A general and efficient method for scaling window sidelobe magnitude has been reported by Lim et al. Although the method always converges in practice, a rigorous proof of convergence is unavailable. In this paper, we introduce a new technique with guaranteed convergence for window sidelobe magnitude reduction. Without further modifications, the convergence speed of this new algorithm is quite the same as that of the previous one. Modifications aimed at speeding up convergence while maintaining the guaranteed convergence property are also presented.

A rectangular-window sidelobe magnitude reduction method by widening the main lobe width was proposed by Saramäki. A technique for trading off main lobe width against sidelobe magnitude for any arbitrary window was reported by Lim et al.; a fast convergence algorithm for its implementation was proposed by the same authors in another article, where the derivatives of the window function are expressed in Chebyshev polynomials which have high arithmetic complexity. All the coefficients of a rectangular-window are equal; this special property is exploited, in this paper, for deriving the window function’s derivatives without the use of Chebyshev polynomials resulting in a great reduction in the arithmetic complexity.

A technique for trading off the main lobe width against sidelobe magnitude for any arbitrary window was reported in Lim et al. and subsequently, a fast convergence method for its implementation was proposed by the same authors. These methods require the computation of derivatives involving the evaluation of trigonometric and hyperbolic functions. In this paper, we show that the derivatives can be computed without evaluating trigonometric and hyperbolic functions if the window function is a sum of exponentials such as a Fourier series.

Many types of windows have been designed in the past decades for various applications. Each window type has its own specific characteristics. In this letter, we present a general technique for trading off main lobe width against sidelobe magnitude for any arbitrary window while keeping the number of sidelobe peaks and their relative magnitudes unchanged although their exact locations and magnitudes are changed.

Windows such as Dolph-Chebyshev window and Kaiser window are adjustable, whereas windows such as Hamming window and Blackman window are traditionally not adjustable. In [1], a technique for trading off main lobe width against sidelobe magnitude for any arbitrary window, including the traditionally non-adjustable windows, was presented. However, the method in [1] requires a large number of iterations if the specification is very tight. Developed based on a new perspective on the window adjustment principle, a new method to achieve the same adjustment capability as in [1], but at a very much fewer iterations is presented in this letter. Our new method is particular useful if the specification is very tight.

A very efficient technique for significantly reducing the number of multipliers and adders in implementing narrow transition band linear-phase finite-impulse response (FIR) digital filters is to use the frequency-response masking (FRM) approach. This paper studies the construction of the masking filter pair in the FRM technique using a common part for further reducing the arithmetic complexity. Extensive simulations are included showing that the use of the common part always considerably decreases the arithmetic complexity at the expense of a slight increase in the overall filter order.

This letter presents a class of infinite impulse response (IIR) filters synthesized using a system of IIR subfilters based on the frequency-response masking (FRM) technique. In the proposed class of filters, the bandedge shaping filters are a parallel connection of two allpass filters, and the masking filters are approximately linear phase IIR filters composed of a parallel connection of a delay line and an allpass filter. A design method which jointly optimizes the IIR subfilters is introduced. The proposed class of IIR filters has lower coefficient sensitivity and roundoff noise compared with conventional IIR filters.

IIR frequency-response masking (FRM) filter where the prototype filter is an IIR filter and the masking filters are FIR filters is effective in reducing the group delay of FRM filters. In this paper, we present a constrained optimization method for the design of near linear phase IIR FRM filters, where the phase error and magnitude error are independently controlled. A design example is presented to demonstrate the performance of the method.

In this paper, we have proposed a new steering direction determination mechanism and step-size update algorithm for piloted adaptive notch filter architecture. A time-domain averaging based gradient analysis of the piloted notch cost function has been utilized to determine the direction of the main notch with respect to the input sinusoid frequency. The steering direction will indicate the distance between the frequency of the input sinusoid and the zero of the main notch. This frequency domain information has been interleaved with time domain information to develop a novel algorithm for determination of variable step-sizes for improved speed of convergence with comparatively huge reduction in steady-state mean square error (MSE). The simulation results verifies the excellent performance exhibited by our proposed steering mechanism and the step-size update algorithm over original piloted adaptive notch filter with respect to the speed of convergence and MSE.

A simplified version of a recently developed structure is derived for all-pass filters. The proposed structure possesses 4N non-trivial multipliers and 2N adders used for computing one output sample of an Nth order all-pass filter. It is shown that such a structure yields a roundoff noise gain of 4N, compared with that of (N +1)2for the classical minimum roundoff noise realizations that have in general (N+1)2multipliers and N(N + 1) adders. The proposed structure is applied to a class of all-pass based filters. The performance of such a filter is analyzed in terms of sensitivity measure and roundoff noise gain. Numerical examples are presented to demonstrate the excellent properties of the proposed structure in terms of robustness against quantization errors and reducing implementation complexity.

This paper presents an approach for digital lattice filter roundoff noise reduction using error spectrum shaping (ESS). ESS roundoff noise expression for the one-, two-, three-, and four-multiplier lattice structures are derived. A numerical example for demonstrating the performance of the proposed ESS noise reduction in lattice filters is also presented.

Most of the existing design methods for digital filters that are to be implemented with finite precision device are given by two independent stages. The first stage is to determine a transfer function (in infinite precision) that meets the specifications given, while the second one is to choose a proper filter structure to reduce finite wordlength (FWL) errors as much as possible. In this paper, we propose a new digital filter design strategy that merges the two stages such that both the performance and the structure issue are considered simultaneously with the FWL effects taken into account. The idea is developed with a recently proposed lattice-based filter structure [8]. A design example is given, which shows that the obtained structure-based filter not only outperforms existing lattice-based filters in terms of reducing the FWL effects but also has a much lower implementation complexity than the latter and the canonical filter realizations.

The excellent finite wordlength property of the lattice digital filter is well known. The four-multiplier normalized lattice, with signal power at all delay elements normalized to unity, has particular advantage in its overflow property. However, when used to implement an Nth order digital filter, the normalized lattice implementation requires 5N +1 multipliers. In this paper, we present a novel lattice filter structure derived by combining the "tapped numerator" and "injected numerator" lattices. This new "tapped numerator" and "injected numerator" hybrid lattice has overflow property close to that of the normalized lattice but requires only 3N+1 multipliers when used to realize an Nth order IIR digital filter.

New multiplication-free FIR digital filters are introduced to replace the masking filter in narrowband frequency response masking (NBFRM) based filter. The proposed filters not only significantly improve the computational efficiency of NBFRM filters but also minimize the increment of the group delays compared with existing NBFRM design techniques.

Earlier research has shown that filter impulse responses are quasi-periodic and filter coefficients can be approximated by extrapolation techniques. In this paper, a discrete coefficient extrapolated impulse response filter is proposed. Residual compensation technique is introduced to perfectly realize the filter coefficients. Both the extrapolated filter coefficients and the residuals are subexpression encoded to minimize the filter complexity. Numerical example shows that the proposed technique achieves minimum number of adders in the synthesis of the filter when compared with any other existing techniques.

In this paper, we present two new computationally efficient frequency-response masking (FRM) filter structures that combine the well-known FRM technique and prefilter-equalizer approach. Several multiplication-free prefilters are introduced for the proposed FRM filter structures. We show, by means of an example, that the newly developed prefilter-equalizer based FRM structures yield as much as 32% reduction in terms of the number of arithmetic operations compared to the original FRM approach.

A method for optimizing FRM-based FIR filters with optimum coefficient sensitivity is presented. This technique can be used in conjunction with nonlinear optimization techniques to design very sharp filters that do not only have very sparse coefficient values but also very low coefficient sensitivity.

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

In this paper, we propose a filter bank architecture based on a frequency response masking design for variable bandwidth systems. The proposed method is shown to provide a greatly reduced complexity and delay for designs with sharp transition widths, compared to the conventional octave filter banks. Furthermore, the proposed architecture allows for greater flexibility in defining the bandwidths of each channel by combining channels with smaller bandwidths, and is also able to accommodate arbitrary decimation factors and is suitable for oversampled or critically-sampled systems. A 5-channel design example is provided in which we used a multiplierless design for the masking subfilters.

The fast filter bank (FFB) describes a class of tree-structured filter banks that operate on a frequency response masking principle. Although the structure is highly regular and conveniently implemented in hardware designs, real-time software implementations lead to inefficiencies due to its branching structure. In this paper, an alternative formulation of the FFB is proposed in terms of matrix computations. This allows an efficient approach in its implementation, and significantly reduces the overall buffer memory size required. The matrix operations can be carried out using easily available highly-optimized mathematical software packages, resulting in improvements in computational speed. Savings of up to a factor of 3 in the computer time have been observed during tests on a Pentium 4 computational platform workstation.

In this paper, we propose a new adaptive system where the main zero of the notch filter is sandwiched between two piloted zeros. The gradient of the cost function provides information on the direction that the main zero should be steered towards the input sinusoid frequency. The piloted zeros are used to provide an indication on the distance between the frequency of the sinusoid and the zero location of the main notch filter. This information is used to control the adaptive step-size, for fast convergence if the frequency of the sinusoid is far away from the main zero of the notch and for small misadjustment if that distance is small. The technique is very effective for locking on frequencies, which are neither very close to dc nor very close to half sampling frequency. The complexity of the piloted filter is comparable to the conventional normalized LMS (NLMS) notch filter.

This paper presents a weighted lease squares (WLS) algorithm for the design of low-delay quadrature mirror filter (QMF) banks with a prescribed number of zeros of the low-pass filter at /spl omega/=/spl pi/: this is desirable when the filter bank is used for the wavelet decomposition of a signal. The algorithm needs only a few iterations to obtain a solution which optimizes the filter bank design problem in the weighted minimax sense. A design example is provided for illustration.

The lattice structure quadrature mirror filter (QMF) bank structurally guarantees the perfect reconstruction (PR) property. Thus, it is eminently suitable for hardware realization even under the severe coefficient quantization condition. Nevertheless, its frequency response is still adversely affected by coefficient quantization. In this paper, a novel technique is presented for the design of lattice structure PRQMF banks subject to discrete coefficient value constraints. In our technique, the coefficient values are quantized sequentially one at a time. After each coefficient is being quantized, the remaining unquantized coefficient values are reoptimized to partially compensate for the frequency response deviation caused by the quantization of that coefficient value. The order of selection of the coefficients for quantization is based on a coefficient sensitivity measure. Coefficients with higher sensitivity measures are quantized earlier than coefficients with lower sensitivity measures. The improvement in the frequency response ripple magnitude achieved by our algorithm over that by simple rounding of coefficient values differs widely from example to example ranging from a fraction of a dB to over 10 dB.

The frequency response masking technique is an efficient method to realize sharp 1-D filters. This technique can synthesize sharp 1-D filters with a considerably lower complexity when compared to direct-form implementations. We extend the frequency response masking technique to the design of 2-D diamond-shaped filters. The design procedure as well as the prototype and masking filters specifications are presented. A design example is also provided to illustrate the effectiveness of the approach.

A novel computationally highly efficient realization of sharp symmetrical bandstop FIR filter is proposed. The new structure is derived using the frequency-response-masking technique, where the bandedge-shaping filter is derived from a half-band filter by substituting each delay of the half-band filter by M delays. The masking filters are unconventional. They are quadrature filters derived from linear combinations of the masking filters in the conventional frequency-response-masking technique. Approximate expressions for the optimal value of M and the corresponding number of multipliers are derived.

We present an efficient weighted L/sub p/ algorithm for the design of quadrature mirror filters. The filterbank design process is formulated as an iterative weighted least-squares optimization problem. Our algorithm minimizes the pth power of the error function, where p may vary in different frequency bands. Good designs are obtained, typically, in a few iterations.

This paper presents a multiplierless realization structure for the implementation of adaptive digital filters. Multiplierless realization is achieved by quantizing input signals in such way that each input sample is expressed as a sum of a fixed number of signed power-of-two (SPT) terms. This simplifies all multiplications involving input signal data. Simulation results for suppressing a narrow-band interference in a direct-sequence spread-spectrum communication system show that the performance of our technique with input signal quantized to 2 SPT terms is comparable to a conventional filter with input uniformly quantized to 10 bits. However, our technique reduces the number of transistors required for realization in a custom VLSI circuit to about 1/3 of that required by conventional realization.>

A low complexity high selectivity fast filter bank (FFB) which does not involve down-sampling and up-sampling of signals has been developed. Since a single sampling rate is used throughout the filtering process, aliasing problem does not exist. The FFB was derived from the FFT. In this paper, we present an alternative derivation for the FFB. This alternative derivation renders detailed analysis of the performance of the FFB possible. This in turn leads to the optimum design of the FFB. In this paper, we also show by means of an example that the computational complexity of the FFB is significantly less than that of a single rate polyphase filter.>

The implementation of a high-speed, programmable finite impulse response (FIR) filter using coefficients consisting of two power-of-two terms is presented. The area and speed performance figures for this application-specific IC (ASIC) demonstrate the superiority of this architecture for high-speed and high-density implementation. This implementation was developed using a relatively primitive CMOS process. Simple lambda -rule scaling suggests that by using a 1.25- mu m and double-level metal process of the same die size, this architecture will allow the implementation of a filter of approximately 200 taps operating at a 10-MHz sampling rate.>

The performance of the enhanced covariance matrix technique (ECMT), which permits a substantial improvement in resolving the incident direction of noncoherent and coherent signals, is analyzed. It is found that the ECMT technique can achieve arbitrarily high resolution in resolving low signal-to-noise ratio (SNR) and closely spaced signals. The technique involves the suppression of the noise eigenvalue in the signal subspace covariance matrix, which results in the enhancement of the resolution and SNR output of the array processor. The signal covariance matrix is then decomposed to resolve the direction of arrival of the incident sources.>

When an FIR (finite-impulse response) filter with discrete valued coefficients is implemented in direct form, the peak of the amplitude response decreases with increasing filter length, but only up to certain length. Further reduction in peak ripple beyond that point cannot be realized easily without increasing the coefficient precision. It is shown that by cascading two direct-form FIR filters, each with coefficients that are sum or difference of two power-of-two terms, it is possible to achieve very small peak ripple.>

This paper presents a new filtering scheme for splitting speech signals into subbands which results in no aliasing problem when the subband signals are sub-sampled and recombined. The highpass and lowpass filters are an odd-length complementary linear phase filter pair. As a consequence, the highpass filter output can be obtained by subtracting the lowpass filter output from the appropriately delayed input. This produces a factor-of-two reduction in the computation load when compared to the conventional even-length quadrature mirror filter. Another factor-of-two saving in computation load can be gained by using halfband lowpass filters whose every other coefficient is zero. Furthermore, the filters can be designed using well known minimax optimization techniques such as the Remez exchange algorithm and integer programming.

In this paper we presented a novel on-line adaptive recursive algorithm which is capable of resolving multiple coherent spatial sources, as is often the case in radar situation. Most of the adaptive beamforming algorithms fail to operate in such situation or their performance will be degraded. Our algorithm is based upon the "travelling antenna" concept introduced by Gabriel [1]. We test the performance of this algorithm using computer simulation. An eight-element array involving coherent sources of equal and unequal strength are used for the test. We compared the performance of this algorithm with the performance of the SMI algorithm. We find that this algorithm can successfully seperate two coherent sources.

This paper describes and analyses a simple adaptive array based on the use of perturbation algorithms on a null steering beamformer proposed by Davies [1]. The convergence time constants and misadjustments of using these algorithms are derived. It is shown that, from choosing the feedback factors appropriately, the time constants can be roughly equalized, resulting in faster convergence behaviour.

A new technique for the adaptive suppression of clutter signals and narrow band interference in pulse doppler radar system is presented. In this new technique two filters F1 and F2 in cascade are used, where the filter weights of F2 are updated from the filter weights of F1. Two different filter structures, namely, the lattice structure and the taped delay line structure are considered for the implementation of both F1 and F2. Burg's algorithm and a block recursive adaptive gradient algorithm are used to calculate the filter weights of the lattice and the taped delay filter respectively.

This paper describes a new technique for estimating the frequency of a sinusoidal signal immersed in broad-band noise. The technique is eminently suitable for identifying a single spectral peak in broad-band noise when the signal-to-noise ratio is very poor. This situation is a characteristic of a phased detected pulse doppler radar return in an ECM environment, or a very weak target signal immersed in broad-band receiver noise. Computer simulation results are included. The results show that for a single sinusoidal signal in a background of additive broad-band noise, this new technique is supperior in performance when compared with the conventional MEM doppler processor.

The synthesis of lattice parameter digital filters from a given z-transform transfer function is considered. Included are several versions of AR, MA and ARMA structures. The approach is based upon partial fraction expansions and leads to numerical algorithms for parameter calculation which are numerically robust in terms of zero and poles close to the unit circle as well as self correcting for finite precision coefficients.

An efficient approach for direct form FIR filter implementation using microprocessor is presented. The approach uses the positive number and the coefficient partitioning techniques.

New methods for designing digital lattice parameter all-pole (IIR) and all-zero (FIR) filters to meet a frequency response specification in a minimum least square error sense are presented.