In this paper, the fixed-point implementation of adjustable fractional-delay filters using the Farrow structure is considered. Based on the observation that the sub-filters approximate differentiators, closed-form expressions for the L-2-norm scaling values at the outputs of each sub-filter as well as at the inputs of each delay multiplier are derived. The scaling values can then be used to derive suitable word lengths by also considering the round-off noise analysis and optimization. Different approaches are proposed to derive suitable word lengths including one based on integer linear programming, which always gives an optimal allocation. Finally, a new approach for multiplierless implementation of the sub-filters in the Farrow structure is suggested. This is shown to reduce register complexity and, for most word lengths, require less number of adders and subtracters when compared to existing approaches.
In this work we consider scaling of fractional delay filters using the Farrow structure. Based on the observation that the subfilters approximate the Taylor expansion of a differentiator, we derive estimates of the L_{2}-norm scaling values at the outputs of each subfilter as well as at the inputs of each delay multiplier. The scaling values can then be used to derive suitable wordlengths in a fixed-point implementation.
FIR filters are often used because of their linear-phase response. However, there are certain applications where the linear-phase property is not required, such as signal energy estimation, but IIR filters can not be used due to the limitation of sample rate imposed by the recursive algorithm. In this work, we discuss multiplierless implementation of minimum order, and therefore nonlinear-phase, FIR filters and compare it to the linear-phase counterpart.
A formulation based on multirate theory is introduced for analog-to-digital converters using parallel sigma-delta modulators in conjunction with modulation sequences. It is shown how the formulation can be used to analyze a system's sensitivity to channel mismatch errors by means of circulant and pseudo-circulant matrices. It is demonstrated how the time-interleaved-modulated (TIM), Hadamard-modulated (HM) and frequency-band decomposition (FBD) converters can be viewed as special cases of this more general description, and it is shown why the TIM and HM ADCs are sensitive to channel mismatch errors, whereas the FBD ADCs are not.
A general formulation based on multirate filterbanktheory for analog-to-digital converters using parallel sigmadeltamodulators in conjunction with modulation sequences ispresented. The time-interleaved modulators (TIMs), Hadamard modulators(HMs), and frequency-band decomposition modulators(FBDMs) can be viewed as special cases of the proposeddescription. The usefulness of the formulation stems from itsability to analyze a system's sensitivity to aliasing due to channel mismatch and modulation sequence level errors. BothNyquist-rate and oversampled systems are considered, and it isshown how the matching requirements between channels canbe reduced for oversampled systems. The new formulation isuseful also for the derivation of new modulation schemes, andan example is given of how it can be used in this context.
In this paper we examine the relation between signal-to-noise-ratio, oversampling ratio, transition bandwidth, and filter order for some commonly used sigma-delta-modulators and corresponding decimation filters. The decimation filters are equi-ripple finite impulse response filters and it is demonstrated that, for any given filter order, there exists an optimum choice of the stopband ripple and stopband edge which minimizes the signal-to-noise-ratio degradation.
This paper introduces a class of reconfigurable two-stage Nyquist filters where the Farrow structure realizes the polyphase components of linear-phase finite-length impulse response (FIR) filters. By adjusting the variable predetermined multipliers of the Farrow structure, various linear-phase FIR Nyquist filters and integer interpolation/decimation structures are obtained, online. However, the filter design problem is solved only once, offline. Design examples, based on the reweighted l(1)-norm minimization, illustrate the proposed method. Savings in the arithmetic complexity are obtained when compared to the reconfigurable single-stage structures.
This paper proposes a method to design low-delay fractional delay (FD) filters, using the Farrow structure. The proposed method employs both linear-phase and nonlinear-phase finite-length impulse response (FIR) subfilters. This is in contrast to conventional methods that utilize only nonlinear-phase FIR subfilters. Two design cases are considered. The first case uses nonlinear-phase FIR filters in all branches of the Farrow structure. The second case uses linear-phase FIR filters in every second branch. These branches have milder restrictions on the approximation error. Therefore, even with a reduced order, for these linear-phase FIR filters, the approximation error is not affected. However, the arithmetic complexity, in terms of the number of distinct multiplications, is reduced by an average of 30%. Design examples illustrate the method.
This brief proposes a method for designing modulated filter banks (FBs) with a large number of channels. The impulse response of the long prototype filter is parameterized in terms of a few short impulse responses, thus significantly reducing the number of unknown parameters. The proposed method starts by first obtaining an FB with a few channels. The solution of this FB is then partly reused as an initial (very close to final) solution in the design of FBs with a large number of channels. The number of unknown parameters hence drastically reduces. For example, we can first design a cosine modulated FB (CMFB) with three channels whose prototype filter has a stopband attenuation of about 40 dB. We can then reuse the solution of this CMFB in the design of a CMFB with 16 384 channels whose prototype filter has a similar stopband attenuation. With our proposed method, we need to reoptimize only 14 parameters to design the CMFB with 16 384 channels.
This paper proposes a method for designing high-order linear-phase finite-length impulse response (FIR) filters which are required as, e.g., the prototype filters in filter banks (FBs) and transmultiplexers (TMUXs) with a large number of channels. The proposed method uses the Farrow structure to express the polyphase components of the desired filter. Thereby, the only unknown parameters, in the filter design, are the coefficients of the Farrow subfilters. The number of these unknown parameters is considerably smaller than that of the direct filter design methods. Besides these unknown parameters, the proposed method needs some predefined multipliers. Although the number of these multipliers is larger than the number of unknown parameters, they are known a priori. The proposed method is generally applicable to any linear-phase FIR filter irrespective of its order being high, low, even, or odd as well as the impulse response being symmetric or antisymmetric. However, it is more efficient for filters with high orders as the conventional design of such filters is more challenging. For example, to design a linear-phase FIR lowpass filter of order 131071 with a stopband attenuation of about 55 dB, which is used as the prototype filter of a cosine modulated filter bank (CMFB) with 8192 channels, our proposed method requires only 16 unknown parameters. The paper gives design examples for individual lowpass filters as well as the prototype filters for fixed and flexible modulated FBs.
This paper introduces reconfigurable two-stage finite-length impulse response (FIR) Nyquist filters. In both stages, the Farrow structure realizes reconfigurable lowpass linear-phase FIR Nyquist filters. By adjusting the variable multipliers of the Farrow structure, various FIR Nyquist filters and integer interpolation/decimation structures are obtained, online. However, the filter design problem is solved only once, offline. Design examples illustrate the method.
This paper proposes optimal finite-length impulse response (FIR) digital filters, in the least-squares (LS) sense, for compensation of chromatic dispersion (CD) in digital coherent optical receivers. The proposed filters are based on the convex minimization of the energy of the complex error between the frequency responses of the actual CD compensation filter and the ideal CD compensation filter. The paper utilizes the fact that pulse shaping filters limit the effective bandwidth of the signal. Then, the filter design for CD compensation needs to be performed over a smaller frequency range, as compared to the whole frequency band in the existing CD compensation methods. By means of design examples, we show that our proposed optimal LS FIR CD compensation filters outperform the existing filters in terms of performance, implementation complexity, and delay.
This paper introduces multimode transmultiplexers (TMUXs) in which the Farrow structure realizes the polyphase components of general lowpass interpolation/decimation filters. As various lowpass filters are obtained by one set of common Farrow subfilters, only one offline filter design enables us to cover different integer sampling rate conversion (SRC) ratios. A model of general rational SRC is also constructed where the same fixed subfilters perform rational SRC. These two SRC schemes are then used to construct multimode TMUXs. Efficient implementation structures are introduced and different filter design techniques such as minimax and least-squares (LS) are discussed. By means of simulation results, it is shown that the performance of the transmultiplexer (TMUX) depends on the ripples of the filters. With the error vector magnitude (EVM) as the performance metric, the LS method has a superiority over the minimax approach.
This paper introduces a multi-mode transmultiplexer (TMUX) consisting of Farrow-based variable integer sampling rate conversion (SRC) blocks. The polyphase components of general interpolation/ decimation filters are realized by the Farrow structure making it possible to achieve different linear-phase finite-length impulse response (FIR) lowpass filters at the cost of a fixed set of subfilters and adjustable fractional delay values. Simultaneous design of the subfilters, to achieve overall approximately Nyquist (Mth-band) filters, are treated in this paper. By means of an example, it is shown that the subfilters can be designed so that for any desired range of integer SRC ratios, the TMUX can approximate perfect recovery as close as desired.
This paper introduces a multimode transmultiplexer (TMUX) structure capable of generating a large set of user-bandwidths and center frequencies. The structure utilizes fixed integer sampling rate conversion (SRC) blocks, Farrow-based variable interpolation and decimation structures, and variable frequency shifters. A main advantage of this TMUX is that it needs only one filter design beforehand. Specifically, the filters in the fixed integer SRC blocks as well as the subfilters of the Farrow structure are designed only once. Then, all possible combinations of bandwidths and center frequencies are obtained by properly adjusting the variable delay parameter of the Farrow-based filters and the variable parameters of the frequency shifters. The paper includes examples for demonstration. It also shows that, using the rational SRC equivalent of the Farrow-based filters, the TMUX can be described in terms of conventional multirate building blocks which may be useful in further analysis of the overall system.
In this paper, we introduce a non-uniform transmultiplexer capable of generating arbitrary-bandwidth user signals. The transmultiplexer consists of linear-phase finite-length impulse response (FIR) filters and Farrow structures for arbitrary-rate interpolation/decimation. By applying the FIR rational sampling rate conversion (SRC) equivalent of the Farrow structure, we model the behavior of the multiplexer and derive the conditions under which the system can approximate perfect reconstruction. Futhermore, we illustrate the functionality of the proposed transmultiplexer and we analyze the performance and functionality of a flexible frequency-band reallocation (FFBR) network using this transmultiplexer.
This paper discusses a new approach for implementing flexible frequency-band reallocation (FFBR) networks for bentpipe satellite payloads which are based on variable oversampled complex-modulated filter banks (FBs). We consider two alternatives to process real signals using real input/output and complex input/output FFBR networks (or simply real and complex FFBR networks, respectively). It is shown that the real case has a lower overall number of processing units, i.e., adders and multipliers, compared to its complex counterpart. In addition, the real system eliminates the need for two Hilbert transformers, further reducing the arithmetic complexity. An analysis of the computational workload shows that the real case has a smaller rate of increase in the arithmetic complexity with respect to the prototype filter order and number of FB channels. This makes the real case suitable for systems with a large number of users. Furthermore, in the complex case, a high efficiency in FBR comes at the expense of high-order Hilbert transformers; thus, trade-offs are necessary. Finally, the performance of the two alternatives based on the error vector magnitude (EVM) for a 16-quadrature amplitude modulation (QAM) signal is presented.
In this paper, alow-complexity approach to implement a class of flexible frequency-band reallocation (FFBR) multi-input multi-output (MIMO) networks, which use variable oversampled complex-modulated filter banks, is introduced. Two alternatives in processing real signals using real input/output and complex input/output FFBR networks (or simply, real and complex FFBR networks, respectively) are considered. It is shown that to process each sample, the real case requires less number of real operations compared to its complex counterpart. Furthermore, the real case has a smaller growth rate in the number of real operations with respect to the prototype filter order. In addition, the real FFBR network eliminates the need for two Hilbert transformers whereas in the complex FFBR case, to achieve high efficiency in FBR, there is a need for high-order Hilbert transformers.
This paper discusses the complexity trend in different finite length impulse response (FIR) filter structures when using multiplierless (shift-and-add) realization. We derive the total number of adders required by the transposed direct form, polyphase, and reduced-complexity polyphase FIR filter structures. A comparison of the arithmetic complexities of these structures for different filter characteristics is performed. The simulation results show that considering both the high level structure and the algorithm used to realize the subfilters gives a more accurate measure of complexity comparison between different FIR filter structures.
This paper discusses some issues related to the filter design in a class of multimode transmultiplexers (TMUXs). These TMUXs cover a large set of frequency division multiplexed (FDM) scenarios with simple reconfigurations. The reconfiguration is performed by changing the values of some multipliers. The paper outlines a direct filter design to decrease the level of inter-symbol and inter-carrier interference by the use of time-varying periodic filters. These time-varying periodic filters are derived from the known FDM scenarios and they are included as additional constraints in the filter design. Both minimax and constrained least-squares approaches are treated and it is shown that by including the additional constraints, the level of the TMUX noise can be reduced. This results in a better approximation of perfect reconstruction and makes the filter design direct.
This paper introduces reconfigurable nonuniform transmultiplexers (TMUXs) based on uniform modulated filter banks (FBs). Polyphase components, of any user, are processed by a number of synthesis FB and analysis FB branches of a uniform TMUX. One branch, of the TMUX, represents one granularity band and any user occupies integer multiples of a granularity band. By adjusting the number of branches, assigned to each user, a nonuniform TMUX is obtained. This only requires adjustable commutators which add no extra arithmetic complexity. The application of both cosine modulated and modified discrete Fourier transform FBs are considered and the formulations related to the appropriate choice of parameters are outlined. Examples are provided for illustration.
This paper introduces reconfigurable nonuniform transmultiplexers (TMUXs) based on fixed uniform modulated filter banks (FBs). The TMUXs use parallel processing where polyphase components, of any user, are processed by a number of synthesis FB and analysis FB branches. One branch represents one granularity band, and any user can occupy integer multiples of a granularity band. The proposed TMUX also requires adjustable commutators so that any user occupies any portion of the frequency spectrum. The location and width of this portion can be modified without additional arithmetic complexity or filter redesign. This paper considers both cosine modulated and modified discrete Fourier transform FBs. It discusses the filter design, TMUX realization, and the parameter selection. It is shown that one can indeed decrease the arithmetic complexity by proper choice of system parameters. For the critically sampled case and if the number of channels is higher than necessary, we can reduce the arithmetic complexity. In case of an oversampled system, the arithmetic complexity can be reduced by proper choice of the number of channels and the roll-off factor of the prototype filter. The proposed TMUX is compared to existing reconfigurable TMUXs, and examples are provided for illustration.
This paper discusses two approaches for the baseband processing part of cognitive radios. These approaches can be used depending on the availability of (i) a composite signal comprising several user signals or, (ii) the individual user signals. The aim is to introduce solutions which can support different bandwidths and center frequencies for a large set of users and at the cost of simple modifications on the same hardware platform. Such structures have previously been used for satellite-based communication systems and the paper aims to outline their possible applications in the context of cognitive radios. For this purpose, dynamic frequencyband allocation (DFBA) and reallocation (DFBR) structures based on multirate building blocks are introduced and their reconfigurability issues with respect to the required reconfigurability measures in cognitive radios are discussed.
This paper proposes a method to design variable fractional-delay (FD) filters using the Farrow structure. In the transfer function of the Farrow structure, different subfilters are weighted by different powers of the FD value. As both the FD value and its powers are smaller than 0.5, our proposed method uses them as diminishing weighting functions. The approximation error, for each subfilter, is then increased in proportion to the power of the FD value. This gives a new distribution for the orders of the Farrow subfilters which has not been utilized before. This paper also includes these diminishing weighting functions in the filter design so as to obtain their optimal values, iteratively. We consider subfilters of both even and odd orders. Examples illustrate our proposed method and comparisons, to various earlier designs, show a reduction of the arithmetic complexity.
This paper introduces a new structure for reconfigurable two-stage finite-length impulse response (FIR) Nyquist filters using the Farrow structure. The Nyquist filter is split into two equal and linear-phase FIR spectral factors. In the first stage, the Farrow structure realizes reconfigurable lowpass linear-phase FIR interpolation/decimation filters whereas the second stage is composed of a fixed lowpass linear-phase FIR filter. By adjusting the variable multipliers of the Farrow structure, the overall filter can be modified. Hence, various FIR Nyquist filters and integer interpolation/decimation structures are obtained. However, the filter design problem is solved only once and offline. Design examples illustrate the method.
This paper proposes a systematic method to design adjustable fractional delay (FD) filters using the Farrow structure. The Farrow structure has even-order subfilters and the maximum magnitude approximation error determines the number of these subfilters. In the Farrow structure, different powers of the FD value are multiplied by the subfilters. As both the FD value and its powers are smaller than unity, they are considered as weighting functions. The approximation error for each subfilter can then increase in proportion to the power of the FD value. With the proposed design method, the first Farrow subfilter is a pure delay whereas the remaining subfilters are digital differentiators. Examples illustrate the proposed design method and comparison to some earlier designs shows an average reduction of 20% in arithmetic complexity.
This correspondence outlines a method for designing two-stage Nyquist filters. The Nyquist filter is split into two equal and linear-phase finite-length impulse response spectral factors. The per-time-unit multiplicative complexity, of the overall structure, is included as the objective function. Examples are then provided where Nyquist filters are designed so as to minimize the multiplicative complexity subject to the constraints on the overall Nyquist filter. In comparison to the single-stage case, the two-stage realization reduces the multiplicative complexity by an average of 48%. For two-stage sampling rate conversion (SRC), the correspondence shows that it is better to have a larger SRC ratio in the first stage. © 2006 IEEE.
This paper presents formulas for the number of optimization parameters (degrees of freedom) when designing Type I linear-phase finite-length impulse response (FIR) Lth-band filters of order 2N as cascades of identical linear-phase FIR spectral factors of order N. We deal with two types of degrees of freedom referred to as (i) the total degrees of freedom D-T, and (ii) the remaining degrees of freedom D-R. Due to the symmetries or antisymmetries in the impulse responses of the spectral factors, D-T roughly equals N/2. Some of these parameters are specifically needed to meet the Lth-band conditions because, in an Lth-band filter, every Lth coefficient is zero and the center tap equals 1/L. The remaining D-R parameters can then be used to improve the stopband characteristics of the overall Lth-band filter. We derive general formulas for D-R with given pairs of L and N. It is shown that for a fixed L, the choices of N, in a close neighborhood, may even decrease D-R despite increasing the arithmetic complexity, order, and the delay.
A class of M-channel tree-structured digital filter banks is considered with half-band IIR analysis filters and FIR synthesis filters. The filter banks approximate perfect reconstruction with an exact linear phase response and zero aliasing. This particular configuration has a very low-complexity analysis filter bank. In this paper we address the problem of minimizing the synthesis filter complexity, given the minimum-complexity analysis filters. The filter banks are designed using linear and nonlinear programming
A class of tree-structured octave-band digital filter banks is introduced. The filter banks make use of half-band IIR filters in the analysis bank and FIR filters in the synthesis bank which results in very low-complexity analysis filters. Further, the overall complexity is lower than, or comparable to, that of conventional filter banks. The overall filter banks approximate perfect reconstruction in the following sense. The distortion function is a linear-phase function approximating one in magnitude whereas the aliasing terms approximate zero. The filter banks are designed using linear and nonlinear programming. Design examples are included demonstrating the properties of the new filter banks
This paper introduces new tree-structured uniform-band and octave-band digital filter banks (FBs). These FBs make use of half-band IIR filters in the analysis FBs and FIR filters in the synthesis FBs. The resulting FBs are asymmetric in the sense that the analysis FB has a very low arithmetic complexity whereas that in the synthesis FB is higher. However, compared with other asymmetric FBs, the proposed ones have in many cases a lower overall arithmetic complexity and delay. The proposed FBs have magnitude distortion but no phase distortion, further, the aliasing components are either zero (uniform-band case) or approximately zero (octave-band case). The FBs are designed using linear and nonlinear programming. Design examples are included demonstrating the properties of the proposed filters banks. ⌐ 2003 Published by Elsevier B.V.
A new class of two-channel IIR/FIR filter banks was introduced by the authors in 2000 with half-band IIR analysis filters and FIR synthesis filters. This type of filter bank features very low-complexity analysis filters and simultaneously a low overall complexity. In this paper, we consider finite-wordlength effects of these filter banks
For high-speed delta-sigma modulators the decimation filters are typically polyphase FIR filters as the recursive CIC filters can not be implemented because of the iteration period bound. In addition, the high clock frequency and short input word length make multiple constant multiplication techniques less beneficial. Instead a realistic complexity measure in this setting is the number of non-zero digits of the FIR filter tap coefficients. As there is limited control of the passband approximation error for CIC-based filters these must in most cases be compensated to meet a passband specification. In this work we investigate the complexity of decimation filters meeting CIC-like stopband behavior, but with a well defined passband approximation error. It is found that the general approach can in many cases produce filters with much smaller passband approximation error at a similar complexity.
In this work we formulate a mixed integer linear programming (MILP) problem that minimizes the number of signed-power-of- two (SPT) terms given a filter specification for linear-phase frequency-response masking (FRM) filters. The proposed method designs the filters in two steps. The model filter and the masking filters are designed separately, but subject to each other. Hence, it is not guaranteed that the global minimum is obtained. However, each solution is optimal given the other filter(s), and iteration may improve the overall solution. The filter design problems are formulated using normalized peak ripple magnitude (NPRM), which for FRM filters introduces some implications, which is also discussed in this work.
For recursive filter the maximal sample frequency is bounded by the recursive loops in the filter. [In this paper, it is understood that recursive filters are infinite-length impulse response (IIR) filters.] In this work, a filter structure based on the use of the frequency masking approach is presented that increases the maximal sample frequency for narrowband and wideband filters by introducing more delay elements in the recursive loops. By using identical subfilters (except for the periods), the subfilters can be mapped using folding to a single pipeline/interleaved arithmetic structure yielding an area-efficient implementation. The filters are potentially suitable for low-power implementation by using power supply voltage scaling techniques. In this work, the design of the filters is discussed and estimations of the ripples are derived. Two examples show the viability of the proposed method.
In this work filter structures that decrease the required number of multipliers and adders for implementation of linear-phase FIR filters using frequency-response masking techniques are introduced. The basic idea of the proposed structures is that identical subfilters are used. This leads to the same arithmetic structure can be multiplexed in the implementation, reducing the number of required multipliers and adders. The subfilters are mapped using the folding transformation to obtain an area-efficient time-multiplexed (or pipeline/interleaved) implementation. Both narrow-band and wide-band frequency-response masking as well as arbitrary bandwidth frequency-response masking techniques are considered. The filter design is discussed and for each filter structure the limits on the specifications are derived. Designed examples show the usefulness of the proposed structures.
Multiple constant multiplication (MCM), i.e., realizing a number of constant multiplications using a minimum number of adders and subtracters, has been an active research area for the last decade. Almost all work has been focused on single rate FIR filters. However, for polyphase interpolation and decimation FIR filters there are two different implementation alternatives. For interpolation, direct form subfilters lead to fewer registers as they can be shared among the subfilters. The arithmetic part corresponds to a matrix vector multiplication. Using transposed direct form subfilters, the registers can not be shared, while the arithmetic part has the same input to all coefficients, and, hence, the redundancy between the coefficients is expected to be higher. For decimation filters the opposite holds for direct form and transposed direct form subfilters. In this work we discuss the trade-off between adders/subtracters and registers, and present implementation results for area, speed, and power for different realizations
In this paper, we present a novel complex discrete-time filter. This is a fractionally delaying (FD) Hilbert transform filter (HTF) further called the FD HTF. The filter is based on a pair of rotated variable fractional delay (VFD) filters. It is capable of performing the Hilbertian as well as VFD filtering of the incoming discrete-time signal at the same time. Thus, one can substitute a cascade of the HTF and the VFD filters with an aggregated filter proposed here. The technique is simple to implement. The advantages lie in lower total delay introduced by the compound filter and in a modular structure. The rotated VFD filters in the pair differ only in the value of one parameter-the VFD. The proposed FD HTF can be applied to adaptive quadrature sub-sample estimation of delay. © 2008 IEEE.
The paper proposes an optimization technique for the design of variable digital filters with simultaneously tunable bandedge and fractional delay using a fast filter bank (FFB) approach. In the FFB approach, full band signals are split into multibands, and each band is multiplied by a proper phase shift to realize the variable fractional delay. In the proposed technique, in the formulation of the optimization of the 0th stage prototype filter of the FFB, the ripples of the filters in the subsequent stages are all taken into consideration. In addition, a shaping filter is applied to the last retained band of the FFB to form the transition band of the variable filter, such that the transition width of each band in the FFB can be relaxed to reduce the computational complexity. In total three shaping filters, constructed from a prototype filter, can be shared by different bands, so that the extra cost incurred due to the shaping filter is low.
This paper introduces a class of high-speed approximately linear-phase recursive digital filters based on the frequency-response masking approach. By using this approach, filters with a high maximal sample frequency, low computational complexity, and good numerical properties are obtained.
This paper introduces a class of high-speed wide-band frequency masking recursive digital filters with approximately linear-phase. These filters feature a high maximal sample frequency, low computational complexity, and good numerical properties.
This paper introduces a class of Mth-band linear-phase FIR filters synthesized using the frequency-response masking (FRM) approach. In the FRM approach, the overall filter makes use of periodic model filters and nonperiodic masking filters which makes it possible to obtain FIR filters requiring few arithmetic operations even when the transition band is narrow. The proposed filters are designed using linear and nonlinear programming. Design examples are included illustrating the efficiency of the proposed filters.
This paper introduces a structure for the compensation of frequency-response mismatch errors in M-channel time-interleaved analog-to-digital converters (ADCs). It makes use of a number of fixed digital filters, approximating differentiators of different orders, and a few variable multipliers that correspond to parameters in polynomial models of the channel frequency responses. Whenever the channel frequency responses change, which occurs from time to time in a practical time-interleaved ADC, it suffices to alter the values of these variable multipliers. In this way, expensive on-line filter design is avoided. The paper includes several design examples that illustrate the properties and capabilities of the proposed structure.
This paper introduces an approach to increase the maximal sample frequency of lattice wave digital filters based on circulators and Richards- structures. In this approach the allpass branches of the filters make use of cascaded first-order and constrained third-order Richards- allpass sections. Compared with the case in which regular first- and second-order Richards- allpass sections are used, the maximal sample frequency is here two times higher. This is generally paid for by a somewhat higher computational complexity.