Equiripple Passband Research Articles

Recursive digital filters with optimum equiripple passband magnitude characteristic

The paper investigates, for the first time, the design of recursive digital filters that exhibit optimum equiripple passband magnitude characteristics. After a brief description of the optimum equiripple filters in the analog domain, digital optimum C (Chebyshev) tan and sine filters are derived directly in the digital domain through the minimization of the area under the passband characteristic function. The influence of the truncated coefficients is also considered and its effects are demonstrated through an example proving the robustness of the magnitude function. Furthermore, a design procedure is proposed for the optimum C tan half-band filter. To highlight the effectiveness of the proposed approximation, a comparative analysis is conducted with the staircase digital filter, as both filters optimize passband responses by minimizing the area under the characteristic function. The results of comparison demonstrate that the optimum equiripple approximation surpasses the staircase approximation, not only in the analog but also in the digital domain.

An improved design method for even-degree optimum allpole filters with equiripple passband responses

The maximum power transfer between source and load is extremely important in analog signal processing. The main disadvantage of signal processing using the even-degree Chebyshev filter is the impossibility of LC ladder network realization between two equal resistors. Therefore, either the utilization of the ideal transformer or the Chebyshev filter of odd-degree is required to achieve the maximum power transfer. To overcome this limitation, the class of even-degree polynomials with the equiripple behavior, referred to as scaled modified Chebyshev polynomials, can be used as the filter’s characteristic function. Passband ripples of obtained filters can be controlled through an embedded parameter, while normalized half-power frequency is kept equal to unity. Furthermore, these filters can be optimized for the minimum amount of reflected power at the input terminals. In this paper, the optimum modified Chebyshev filters are first compared to the classic Chebyshev filters to show that both filters exhibit similar performances. Second, proposed filters are compared to the Least Square Monotonic (LSM) filters that are optimized by minimizing the area under the characteristic function in the passband. Results of comparison reveal that the proposed even-degree scaled modified Chebyshev filters outperform the LSM filters, as is already proved for the odd-degree filters.

RF Channel-Select Micromechanical Disk Filters-Part II: Demonstration.

This Part II of a two-paper sequence presents fabrication and measurement results for a micromechanical disk-based RF channel-select filter designed using the theory and procedure of Part I. Successful demonstration of an actual filter required several practical additions to an ideal design, including the introduction of a 39-nm-gap capacitive transducer, voltage-controlled frequency tuning electrodes, and a stress relieving coupled array design, all of which combine to enable a 0.1% bandwidth 223.4-MHz channel-select filter with only 2.7 dB of in-band insertion loss and 50-dB rejection of out-of-band interferers. This amount of rejection is more than 23 dB better than a previous capacitive-gap transduced filter design that did not benefit from sub-50-nm gaps. It also comes in tandem with a 20-dB shape factor of 2.7 realized by a hierarchical mechanical circuit design utilizing 206 micromechanical circuit elements, all contained in an area footprint of only [Formula: see text]. The key to such low insertion loss for this tiny percent bandwidth is Q 's >8800 supplied by polysilicon disk resonators employing for the first time capacitive transducer gaps small enough to generate coupling strengths of Cx/Co ∼ 0.1 %, which is a 6.1× improvement over previous efforts. The filter structure utilizes electrical tuning to correct frequency mismatches due to process variations, where a dc tuning voltage of 12.1 V improves the filter insertion loss by 1.8 dB and yields the desired equiripple passband shape. Measured filter performance, both in- and out-of-channel, compares well with predictions of an electrical equivalent circuit that captures not only the ideal filter response, but also parasitic nonidealities that distort somewhat the filter response.

Design of Least-Squares and Minimax Composite Filters

We study a class of composite FIR filters (C-filters), each is composed of a prototype filter and a shaping filter in cascade, where the shaping filter is constructed by cascading several complementary comb filters. In particular, the problems of designing C-filters that are optimal in least-squares, equiripple passband and lease-squares stopband, and minimax sense are formulated, and three algorithms for designing such linear-phase FIR C-filters are proposed. The algorithms are based on an alternating optimization strategy in that the prototype and shaping filters are optimized in separate steps, which are coupled and carried out in a sequential manner to yield a satisfactory design. Design examples are presented to illustrate the algorithms and demonstrate the performance of the C-filters relative to their conventional FIR counterparts.

Design and Comparison of Equiripple Bandpass Filter for Wireless Applications at Varying Bandwidths

Design and Comparison of Equiripple Bandpass Filter for Wireless Applications at Varying Bandwidths

Performance Analysis of Non-uniform Filter Bank with Equi ripple Band pass Filter

In this paper we present a non-uniform filter bank (NUFB) matched to a given signal. To obtain matched M- channel NUFB, first, we choose the decimation set having M-down sampling/decimation factors for which perfect reconstruction NUFB exist and then using novel approach proposed in this paper, M-channel signal matched analysis bank is estimated. The outputs of all filters at the analysis side of proposed filter bank are mutually as well as across various channels are uncorrelated. By using well established theory of multirate filter bank, M-channel NUFB matched to signal is obtained. The equiripple band pass filter will provide better tradeoff compared to previous non uniform Filter bank obtained in this fashion will be useful to compress code or represent the signal or image in the best possible manner.

A Simulation Study of FIR Anti-Aliasing Filters

This paper brief describes FIR anti-aliasing filters with equiripple pass bands and stop bands. We designed equiripple linear-phase FIR filters with one stage, two stages and three stages. The simulation results of the proposed design scheme are very encouraging as far as robustness and computational complexity are concerned

Research of Chebyshev Equivalent Ripple Approximation Filter Based on DSP

Abstract: Researched Chebyshev equiripple approximation FIR filter theory. In the algorithm process, we adopt direct remez algorithm, by a recursive formula to calculate the filter coefficients directly. Combined TMS320VC5502, we designed software and hardware system of Chebyshev equiripple band-pass filter to realize the voice signal filtering. In hardware system TLC320AC01 complete A/D and D/A converter, TMS320VC5502 complete data processing and filtering.

A De-Noising Algorithm for ECG Signals Based on FIR Filter and Wavelet Transform

This paper adopts a synthesis algorithm which combines FIR filters and wavelet threshold de-noising method to complete ECG de-noising. Firstly, we designed a FIR equiripple bandpass filter using Matlab FDATool to remove baseline drift, power interference and the high frequency part of muscle moments. Then we adopted an improved wavelet threshold de-noising algorithm to remove the remaining muscle moments with less decomposing levels. The algorithm was implemented on Matlab platform. The experimental results show that the algorithm is simple in design and has less calculation and good de-noising effect, which is superior to conventional wavelet threshold de-noising algorithm, and can be used in clinical analysis.

Realization of reduced-delay finite impulse response filters for audio applications

This article aims to present a development of reduced-delay finite impulse response digital filters with amplitude requirements using equiripple passband, peak constrained least squares stopbands, ...

An Analytical Approach for Design of Nth-band FIR Digital Filters with Equi-Ripple Passband

In FIR (Finite Impulse Response) filter applications, Nth-band FIR digital filters are known to be important due to their reduced computational requirements. The conventional methods for de- signing FIR filters use iterative approaches such as the well-known Parks-McClellan algorithm. The Parks-McClellan algorithm is also used to design Nth-band FIR digital filters after Mintzer's research. However, a disadvantage of the Parks-McClellan algorithm is that it needs a large amount of design time. This paper describes a direct design method for Nth-band FIR Filters using Chebyshev polyno- mials, which provides a reduced design time over indirect methods such as the Parks-McClellan algo- rithm. The response of the resulting filter is equi-ripple in passband. Our proposed method produces a passband response that is equi-ripple to within a minuscule error, comparable to that of Mintzer's de- sign method which uses the Parks-McClellan algorithm.

Realization of reduced-delay finite impulse response filters for audio applications

This article aims to present a development of reduced-delay finite impulse response digital filters with amplitude requirements using equiripple passband, peak constrained least squares stopbands, and nearly constant group delay in passband for real-time applications. The filter length, passband and stopband frequencies, ripples, and attenuation are specified for realizations. The obtained results of realized filters have group delays with a reduction of about 12–22% in passband compared to the existing linear phase finite impulse response filters for audio applications.

Design of a low-pass filter by multi-scale even order Gaussian derivatives

In this paper, a new low-pass FIR filter design technique for achieving variable stopband attenuation without altering the passband and stopband edges, is proposed. The filter function is a linear combination of multi-scale Gaussian derivatives. In the frequency domain, the spectral modes corresponding to the continuous Gaussian derivatives have monotonic tails. In discrete domain, this amounts to variable stopband attenuation which depends upon the truncation length of the continuous kernel, the ‘scale’ and the order of Gaussian derivatives. The proposed algorithm consists of derivation of some useful mathematical relations between the basic design parameters and the parameters of the Gaussian derivatives and an optimization technique that finally produces an equiripple passband lowpass FIR filter with a higher falloff rate at the beginning of the transition band. Such a filter with variable stopband attenuation may be effective at the time of reconstruction of the desired passband signal in a Σ– Δ modulator output.

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.

A CMOS gyrator low-IF filter for a dual-mode Bluetooth/ZigBee transceiver

A low-IF polyphase channel filter for a dual-mode Bluetooth/Zigbee transceiver is described. Implemented in a standard 0.18-/spl mu/m CMOS process, the filter has a fifth-order 0.5-dB equiripple bandpass response and employs novel transconductor and preamplifier designs. It consumes /spl les/1 mW and achieves image band rejection /spl ges/44 dB, input referred noise of /spl les/52.2 /spl mu/Vrms and input referred third-order intermodulation intercept of /spl ges/20 dBVp, which gives a spurious-free dynamic range of /spl ges/68.4 dB. Chip area including its tuning circuit is 0.23 mm/sup 2/.

Approximation of complex IIR bandpass filters without arithmetic symmetry

Complex transfer functions are not restricted to having complex-conjugate symmetry in the frequency-domain, as is the case for real filters. This gives them more flexibility when they are used in communication systems with complex signals, such as intermediate frequency signals of wireless communication systems. This paper describes a set of algorithms and procedures that can be used in solving the approximation problem involved in deriving complex infinite-impulse-response bandpass transfer functions directly, without the requirement of first designing a real-transfer-function prototype filter, which is then frequency translated. Because the requirement for a real prototype filter is eliminated, the filters need not have arithmetic symmetry; this results in superior stopbands with smaller filter orders. The procedures can be used for both continuous and discrete-time filters, can allow for arbitrary stopband specifications, and can be used for either equi-ripple or monotonic passbands.

A Note on Approximate Synthesis of a Passive Complex Filter Including No Transformers

An approximate complex filter including no transformers is proposed. The proposed filter does not have the equiripple passband response. However, the narrower the passband width of the prototype filter, the smaller the deviation of the proposed filter from the prototype filter is. A third-order complex filter is designed.

Design of IIR digital filters with flat passband and equiripple stopband responses

AbstractIn the design of IIR digital filters, the method that utilizes the classic analog filter design theory to design analog filters and then obtain the corresponding digital filters by s–z transformation is well‐known. However, IIR digital filters obtained via the bilinear s–z transformation have just equal‐order numerator and denominator. Having unequal‐order numerator and denominator will give more degrees of freedom in filter design. In this paper, we consider the design of IIR digital filters with unequal‐order numerator and denominator, and propose a method for designing the flat passband and equiripple stopband filters in z‐domain directly. First, we present a design method of IIR filters with flat stopband and equiripple passband responses. The flat stopband response can be easily obtained only by locating multiple zeros on the specified frequency points, while the equiripple passband response can be designed by using the Remez exchange algorithm and specifying the maximum magnitude error. Second, we can obtain IIR filters with flat passband and equiripple stopband responses via a magnitude transformation such that the passband and stopband become the corresponding stopband and passband, respectively. However, the numerator order of IIR filters obtained by the above method is equal to or higher than the denominator. Finally, we consider the design of IIR filters that have lower‐order numerator than denominator, and present a method for designing the flat passband and equiripple stopband filters directly. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(11): 37–44, 2001

On the design of two channel perfect construction QMF filters

This paper presents two rapidly convergent methods for the design of two-channel odd degree linear phase FIR banks as well as IIR filter banks. In both cases, zeros of arbitrary multiplicity are assumed at z = −1, to ensure regularity of the generated wavelet basis. It is shown that in the FIR case, the problem reduces to the solution of an eigenvalue problem. A simple minimization method is proposed for its solution to reduce most of the computational complexities of eigenvalue evaluations. In the IIR case, a simple rapidly convergent algorithm is also described for the determination of a perfect as well as pseudo-perfect reconstruction stable IIR function having equiripple pass and stop band responses and with almost constant group delay. It is also shown that the analysis and synthesis banks are of same complexities, and as a result of being expressed as sum of two all-pass functions, they are realized in a lattice form. Therefore, they are immune from quantization effects. Illustrative examples are also given. Copyright © 2000 John Wiley & Sons, Ltd.

Single-passband single-stopband narrow-band filters

Techniques are presented for obtaining an optimum filter response for narrow-band requirements of a single passband and a single stopband. For certain transformed equiripple passband responses, including Chebyshev and elliptic function responses and a new "double n/2 poles" response, the minimum number of resonators can be easily determined, resulting in reduced size and weight relative to more conventional frequency-symmetric bandpass or bandstop filters.