconstruction designs (the same number of subchannels and same prototype filter order), the levels of interferences are practically the same. However, when the system is affected by a strong narrowband interference, the proposed transmultiplexers outperform their PR counterparts. Design examples are included illustrating the efficiency of the proposed design approach over other existing techniques based on the use of the windowing method.

Frequency-Response Masking-Based Design of Nearly Perfect-Reconstruction Two-Channel FIR Filterbanks With Rational Sampling Factors

In order to ensure a good filterbank (FB) performance in cases where there are significant changes in the subband signals, the filters in such FBs must have very narrow transition bandwidths. When using conventional finite-impulse response (FIR) filters as building blocks for generating these FBs, this implies that their orders become very high, thereby resulting in a high overall arithmetic complexity. For considerably reducing the overall complexity, this contribution exploits the frequency-response masking (FRM) technique for synthesizing FIR filters for the above-mentioned FBs, where rational sampling factors are used. Comparisons between various optional methods of utilizing the FRM technique for designing FBs under consideration shows that the most efficient one, from both the design and the implementation viewpoints, are FBs that are constructed such that the bandedge-shaping or periodic filters are evaluated at the input sampling rate and the masking filters at the output sampling rate. This is shown by means of illustrative examples.

An efficient implementation of linear-phase FIR filters for a rational sampling rate conversion

This paper considers how to efficiently implement linear-phase FIR filters for providing a sampling rate conversion by an arbitrary rational factor of M/L, where L(M) is the up-sampling (down-sampling) factor to be implemented before (after) the actual filter. In the proposed implementation, the coefficient symmetry of the linear-phase FIR filter is exploited as well as possible when taking into account the following facts. When increasing (decreasing) the sampling rate by the factor of L(M), only every Lth input sample has a nonzero value (only every Mth output sample has to be evaluated). The proposed implementation is, first, presented by two illustrative examples and, then, guidelines are given on how to efficiently implement a sampling rate converter having an arbitrary rational sampling rate factor M/L

Visual-quality evaluation methodology for multiview displays

Abstract Multiview displays are characterized by a multitude of parameters, such as spatial resolution, brightness, 3D-crosstalk, and so forth, which individually and in combination influence the visual quality of 3D scenes. These parameters are specified by values precisely measured by optical means. However, it is difficult for an average consumer or content producer to compare the visual quality of two displays or to judge whether given 3D content is suitable for a certain display using only this set of parameter values. In this paper, we propose a quality-measurement methodology that aims to measure the visibility of structural distortions introduced by a multiview display by using a number of test signals with different frequency content and apparent depth. We use these measurements to derive what we call display passband for signals at different disparity levels. The passband determines the frequency components for which the intended signal is predominantly visible with respect to the distortion introduced by the display. Additionally, we propose a method to determine the approximate effective resolution of a display for signals with a given apparent depth. The result of the measurements can be used to compare the perceived visual quality of different multiview displays.

Implementation of Linear-Phase FIR Filters for a Rational Sampling-Rate Conversion Utilizing the Coefficient Symmetry

This paper proposes an efficient structure for implementing a linear-phase finite-impulse-response (FIR) filter of an arbitrary order N for the sampling-rate conversion by a rational factor of L/M , where L(M) is the integer upsampling (down-sampling) factor to be performed before (after) the actual filter. In this implementation, the coefficient symmetry of the linear-phase filter is exploited as much as possible and the number of delay elements is kept as low as possible while utilizing the following facts. When increasing (decreasing) the sampling rate by a factor of L(M), only every Lth input sample has a nonzero value (only every M th output sample has to be evaluated). In this way, the number of required multiplications per output sample is reduced approximately by a factor of two compared with the conventional polyphase implementation. The proposed implementation is first illustrated using two examples. Based on these examples, guidelines are then given on how to efficiently realize an Nth-order linear-phase FIR filter for a sampling-rate converter having an arbitrary rational conversion factor L/M. Finally, the implementation complexity of the proposed approach is evaluated and some examples are included, showing the efficiency of the proposed implementation compared with other existing ones.