Symmetric Finite Impulse Response Filters Research Articles

Higher order and optimized symmetric 2D FIR filter design and hardware architecture implementation using CSD-CSE

In this paper, an optimized and high-performance Two-Dimensional (2D) Finite Impulse Response (FIR) filter is designed and hardware architecture is implemented for image processing applications. The higher-order circular symmetric 2D FIR filter is designed using a modified McClellan Transformation called a P4 transformation. The perfect circular symmetry in the contour of the 2D FIR filter and less complexity and error are attained by this proposed P4 Transformation. Next, the designed filter coefficients are represented by the Canonical Signed Digit (CSD) number format to attain the multiplier-less design to avoid the power complexity multipliers. Further, to reduce the hardware complexity, the Common Subexpression Elimination (CSE) technique is utilized to reduce the number of adders and hence area and power are decreased. Each sub-filter corresponding to the CSD coefficient rows is realized and integrated as a 2D FIR filter using a Fully Direct-type architecture. This 2D FIR filter architecture is coded by Verilog and synthesized by Cadence tools in a 45 nm CMOS technology library. The Delay, Power Consumption (PC), and Area reports were generated by the Genus synthesis tool and compared with the state-of-the-art works. The PC, area, and delay of the proposed filter architecture are reduced to the minimum of 13.96%, 69.1%, and 1.4%, respectively when compared to the existing filter architectures. The maximum of 10.48 times and a minimum of 1.18 times of Area Delay Product (ADP), and a maximum of 10.69 times and a minimum of 1.063 times of Power Delay Product (PDP) are smaller than the existing 2D filter architectures.

The Comparison Features of ECG Signal with Different Sampling Frequencies and Filter Methods for Real-Time Measurement

Electrocardiogram (ECG) signals have been used to monitor and diagnose signs of cardiovascular disease and abnormal signals about the human body. ECG signals are typically characterized by the PR, QRS, QT interval, ST-segment, and heart rate (HR) parameters. ECG devices are widely used for many applications, especially for the elderly. However, ECG signals are often affected by noises from the environment. There are mainly two types of noises that affect the ECG signals: low frequencies from muscle activity and 50/60 Hz from the electrical grid. Removing these noises is important for improving the quality of the ECG signal. A clear ECG signal makes it easy to diagnose cardiovascular problems. ECG signals with high sampling frequency are more accurate. However, the noises in the signal will be more obvious and it will be difficult to remove these noises with filters. We analyzed the symmetrical correlation between the sampling frequency of the signal and the parameters of the signal such as signal to noise ratio (SNR) and signal amplitude. This study will compare characterization of ECG signals performed at different sampling frequencies before and after applying infinite impulse response (IIR) and symmetric finite impulse response (FIR) filters. Therefore, it is critical that the sampling frequency is consistent at the same frequency of the ECG signal for accurate diagnosis. Furthermore, the approach can be also important for the device to help reduce the device’s computing power and hardware resources. Our results were tested with the MIT/ BIH database at 360 Hz sampling frequency with 11-bit resolution. We also experimented with the device operating in real-time with a sampling frequency from 100 Hz to 2133 Hz and a 24-bit resolution. The test results show the advantages of the symmetric FIR filter over IIR when applied to the filtering of ECG signals. The study’s conclusions can be applied to real-world devices to improve the quality of ECG signals.

Design and implementation of low complexity circularly symmetric 2D FIR filter architectures

This paper presents a low complexity two dimensional (2D) circular symmetric Finite Impulse Response (FIR) filter design and implementation of architecture. The optimized circular symmetric 2D FIR filter is designed using a modified Park–McClellan transformation method and filter coefficients are quantized using a canonical signed digit (CSD) binary number format. The CSD encoded coefficients are optimized to reduce the number of adder/subtractors using common subexpression elimination (CSE) algorithms. Based on the modified filter coefficients, the two structures fully direct form and hybrid-II form 2D FIR filter architectures are implemented using CSD and CSD with Horizontal CSE and Vertical CSE techniques. The proposed architectures compared with the conventional symmetry 2D filters and state-of-the-art architectures in terms of area, power, and speed.

Fast Converging Cuckoo Search Algorithm to design symmetric FIR filters

Elimination of noise from transmitted signals inevitably incorporated during transmission persisted important task for the researchers from the preliminary days of Signal Processing. Among different techniques proposed regarding this purpose, use of digital filters has become most effectual in multiple ways. Feasible design, lower hardware costs have made the Finite Impulse Response (FIR) filters popular. Among different techniques, using perfect set of filter coefficients to implement FIR filters is most acceptable. Process of determining appropriate set of filter coefficients is characterized as an optimization problem with the objective of minimizing error function. Error function is conceptualized as an approximation function signifying deviancy between the designed filter responses from the ideal filter responses. Present work proposes Fast Converging Cuckoo Search Algorithm to obtain optimized filter coefficients to implement lowpass, highpass and bandpass FIR filters. Responses of the implemented filters using the proposed method are compared with the responses obtained by the filters designed using conventional Cuckoo Search Algorithm and Parks McClellan algorithm.

Design of efficient circularly symmetric two-dimensional variable digital FIR filters

Circularly symmetric two-dimensional (2D) finite impulse response (FIR) filters find extensive use in image and medical applications, especially for isotropic filtering. Moreover, the design and implementation of 2D digital filters with variable fractional delay and variable magnitude responses without redesigning the filter has become a crucial topic of interest due to its significance in low-cost applications. Recently the design using fixed word length coefficients has gained importance due to the replacement of multipliers by shifters and adders, which reduces the hardware complexity. Among the various approaches to 2D design, transforming a one-dimensional (1D) filter to 2D by transformation, is reported to be an efficient technique. In this paper, 1D variable digital filters (VDFs) with tunable cut-off frequencies are designed using Farrow structure based interpolation approach, and the sub-filter coefficients in the Farrow structure are made multiplier-less using canonic signed digit (CSD) representation. The resulting performance degradation in the filters is overcome by using artificial bee colony (ABC) optimization. Finally, the optimized 1D VDFs are mapped to 2D using generalized McClellan transformation resulting in low complexity, circularly symmetric 2D VDFs with real-time tunability.

Area and Speed Efficient Implementation of Symmetric FIR Digital Filter through Reduced Parallel LUT Decomposed DA Approach

This brief proposes an area and speed efficient implementation of symmetric finite impulse response (FIR) digital filter using reduced parallel look-up table (LUT) distributed arithmetic (DA) based approach. The complexity lying in the realization of FIR filter is dominated by the multiplier structure. This complexity grows further with filter order, which results in increased area, power, and reduced speed of operation. The speed of operation is improved over multiply-accumulate approach using multiplier less conventional DA based design and decomposed DA based design. Both the structure requires B clock cycles to get the filter output for the input width of B, which limits the speed of DA structure. This limitation is addressed using parallel LUTs, called high speed DA FIR, at the expense of additional hardware cost. With large number of taps, the number of LUTs and its size also becomes large. In the proposed method, by exploiting coefficient symmetry property, the number of LUTs in the decomposed DA form is reduced by a factor of about 2. This proposed approach is applied in high speed DA based FIR design, to obtain area and speed efficient structure. The proposed design offers around 40% less area and 53.98% less slice-delay product (SDP) than the high throughput DA based structure when it’s implemented over Xilinx Virtex-5 FPGA device-XC5VSX95T-1FF1136 for 16-tap symmetric FIR filter. The proposed design on the same FPGA device, supports up to 607 MHz input sampling frequency, and offers 60.5% more speed and 67.71% less SDP than the systolic DA based design.

Design of Frequency Invariant Wideband Beamformer with Real and Symmetric FIR Filters

An approach to wideband beamformer with frequency invariant property is proposed by optimising the space-time two-dimensional finite impulse response (FIR) filters. Frequency invariant beam pattern brings some restrictions on frequency bandwith and filter length. Using the Landau-Pollak theorem to estimate the rank of wideband signals, we give the lower bound of filter length respect to array element numbers and the relative bandwidth of wideband signal. With the expression of beam pattern using real and symmetric FIR filters, we develop corresponding optimisation formation considering the robustness of beamformer as well, which can be easily solved by the least mean square (LMS) algorithm. A design example is provided to show the effectiveness of the proposed method. Defence Science Journal, 2012, 62(4), pp.243-247 , DOI:http://dx.doi.org/10.14429/dsj.62.965

A fast matrix iterative technique for the WLS design of 2-D quadrantally symmetic FIR filters

High computational complexity is a major problem encountered in the optimal design of two-dimensional (2-D) finite impulse response (FIR) filters. In this paper, we present an iterative matrix solution with very low complexity to the weighted least square (WLS) design of 2-D quadrantally symmetric FIR filters with two-valued weighting functions. Firstly, a necessary and sufficient condition for the WLS design of 2-D quadrantally symmetric filters with general nonnegative weighting functions is obtained. Then, based on this optimality condition, a novel iterative algorithm is derived for the WLS design problem with a two-valued weighting function. Because the filter parameters are arranged in their natural 2-D form and the transition band is not sampled, the computation amount of the proposed algorithm is reduced significantly, especially for high-order filters. The exponential convergence of the algorithm is established, and its computational complexity is estimated. Design examples demonstrating the convergence rate and solution accuracy of the algorithm, as well as the relation between the iteration number of the algorithm and the size and transition-band width of the filter are given.

Reduction of Symmetric Complex Filters

Due to their linear-phase property, symmetric filters are an interesting class of finite-impulse-response (FIR) filters. Moreover, symmetric FIR filters allow an efficient implementation. In this paper we extend the classical definition of Hermitian symmetry to a more general symmetry that is also applicable to complex filters. This symmetry is called generalized-Hermitian symmetry. We show the usefulness of this definition as it allows for a unified treatment of even and odd-length filters. Central in this paper is a theorem on the reduction of generalized-Hermitian-symmetric filters to Hermitian-symmetric filters, both with finite precision coefficients. A constructive proof of this theorem is presented and an associated procedure for reducing generalized-Hermitian-symmetric filters is derived. Two of the examples show the application of the reduction procedure and the achieved savings on arithmetic costs. Finally, all three examples show that a special instance of the generalized-Hermitian-symmetric filters with finite precision coefficients, may have lower arithmetic costs than the Hermitian-symmetric filter from which it is derived.

Implementation of 2D explicit depth extrapolation FIR digital filters for 3D seismic volumes using singular value decomposition

We propose a new scheme for implementing predesigned 2D complex-valued wavefield extrapolation finite impulse response (FIR) digital filters, which are used for extrapolating 3D seismic wavefields. The implementation is based on singular value decomposition (SVD) of quadrantally symmetric 2D FIR filters (extrapolators). To simplify the SVD computations for such a filter impulse response structure, we apply a special matrix transformation on the extrapolation FIR filter impulse responses where we guarantee the retention of their wavenumber phase response. Unlike the existing 2D FIR filter implementation methods that are used for this geophysical application such as the McClellan transformation or its improved version, this implementation via SVD results in perfect circularly symmetrical magnitude and phase wavenumber responses. In this paper, we also demonstrate that the SVD method can save (depending on the filter size) more than 23% of the number of multiplications per output sample and approximately 62% of the number of additions per output sample when compared to direct implementation with quadrantal symmetry via true 2D convolution. Finally, an application to extrapolation of a seismic impulse is shown to prove our theoretical conclusions.

Novel Area-Efficient FPGA Architectures for FIR Filtering With Symmetric Signal Extension

This paper presents four novel area-efficient field-programmable gate-array (FPGA) bit-parallel architectures of finite impulse response (FIR) filters that smartly support the technique of symmetric signal extension while processing finite length signals at their boundaries. The key to this is a clever use of variable-depth shift registers which are efficiently implemented in Xilinx FPGAs in the form of shift register logic (SRL) components. Comparisons with the conventional architecture of FIR filter with symmetric boundary processing show considerable area saving especially with long-tap filters. For instance, our architecture implementation of the 8-tap low Daubechies-8 FIR filter achieves ~ 30% reduction in the area requirement (in terms of slices) compared to the conventional architecture while maintaining the same throughput. Two of the above-cited novel architectures are dedicated to the special case of symmetric FIR filters. The first architecture is highly area-efficient but requires a clock frequency doubler. While this reduces the overall processing speed (to a maximum of 2), it does maintain a high throughput. Moreover, this speed penalty is cancelled in bi-phase filters which are widely used in multirate architectures (e.g., wavelets). Our second symmetric FIR filter architecture saves less logic than the first architecture (e.g., 10% with the 9-tap low Biorthogonal 9&7 symmetric filter instead of 37% with the first architecture) but overcomes its speed penalty as it matches the throughput of the conventional architecture.

Designing Compact Causal Digital Filters for Low-Frequency Strainmeter Data

For the strainmeter component of the Plate Boundary Observatory, filters are needed to produce low-frequency series (5-minute samples) from the higher- frequency (1 Hz) data generated by the instruments. We present design methods for finding filters that are efficient, causal, and compact. We use standard methods for generating symmetric finite impulse response filters, followed by root finding, selection of roots, and reconstruction of the weights, using procedures that make these processes numerically stable. The final filters show appropriate performance even in the presence of large teleseismic signals, but introduce unavoidable artifacts for strain data from large local earthquakes.

Minimal structures for symmetric FIR filters of arbitrary length

It is shown that, even in the very basic direct-form symmetric FIR (finite impulse response) filter structure, redundancy exists in terms of additive complexity. Methods for removing it are presented. A conventional direct-form implementation of an L-tap symmetric FIR filter requires L/2 or (L+1)/2 multiplications, L-1 additions, and L-1 delay units. The symmetry is exploited in such a way that the number of additions is significantly reduced, while the number of multiplications and the memory requirement remain the same. It is shown that the additive complexity can be reduced nearly to L/2. A complete solution is provided, for any L, to the derivation of the filter structure that requires the minimal number of additions, L/2 or (L+1)/2 multiplications, and L-1 delay units. Thus a new class of structures and algorithms for symmetric FIR filters is obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A simplified computational algorithm for implementing FIR digital filters

An N-point finite impulse response (FIR) digital filter, when implemented in software, generally requires N multiplications, N additions, and (N - 1) shifts per output sample. An obvious simplification is to implement the shift register required to store x(n) to x(n - N + 1) using a moving pointer, thereby eliminating the (N - 1) shifts per sample required in the most straightforward implementation. However, this simplification requires a check on the index of every sample to see if the end of the linear storage array has been passed, thereby voiding most of the gain in speed which was obtained. A simple technique is discussed for trading N storage locations for the (N - 1) shifts (or the (N - 1) index checks), thereby leading to an implementation in which only N multiplications, N additions, and one indexing operation are required per output sample. For implementing symmetric (i.e., linear phase) FIR filters, the resulting savings is even somewhat greater because two index pointers are required, and each must normally be checked to see that it remains within the bounds of the array.