Complex Finite Impulse Response Filters Research Articles

Design and Performance Analysis of High Throughput and Low Power RNS-Based FIR Filter Design on FPGA

A cost-effective finite impulse response (FIR) filter is introduced in this research work through Residue Number System (RNS). The moduli set selected provides the same benefit as that of the shift and add method. The implementation Residue Number System with reduced computational complexity, as well as high-performance finite impulse response filters that employ advanced Vivado Design Suite & Artix-7 field-programmable logic (FPL) devices, are presented in this research work. For a specified 64-tap FIR filter, a classical modulo adder tree is substituted by a binary adder with enhanced accuracy pursued by a single modulo reduction stage and as a result reducing the area constraints by approximately 18%. When compared to the three-multiplier-per-tap two's complement filter, the index arithmetic complex FIR filter that is based on the Quadratic Residue Number System outperforms by approximately 75% and at the same time involving some LEs for filters with more than 8 taps. When compared to the traditional design, a 64-tap filter requires only 41% LEs.

A Clustering-Based Approach for Designing Low Complexity FIR Filters

Low power requirements, real-time constraints and big data applications present several challenges to digital signal processing (DSP) that span multiple domains including filtering and frequency analysis. Design of digital filters that can efficiently process signals with low computational complexity is desirable and requires innovative approaches. In this paper, we present an efficient two-step design methodology to design low complexity finite-impulse response (FIR) filters. In the first step, the filter design is formulated as an optimization problem to find the minimum number of coefficients, based on K-means clustering with a Euclidean distance metric. In the second step, a mapping approach is proposed to compensate for the mean square error (MSE) that results from the clustering. We compare the proposed method with three different methods from the literature to demonstrate its effectiveness in terms of computational complexity without compromising the filtering performance.

Harmonic PMU Algorithm Based on Complex Filters and Instantaneous Single-Sideband Modulation

Phasor measurement units (PMUs) have become powerful monitoring tools for many applications in smart grids. In order to address the different issues related to harmonics in power systems, the fundamental phasor estimator in a PMU has been extended to the harmonic phasor estimator by several researchers around the world. Yet, the development of harmonic phasor estimators is a challenge because they have to consider time-varying frequencies since the frequency deviation in the harmonic components is proportional to the harmonic order in a dynamic way. In this work, a new algorithm for harmonic phasor estimation using an instantaneous single-sideband (SSB) modulation is presented. Unlike other SSB-based approaches, its implementation in this work is based on concepts of instantaneous phase and instantaneous frequency. In general, the proposed algorithm is divided into two stages. Firstly, the estimation of the fundamental phasor is carried out by means of a complex finite impulse response (FIR) filter which provides the analytic signal used to compute the instantaneous magnitude, phase, and frequency. Secondly, a complex FIR filter bank is proposed for the estimation of the harmonic components, where the instantaneous SSB modulation technique is applied in order to center the harmonic components into specific narrow bands for each complex filter when an off-nominal frequency occurs. The validation of the proposed algorithm is carried out by means of the current standards of phasor measurement units, i.e., Std. C37.118.1-2011 and C37.118.1a-2014, which involve steady-state, dynamic, and time performance tests.

Влияние режекторного фильтра на эффективность линеаризации фазочастотной характеристики аналогового полосового фильтра

The previously published works of the authors dealt with methods aimed at linearizing the phase frequency responses of analog filters using digital linearizing finite impulse response (FIR) filters. If the operating frequency band contains narrow-band interference, such interference often needs to be suppressed by using a narrow-band analog band-stop filter. However, when a band-stop filter is connected in series, the linearized phase frequency response may become distorted. The article examines the influence of a narrow-band analog band-stop filter on the effectiveness of linearizing the phase frequency responses of a complex analog band-pass filter using a complex band-pass linearizing digital FIR filter. The study was conducted using a circuit simulation program based on a model consisting of the following modules: a complex analog band-pass filter with a sixth-order Butterworth low-pass filter prototype, a narrow-band complex analog band-stop filter with a third-order Butterworth low-pass filter prototype, and a complex digital band-pass linearizing FIR filter. The article presents the results from studying the frequency band in which the phase frequency response linearity is distorted to an acceptable degree. A sharp change in the group delay time level takes place in the stopband vicinity. The frequency band in which the group delay ripple is larger than the pre-linearization group delay ripple is referred to as the linearization effect loss band. If the difference between the band-stop filter’s passband boundary frequencies is much (by dozens of times) smaller than the band of the complex band-pass filter, the linearization effect is retained over most of the passband. With the selected parameters and orders of the complex analog filter and band-stop filter, the frequency band in which the linearization effect vanishes is approximately seven times greater than the difference between the band-stop filter’s passband boundary frequencies. Such an approach is relevant in filtering narrow-band interference within the frequency band of broadband signals.

High-speed spectral calibration by complex FIR filter in phase-sensitive optical coherence tomography.

Swept-laser sources offer a number of advantages for Phase-sensitive Optical Coherence Tomography (PhOCT). However, inter- and intra-sweep variability leads to calibration errors that adversely affect phase sensitivity. While there are several approaches to overcoming this problem, our preferred method is to simply calibrate every sweep of the laser. This approach offers high accuracy and phase stability at the expense of a substantial processing burden. In this approach, the Hilbert phase of the interferogram from a reference interferometer provides the instantaneous wavenumber of the laser, but is computationally expensive. Fortunately, the Hilbert transform may be approximated by a Finite Impulse-Response (FIR) filter. Here we explore the use of several FIR filter based Hilbert transforms for calibration, explicitly considering the impact of filter choice on phase sensitivity and OCT image quality. Our results indicate that the complex FIR filter approach is the most robust and accurate among those considered. It provides similar image quality and slightly better phase sensitivity than the traditional FFT-IFFT based Hilbert transform while consuming fewer resources in an FPGA implementation. We also explored utilizing the Hilbert magnitude of the reference interferogram to calculate an ideal window function for spectral amplitude calibration. The ideal window function is designed to carefully control sidelobes on the axial point spread function. We found that after a simple chromatic correction, calculating the window function using the complex FIR filter and the reference interferometer gave similar results to window functions calculated using a mirror sample and the FFT-IFFT Hilbert transform. Hence, the complex FIR filter can enable accurate and high-speed calibration of the magnitude and phase of spectral interferograms.

New Reconfigurable Architectures for Implementing FIR Filters With Low Complexity

Reconfigurability and low complexity are the two key requirements of finite impulse response (FIR) filters employed in multistandard wireless communication systems. In this paper, two new reconfigurable architectures of low complexity FIR filters are proposed, namely constant shifts method and programmable shifts method. The proposed FIR filter architecture is capable of operating for different wordlength filter coefficients without any overhead in the hardware circuitry. We show that dynamically reconfigurable filters can be efficiently implemented by using common subexpression elimination algorithms. The proposed architectures have been implemented and tested on Virtex 2v3000ff1152-4 field-programmable gate array and synthesized on 0.18 ?m complementary metal-oxide-semiconductor technology with a precision of 16 bits. Design examples show that the proposed architectures offer good area and power reductions and speed improvement compared to the best existing reconfigurable FIR filter implementations in the literature.

Elimination of zero-order diffraction and conjugate image in off-axis digital holography

The presence of zero-order diffraction and a conjugate image in digital holography essentially diminishes the quality of the reconstructed image. In this paper, a novel method that adopts numerical operation to eliminate the zero-order diffraction and conjugate image is presented. The whole process needs only one hologram and a complex finite impulse response (FIR) digital filter. The method of numerical elimination is simple; it filters the hologram directly in the spatial domain instead of in the frequency domain. The design of a complex finite impulse response filter is described in detail. The experimental results demonstrate that the operation can completely eliminate the zero-order diffraction and conjugate image and significantly enhance the quality of the reconstructed image.

Design of Complex FIR Filters With Reduced Group Delay Error Using Semidefinite Programming

This letter proposes an improved method for designing complex finite impulse response (FIR) filters with reduced group delays using semidefinite programming. A key step in the proposed method is to directly impose a group delay constraint, which is formulated as a linear matrix inequality constraint with some reasonable approximations. The main advantage of the proposed design method is the significant reduction in group delay error at the expense of the slight increase in magnitude error. The effectiveness of the proposed design method is illustrated with an example

Least mean squared error-design of complex FIR filters with quantized coefficients

The design of complex finite-impulse response filters with quantized coefficients according to a discrete mean squared error (MSE) criterion in the frequency domain is revisited. In the first approach, the coefficients are quantized step-by-step by recursively solving a system of linear equations. The second approach is a generalized form of the first one: The MSE is repeatedly minimized considering a growing number of fixed, quantized coefficients. The first approach requires the same computational burden as the design of unquantized coefficients, in contrast to the second where the higher flexibility is paid with a higher expenditure. For a considerable number of test cases the first approach and one variant of the second achieves a smaller MSE than the direct quantization method.

Weighted least-squares design and characterization of complex FIR filters

The paper presents two novel weighted least-squares methods for the design of complex coefficient finite impulse response (FIR) filters to attain specified arbitrary multiband magnitude and linear or arbitrary phase responses. These methods are computationally efficient, requiring only the solution of a Toeplitz system of N linear equations for an N-length filter that can be obtained in o(N/sup 2/) operations. Illustrative filter design examples are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Complex eigenfilter design of arbitrary complex coefficient FIR digital filters

The real eigenfilter approach is extended to complex cases for designing arbitrary complex finite impulse response (FIR) filters. By minimizing a quadratic measure of the error in the passband and stopband, a complex eigenvector of an appropriate complex, Hermitian symmetric, and positive-definite matrix is computed to get the filter coefficients. Several arbitrary magnitude and phase FIR filters, such as multiple passband complex filters and staircase-delay allpass phase equalizers, can be easily designed by this approach. This method can be easily extended to design 2-D complex FIR filters. If an appropriate iterative process is used, equiripple filters in the complex Chebyshev sense can be obtained. Several numerical design examples demonstrate the usefulness of the approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>