Lattice Wave Digital Filters Research Articles

On the simultaneous amplitude and phase approximations of wave digital lattice filters

AbstractThe paper presents new solution for the problem of simultaneously approximating the amplitude and phase functions of wave digital lattice filters. The approximation is relying on translating the amplitude and phase specifications into corresponding specifications for the difference and sum phase functions of the two branch polynomials. As a consequence, the phase specifications for each of the two branch polynomials is determined. Accordingly, these two polynomials are generated such that the amplitude and phase functions are approximated alternatively. This means that while one of these functions is approximated, the other is fixed. By iterating this alternative process, the two functions converge to their optimal response. Copyright © 2003 John Wiley & Sons, Ltd.

Flexible Digital Receiver Architecture with Optimized Components

Future wireless communication systems require increased flexibility, lower power consumption, smaller size and decreasing costs for the terminals and therewith for the components. By replacing analogue by digital signal processing the degree of integration and the flexibility of a terminal with respect to multi-mode capability can be improved.In a highly integrated implementation the most critical components are the A/D-converter and the digital filter stages due to high speed and low power requirements. In this contribution a novel concept for a flexible, digital receiver with highly optimized components will be presented. The concept is based on down-conversion of the broadband receive signal to a low intermediate frequency. The main modules of the receiver are a properly designed ΔΣ-modulator for A/D-conversion, and novel digital filtering stages. It will be demonstrated, that the use of cascaded low-order wave digital lattice filters results in a number of advantages and makes a very efficient realization in VLSI-technology feasible.

Design automation with the TSPC circuit technique: a high-performance wave digital filter

In this paper, we demonstrate how the true single-phase clocking (TSPC) circuit technique is utilized fur a high-speed recursive filter application, with a high degree of design automation. This features a quick netlist generation of integral high-speed arithmetic modules, utilization of carry-save architectures, and synthesis and optimization with a TSPC cell library. Implementation results in a 0.8 /spl mu/m standard CMOS process indicate substantial performance improvements over traditional designs, at the same time keeping design time very short. Fabricated samples of the third-order lattice wave digital filter were measured at 265 Msamples/s, which is more than double the sample rate reported in previous works on the same filter and same or comparable technology.

Design of very low-sensitivity and low-noise recursive filters using a cascade of low order lattice wave digital filters

Among the best structures for implementing recursive digital filters are lattice wave digital (LWD) filters (parallel connections of two all-pass filters). They are characterized by many attractive properties, such as a reasonably low coefficient sensitivity, a low roundoff noise level, and the absence of parasitic oscillations. The main drawback is that if the stopband attenuation is very high, then many bits are required for the coefficient representations. In order to get around this problem, a structure consisting of a cascade of LWD filters is introduced in this paper. The main advantage of the proposed structure, compared with the direct LWD filter, is that the poles of the new structure are further away from the unit circle. Consequently, the number of bits required for both the data and coefficient representations are significantly reduced. The price paid for these reductions is a slight increase in the overall filter order. By properly selecting the number of LWD filters and their orders and optimizing them, their coefficients are implementable by using a few powers of two. Filters of this kind are very attractive in very large-scale integration (VLSI) implementations, where a general multiplier is very costly.

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.

Wave digital filter structures for high-speed narrow-band and wide-band filtering

Wave digital filter (WDF) structures for high-speed narrow-band and wide-band filtering are introduced. The narrow-band filter is composed of a periodic model filter and one or several, possibly periodic, masking filters in cascade. Lattice and bireciprocal lattice WDF filters are used for the model and masking filters, respectively. The wide-band filter consists of a narrow-band filter in parallel with an all-pass filter. The overall filters can be designed by separately designing the model and masking filters. The filters obtained in this approach also serve as good initial filters for further optimization. Both nonlinear and approximately linear phase filters are considered. One major advantage of the new filters over the corresponding conventional filters is that they have a substantially higher maximal sample frequency. In the case of approximately linear phase, the computational complexity can also be reduced. Further, the use of bireciprocal lattice wave digital (WD) masking filters also makes it possible to reduce the complexity, compared with the case in which FIR masking filters are used. Several design examples and a discussion of finite wordlength effects are included for demonstrating the properties of the new filters.

Robust simultaneous amplitude and phase approximations oriented to bandpass wave digital lattice filters

A straightforward design method is delivered for bandpass wave digital lattice filters satisfying arbitrary amplitude and linear phase specifications. The optimality and efficiency of this method are ensured by two sources. On the one hand, the approximation is carried out directly without the need to apply frequency transformation techniques. On the other, the amplitude and phase specifications are approximated simultaneously. The approximation process is relying on the pre-construction of one of the two branch all-pass functions to exhibit exact linear phase. The other all-pass function is determined such that it controls the amplitude and/or phase responses in the passband and the two stopbands. Accordingly, the approximation problem is reduced to constructing a strictly Hurwitz polynomial specified by its phase within the Nyquist range. The approximation problem is solved by applying interpolation techniques combined with the iterative Remez-exchange algorithm. The realization of the resulting filter is carried out according to explicit formulae. The delivered method is applied through two examples illustrating its efficiency and reliability. © 1998 John Wiley & Sons, Ltd.

Robust simultaneous amplitude and phase approximations oriented to bandpass wave digital lattice filters

A straightforward design method is delivered for bandpass wave digital lattice filters satisfying arbitrary amplitude and linear phase specifications. The optimality and efficiency of this method are ensured by two sources. On the one hand, the approximation is carried out directly without the need to apply frequency transformation techniques. On the other, the amplitude and phase specifications are approximated simultaneously. The approximation process is relying on the pre-construction of one of the two branch all-pass functions to exhibit exact linear phase. The other all-pass function is determined such that it controls the amplitude and/or phase responses in the passband and the two stopbands. Accordingly, the approximation problem is reduced to constructing a strictly Hurwitz polynomial specified by its phase within the Nyquist range. The approximation problem is solved by applying interpolation techniques combined with the iterative Remez-exchange algorithm. The realization of the resulting filter is carried out according to explicit formulae. The delivered method is applied through two examples illustrating its efficiency and reliability. © 1998 John Wiley & Sons, Ltd.

A custom digital intermediate frequency filter for the American mobile telephone system

A digital filter for intermediate frequency filtering in mobile communication systems is presented. The purpose of the work is to show an alternative to the analog filters which are used in most of today's heterodyne receivers. Bit-serial arithmetic is applied on a twelfth-order wave digital lattice filter algorithm. The paper also shows a method for retiming such algorithms. The power consumption in two fabricated prototypes is compared. By customizing the library cells, the power consumption has been reduced significantly. In the low power prototype, the power dissipation is 8 mW using 3 V supply voltage. The prototype is a 10 MIPS design fabricated in a 0.8-/spl mu/m standard two-metal-layer CMOS process.

THE OPTIMAL AND STRAIGHTFORWARD DESIGN OF BANDPASS WAVE DIGITAL LATTICE FILTERS WITH ARBITRARY LOSS SPECIFICATIONS

An efficient, simple and reliable design method is introduced for bandpass wave digital lattice filters exhibiting arbitrary loss responses. The main feature of this method is that the approximation is straightforward. Thus it is carried out without the need to apply frequency transformation techniques. The method relies on employing the relationship between the amplitude and the two branch phase functions of the filter. As a consequence, the whole problem reduces finally to constructing a polynomial specified by its phase. The generation of this polynomial is achieved through the use of interpolation recurrence formulae. By factorizing this polynomial into its Hurwitz and non-Hurwitz parts, the two branch allpass functions are determined and realized. © 1997 by John Wiley & Sons, Ltd.

Arbitrary amplitude and linear phase approximations for non-prototype ladder and lattice wave digital filters

Two different approaches are introduced for the design of non-prototype ladder and lattice wave digital filters (WDFs) exhibiting arbitrary amplitude in the baseband (passband, transition band and stopband) and linear phase in the passband. The first approach is based on the phase correction of a minimum phase lattice (or ladder) WDF designed to satisfy the amplitude specifications in the three bands. In the second approach the amplitude and phase requirements are approximated simultaneously. It is devoted to the design of a lattice WDF that is constructed from the parallel arrangement of two allpass subfilters. The design procedure relies on preconstructing one of the subfilters to have exact linear phase at all frequencies and constructing the other to interpolate an arbitrary phase at a set of frequencies distributed all over the baseband. The hidden relationship between the amplitude and phase functions of the filter is utilized to approximate both of them. The approximation problem is solved by applying an interpolation technique combined with the Remez exchange algorithm. Prototype filters with amplitude specifications in the passband and stopband and phase specifications in the passband are also considered as special cases. Design examples are presented to show the efficiency of the two methods.

Relative VLSI costs of WDFs implemented usingredundant and non-redundant arithmetic

The lattice wave digital filter (LTWDF) is known to be especially suitable for high speed filtering applications, owing to the low wordlengths required. The authors present a comparison between several LTWDF architectures using redundant and non-redundant arithmetic. It is shown that architectures using non-redundant arithmetic require up to 2.5 times less VLSI area, while offering higher sample rates for most practical filtering applications.

Realisation of lattice wave digital filtersusing three-port adaptors

The second-order allpass section is the main building block of the lattice wave digital filter (LTWDF). This is conventionally realised using two-port adaptors. The authors present a comparison between the two-port realisation of the second-order allpass section and another based on the three-port series adaptor. It is shown that the sample rate of LTWDFs can be increased by up to 90% with the three-port realisation.

Pipelined lattice WDF design for wideband filters

Wideband highpass filters are widely used in applications such as wireless codec design or ECG signal processing. It is well-known that wideband digital filters suffer from large sensitivity and roundoff noise. In this letter, an efficient pipelined WDF (Wave Digital Filter) design method for wideband filters is proposed. Using one design example, it is shown that the hardware cost can be reduced by 45% by using the proposed approach instead of conventional approaches. >

Implementation of complex wave digital lattice filters with asymmetrical frequency response

The Letter presents an implementation of one port complex reactances transformed by using a frequency transformation, and also shows the application to the complex wave digital lattice filter realisation.

An interleaved/retimed architecture for the lattice wave digital filter

An architecture for the lattice wave digital filter (LWDF) that reduces the hardware of the traditional structure by 30%-45% without sacrificing speed is presented. For fixed coefficient filters using canonic signed digit multipliers, the integrated circuit chip area of an LWDF is dominated by the adders. Application of the concept of pipeline interleaving and retiming to the traditional LWDF structure allows its inherent symmetry to be used to reduce the number of adders in the structure by almost 50%.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A synthesis of low‐sensitivity digital filters using T‐cascade connections. Extraction of wave digital lattice filter sections

AbstractDigital filter response is degraded from that desired when the filter is implemented using finite wordlength multipliers. To avoid such degradation, low‐sensitivity filter structures such as wave digital filters (WDF's) often are used. On the other hand, the pipeline processing would be preferable for the high‐speed applications of filters. In general, the pipeline approach is not applicable to WDF's.This paper proposes new low‐sensitivity filter structures which are also suited for the pipeline processing. The fundamental idea to obtain low‐sensitivity structures is to synthesize digital 2‐port circuits with “structurally induced losslessness,” as done by Vaidyanathan and Mitra. The losslessness of a digital 2‐port circuit is characterized by a para‐unitary scattering matrix. WDF's also have this losslessness when they are modeled after reactance filters.The proposed structures are synthesized by factoring such scattering matrices, and constructed using T‐cascade connection of new basic sections, in contrast with the II‐cas‐cade connection used in WDF's and Vaidyana‐than‐Mitra structures. Each section, which is also characterized by a paraunitary scattering matrix, is realized as a lattice WDF. The proposed structures can realize any given transfer function, and if the function has a certain symmetry, they reduce to lattice WDF's.

A low-complexity multiplierless half-band recursive digital filter design

A low-complexity multiplierless design of a half-band recursive digital filter is presented. The filter structure is realized as a bireciprocal lattice wave digital filter. The filter coefficients are represented in a canonic signed-digit code with only two nonzero digits, and thus each filter coefficient can be implemented with only a single adder or subtracter. A fifth-order elliptic filter section is presented which requires only nine adders and five delays. Thus, a cascade of three or four of these fifth-order building blocks could be implemented on a single VLSI chip to obtain a high-performance half-band filter. >

Reconfigurable programmable architecture for cascaded unit elements and lattice WDFs

It is shown that the basic cascaded unit elements wave digital filter can be used to process simultaneously two signals which are skewed by half the sampling period. This property is exploited in the design of a novel architecture which is based on a single two port adaptor and which can be used to implement both cascaded unit elements and lattice wave digital filters.

Novel realization of hilbert transformer using complex wave digital filters

A complex network can be interpreted as a connection consisting of two real networks, one of which transfers the real part of the complex signal and the other transfers the imaginary part. In this paper, a realization of complex filters using wave digital lattice filters is reported. The relation between the real part and the imaginary part of its output fulfills the Hilbert transformation. As the attenuation response of a wave digital lattice filter meets some symmetrical requirements, a certain amount of hardware can be saved. Explicit formulae and the Hilbert transformer table are given. The disgn process is so simple that a pocket programmable calculator is sufficient to carry out the necessary calculations.