Equiripple FIR Filters Research Articles

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.

Design of minimum error digital down-converter (DDC) for GSM mask requirements

In this paper we present a new design of 2 FIR filters for use on a digital down-converter (DDC) to be used to downconvert a GSM signal. The hardware to work with is a Graychip 4016 multi-standard quad DDC chip (Graychip, Inc2001). The design of FIR filters using windows methods leads to good performance filters, however, sometimes there is a need to design a FIR filter that does not only perform well but is optimal. Optimization is the ability to specify a maximum error on each band of interest. This error is expressed as the absolute difference between the ideal or desired frequency response and the actual or resulting frequency response. One of the techniques to design optimal FIR filters is to minimize a Chebyshev error criterion. The resulting filters are known as Equiripple FIR filters. In our design by this method, we get the maximum error in passband ripple of about (- 0.013dB) and compensate the adjacent band rejection and blocker requirements. Therefore we make the development on 3G base station more economical and effective. Key words: Wireless communications, FIR filter, digital down-converter.

Introduction to digital signal processing and filter design

Preface. 1. Introduction. 1.1 Introduction. 1.2 Application of DSP. 1.3 Discrete-Time Signals. 1.4 History of Filter Design. 1.5 Analog and Digital Signal Processing. 1.6 Summary. Problems. References. 2. Time-Domain Analysis and z Transform. 2.1 A Linear, Time-Invariant System. 2.2 z Transform Theory. 2.3 Using z Transform to Solve Difference Equations. 2.4 Solving Difference Equations Using the Classical Method. 2.5 z Transform Method Revisited. 2.6 Convolution Revisited. 2.7 A Model from Other Models. 2.8 Stability. 2.9 Solution Using MATLAB Functions. 2.10 Summary. Problems. References. 3. Frequency-Domain Analysis. 3.1 Introduction. 3.2 Theory of Sampling. 3.3 DTFT and IDTFT. 3.4 DTFT of Unit Step Sequence. 3.5 Use of MATLAB to Compute DTFT. 3.6 DTFS and DFT. 3.7 Fast Fourier Transform. 3.8 Use of MATLAB to Compute DFT and IDFT. 3.9 Summary/ Problems. References. 4. Infinite Impulse Response Filters. 4.1 Introduction. 4.2 Magnitude Approximation of Analog Filters. 4.3 Analog Frequency Transformations. 4.4 Digital Filters. 4.5 Impulse-Invariant Transformation. 4.6 Bilinear Transformation. 4.7 Digital Spectral Transformation. 4.8 Allpass Filters. 4.9 IIR Filter Design Using MATLAB. 4.10 Yule-Walker Approximation. 4.11 Summary. Problems. References. 5. Finite Impulse Response Filters. 5.1 Introduction. 5.2 Linear Phase Fir Filters. 5.3 Fourier Series Method Modified by Windows. 5.4 Design of Windowed FIR Filter Using MATLAB. 5.5 Equiripple Linear Phase FIR Filters. 5.6 Design of Equiripple FIR Filters Using MATLAB. 5.7 Frequency Sampling Method. 5.8 Summary. Problems. References. 6. Filter Realizations. 6.1 Introduction. 6.2 FIR Filter Realizations. 6.3 IIR Filter Realizations. 6.4 Allpass Filters in Parallel. 6.5 Realization of FIR and IIR Filters Using MATLAB. 6.6 Summary. Problems. References. 7. Quantized Filter Analysis. 7.1 Introduction. 7.2 Filter Design-Analysis Tool. 7.3 Quantized Filter Analysis. 7.4 Binary Numbers and Arithmetic. 7.5 Quantization Analysis of IIR Filters. 7.6 Quantization Analyis of FIR Filters. 7.7 Summary. Problems. References. 8. Hardware Design Using DSP Chips. 8.1 Introduction. 8.2 Simulink and Real-Time Workshop. 8.3 Design Preliminaries. 8.4 Code Generation. 8.5 Code Composer Studio. 8.6 Simulator and Emulator. 8.7 Conclusion. References. 9. MATLAB Primer. 9.1 Introduction. 9.2 Signal Processing Toolbox. References. Index.

Design of equiripple FIR filters with constraint using a multiple exchange algorithm

We propose a method of designing equiripple linear-phase FIR filters with linear constraint by using the Remez exchange algorithm. A novel technique is derived to convert a linearly constrained problem into an equivalent unconstrained one. We proposed a technique to modify the original desired frequency response so that the original linear constraint can be reduced to a simpler one (the null constraint) for the new target frequency response. The filter with null constraint can be designed without constraint by transformation of the original basis functions. The transformation is represented by a basis for the null space of the constraint. In this paper, we show that the transformed basis set also forms a Tchebycheff set. This fact indicates the proposed design is optimal in the Tchebycheff sense. The optimal filter is deigned by the Remez method according to the new target frequency response in transformed basis. Design examples suggest that the proposed algorithm converges fast and stably.

Design of equiripple FIR filters using a feedback neural network

The weighted least squares design of FIR filters is implemented in terms of a feedback neural network. The proposed neural network is shown to converge to the global minimum in each iteration for the current weighting function, and as the weighting function is adjusted from iteration to iteration, an equiripple design is achieved. The approach is applicable to FIR filters with piecewise-constant amplitude responses, as well as to digital differentiators and Hilbert transformers. The proposed configuration is amenable to analog very-large-scale integration and can, therefore, be used in real-time signal processing.

Design of equiripple FIR filters using a feedback neural network

The weighted least squares design of FIR filters is implemented in terms of a feedback neural network. The proposed neural network is shown to converge to the global minimum in each iteration for the current weighting function, and as the weighting function is adjusted from iteration to iteration, an equiripple design is achieved. The approach is applicable to FIR filters with piecewise-constant amplitude responses, as well as to digital differentiators and Hilbert transformers. The proposed configuration is amenable to analog very-large-scale integration and can, therefore, be used in real-time signal processing.

Perfect-reconstruction filter banks having linear-phase FIR filters with equiripple response

The design of equiripple linear-phase analysis and synthesis FIR filters of two-channel perfect-reconstruction (PR) filter banks is formulated as the minimization of a weighted peak-error under both linear inequality (arising from the desired responses of the analysis filters) and nonlinear equality (PR) constraints. The effectiveness of a proposed method to solve the design problem (a modified dual-affine scaling variant of Karmarkar's (1989) algorithm and an approximation scheme) is illustrated through several design examples.

A dynamic frequency grid allocation scheme for the efficient design of equiripple FIR filters

In the design of a digital filter, the frequency response is often optimized to meet a given set of specifications on a dense grid of frequency points. The density of the frequency grid points must be sufficiently high so that the frequency response of the filter does not violate the specifications at frequencies in between the grid points. However, the computational complexity of the design process and the storage requirements of the computer increase with the number of frequency grid points. We propose a novel dynamic: grid point allocation technique for the design of minimax optimum FIR filter. It uses a sparse frequency grid but will produce a design that is the same as one designed on very dense frequency grid points. It requires significantly less computer time and memory resources compared with fixed grid point algorithms.

Digital and Kalman filtering: an introduction to discrete-time filtering and optimum linear estimation

A concise introduction to digital filtering, filter design and applications in the form of Kalman and Wiener filters. Each subject is developed gradually with the help of worked examples. Covers both the theory of digital filters and their use in extracting information from noisy data. New to this edition: the graphic method for frequency response computations, FIR filter design by the frequency sampling technique, equiripple FIR filter design, circular convolution and an introduction to multirate digital filters.

An iteration scheme for the design of equiripple Mth-band FIR filters

A new iterative procedure for the design of approximate equiripple Mth-band FIR filters is presented. If the deviation from the Nyquist condition in the initial filter (obtained using standard methods) is small enough, then the error is reduced in the resultant filter, without significant change in the equiripple stop-band attenuation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Improved design of minimum-phase FIR digital filters by cepstrum and fast Hartley transform

An equiripple minimum-phase FIR filter is designed using the cepstrum and the fast Hartley transform (FHT). This fast procedure is performed entirely in the real domain and requires only two short-length FHT computations. This method avoids complicated phase wrapping and greatly reduces the aliasing error.

Design of minimum-phase FIR digital filter through cepstrum

A method to design an equiripple minimum-phase FIR filter using the cepstrum is described. This method avoids the complicated polynomial root-finding algorithm of Herrman and Schuessler (1970), or the phase-unwrapping algorithm associated with the complex cepstrum of Mian and Nainar (1982). The differential cepstrum method proposed by Pei and Lu (1986) has aliasing problems and requires the computation of three FFTs. The proposed method requires only two FFT computations and avoids the processing of phase.

Comments on "A fast procedure to design equiripple minimum-phase FIR filters"

It is shown that the approximation problem for minimum-phase FIR filters with arbitrary specifications on the attenuation can be solved by a method published in [3] although that method is based on the same idea of that developed in the above \footnote[1]{paper}, it is simpler and also easier to apply.

A fast procedure to design equiripple minimum-phase FIR filters

A fast procedure is given to design equiripple minimum-phase FIR filters following the technique proposed by Herrmann and Schuessler [1]: Use is made of cepstral deconvolution, carried out through FFT, to avoid the polynomial root-finding problem inherent in the method.