Optimal design of complex FIR filters with arbitrary magnitude and group delay responses

This paper presents a method for the frequency-domain design of digital finite impulse response filters with arbitrary magnitude and group delay responses. The method can deal with both the equiripple design problem and the peak constrained least squares (PCLS) design problem. Consequently, the method can also be applied to the equiripple passbands and PCLS stopbands design problem as a special case of the PCLS design. Both the equiripple and the PCLS design problems are converted into weighted least squares optimization problems. They are then solved iteratively with appropriately updated error weighting functions. A novel scheme for updating the error weighting function is developed to incorporate the design requirements. Design examples are included in order to compare the performance of the filters designed using the proposed scheme and several other existing methods.     

Least-squares magnitude filters with self-equalised delay characteristic

A new class of nonminimum-phase transfer functions with one pair of real-axis transmission zeros is described. These functions are suitable for determining the lowpass prototype networks in the design of narrow bandpass filters at microwave frequencies with small passband loss and very flat delay response over the central part of the passband.     

A maximally flat group delay recursive digital filter with improved passband magnitude response

A technique is proposed for the design of a recursive digital filter with maximally flat responses in both magnitude and group delay. In comparison to the previous designs [1]-[3], the magnitude and group delay always show smooth responses no matter what the difference is in the polynomial degrees of the numerator and denominator.     

Two-dimensional FIR digital filters with maximally flat magnitude

Generation of a class of maximally flat magnitude two-dimensional FIR functions employing McClellan transformation is described and their properties are discussed.     

A recursive digital filter with simultaneous maximally flat magnitude and group delay at an arbitrary specified frequency

A design technique for a recursive digital filter with simultaneously maximally flat magnitude and group delay at an arbitary specified frequency is presented, It employs the power series expansion to formulate a set of simultaneous linear equations which can be solved with a standard computational algorithm.     

Design of 2-D recursive digital filters satisfying prescribed magnitude and constant group delay response

Generation of the 2-variable very-strictly-Hurwitz polynomial (VSHP) using properties of derivatives of even or odd parts of Hurwitz polynomials and their applications in designing 2-D recursive digital filters satisfying prescribed magnitude and constant group delay response is described.     

Lowpass digital filters with linear phase

A method of synthetising lowpass recursive digital filters is given in the letter. The method relies on the properties of orthogonal functions on the z plane and the impulse response of an ideal lowpass linear phase filter. Considerable saving in computation and storage appears to have been achieved by this method compared with the nonrecursive (with window functions) truncation method.     

A new method for the design of IIR filters with flat magnitude response

This paper presents a new direct design of infinite-impulse response (IIR) filters with a flat magnitude response in both passband and stopband (Butterworth filters). The design specifications are passband and stopband frequencies and passband droop and stopband attenuation. The approach is based on an allpass filter with flatness at frequency points /spl omega/=0 and /spl omega/=/spl pi/. Depending on the parity of the IIR filter order, the allpass filter is either real or complex. However, in both cases, the resulting IIR filter is real.     

Recursive digital filters with predetermined group delay andChebyshev stopband attenuation

Recently, a conformal mapping technique has been described whereby the transfer function of a recursive digital filter with prescribed group delay and Chebyshev stopband can be obtained in such a way that the numerator and denominator polynomials are different in order. It is shown here that such a transfer function can also be determined using the familiar bilinear transformation and the well known method in the s-domain. Numerical examples are included to demonstrate the technique     

Lowpass digital filters using least-squared-error design

A method is presented of designing digital filters which give a least-squared-error fit to a polynomial expression. An example is given of a second-order digital-filter approximation to a first-order continuous filter.     

具有平坦群时延特性的小型高温超导滤波器设计

为制作小型化线性相位高温超导滤波器,提出了一种新型开环分形谐振器,谐振器间耦合小且衰减快,可减小滤波器尺寸与不必要的寄生耦合。再者,使用相邻CQ单元共用谐振器的设计方法减少谐振器的数目进一步减小滤波器的尺寸。最后在MgO基底上设计出一个拥有三对传输零点的十阶高温超导滤波器,其带宽60%范围内群时延的波动在1 ns以内,版图大小仅有20 mm×10 mm,达到了相位均衡与小型化的目的。其边带陡峭度达到2d B/MHz,带外抑制达到40 d B,回波损耗最高为23.92 d B,插入损耗小于0.1 d B。     

PCLS IIR digital filters with simultaneous frequency responsemagnitude and group delay specifications

This paper presents the peak-constrained least-squares (PCLS) approach to designing IIR digital filters. PCLS IIR digital filters that meet simultaneous specifications on the frequency response magnitude and the group delay are introduced. As a point of reference, we consider the IIR digital filter design problem that appears in Deczky's (1972) classic paper and in the popular textbook by Oppenheim and Schafer (1989). In addition, the same design problem appears in the IIR filter design chapter by Higgins and Munson (1993) in the Handbook for Digital Signal Processing. By using our new algorithm with simultaneous optimization of the frequency response magnitude and the group delay, we obtain a dramatic improvement in the solution of this classic IIR digital filter design problem. Starting from the same filter structure and the same specifications for the frequency response magnitude as in the works of Deczky, Oppenheim and Schafer, and Higgins and Munson, we are able to reduce the group delay ripple by a factor of 35. In another design problem that originated in Deczky's work, we use PCLS optimization to reduce the group delay ripple by a factor of 40 at the same time we reduce the stopband energy by 6 dB, without sacrificing any other performance measure. The group delay ripple in this IIR digital filter example is reduced to only ±0.002 samples     

Closed-form design and efficient implementation of variable digital filters with simultaneously tunable magnitude and fractional delay

This paper proposes a closed-form solution for designing variable one-dimensional (1-D) finite-impulse-response (FIR) digital filters with simultaneously tunable magnitude and tunable fractional phase-delay responses. First, each coefficient of a variable FIR filter is expressed as a two-dimensional (2-D) polynomial of a pair of parameters called spectral parameters; one is for independently tuning the cutoff frequency of the magnitude response, and the other is for independently tuning fractional phase-delay. Then, the closed-form error function between the desired and actual variable frequency responses is derived without discretizing any design parameters such as the frequency and the two spectral parameters. Finally, the optimal solution for the 2-D polynomial coefficients can be easily determined through minimizing the closed-form error function. We also show that the resulting variable FIR filter can be efficiently implemented by generalizing Farrow structure to our two-parameter case. The generalized Farrow structure requires only a small number of multiplications and additions for obtaining any new frequency characteristic, which is particularly suitable for high-speed tuning.     

Design of high-order Chebyshev FIR filters in the complex domainunder magnitude constraints

This article discusses the design of FIR filters that approximate a complex-valued target frequency response in a Chebyshev sense. Additionally, the required stopband attenuation can be specified. Solving the dual of a semi-infinite linear program is currently the most efficient way to design such filters, but numerical problems prevent the design of high-order FIR filters. Modifications are proposed to overcome this limitation. Furthermore, an efficient method is presented for generating starting values that are close to the optimal solution such that the number of iterations is considerably reduced. Examples of filters with a length up to 250 taps are included     

2D-spectral estimation based on DCT and modified magnitude group delay

This paper proposes two new 2D-spectral estimation methods. The 2D-modified magnitude group delay (MMGD) is applied to 2D-discrete Fourier transform (2D-DFT) for the first and to the analytic 2D-discrete Cosine transform for the second. The analytic 2D-DCT preserves the desirable properties of the DCT (like, improved frequency resolution, leakage and detectability) and is realized by a 2D-discrete cosine transform (2D-DCT) and its Hilbert transform. The 2D-MMGD is an extension from 1D to 2D, and it reduces the variance preserving the original frequency resolution of 2D-DFT or 2D-analytic DCT, depending upon to which is applied. The first and the second methods are referred to as DFT-MMGD and DCT-MMGD, respectively. The proposed methods are applied to 2D sinusoids and 2D AR process, associated with Gaussian white noise. The performance of the DCT-MMGD is found to be superior to that of DFT-MMGD in terms of variance, frequency resolution and detectability. The performance of DFT-MMGD and DCT-MMGD is better than that of 2D-LP method even when the signal to noise ratio is low.     

General expression for the group delay of digital filters

An expression for the group delay of a digital filter is derived in terms of the numerator and denominator polynomials of the transfer function H(z). The application of this expression to three cases is shown, and an important theorem relating to the exact realisability of linear phase digital filters is given.     

A maximally flat group delay recursive digital filter with Chebyshev stopband attenuation

Due to the monotonically decaying nature of its magnitude response, an all-pole recursive digital filter, with its group delay approximating a prescribed constant value, does not exhibit a sharp transition band. Using transformation as the mathematical means, this correspondence describes a design technique for a recursive digital filter with a maximally flat group delay and a Chebyshev attenuation stopband.     

Lowpass to highpass transformation in vis switched-capacitor filters

A z-transformation for the design of highpass switched-capacitor filters is considered, which refers to a properly designed lowpass filter. The possible switched-capacitor implementation uses the voltage inverter switch approach with fully differential SC recharging devices: therefore, a bilinear design is obtained which introduces one zero at ? = 0.     

Broadband negative group delay networks for compensation ofmicrowave oscillators and filters

The design of distributed broadband negative group delay circuits operating from 3 to 6 GHz with negative group delays of around 50 ps are described. These circuits are designed using LCR prototypes which are then converted to printed transmission line structures. The parameters affecting the value and bandwidth of the group delay are discussed     

Lowpass minimum phase filter design using IFIR filters

A design procedure for minimum-phase FIR filters using an interpolated FIR (IFIR) filter is proposed. The IFIR technique allows two linear-phase filters of much lower order to be designed thereby making it easier to apply mipizing than is possible in high order FIR prototype filters. In this way, the problem of finding the roots of high order polynomials is overcome