A fractional delay filter is a device for bandlimited interpolation between samples. It finds applications in numerous fields of signal processing, including communications, array processing, speech processing, and music technology. We present a comprehensive review of FIR and allpass filter design techniques for bandlimited approximation of a fractional digital delay. Emphasis is on simple and efficient methods that are well suited for fast coefficient update or continuous control of the delay value. Various new approaches are proposed and several examples are provided to illustrate the performance of the methods. We also discuss the implementation complexity of the algorithms. We focus on four applications where fractional delay filters are needed: synchronization of digital modems, incommensurate sampling rate conversion, high-resolution pitch prediction, and sound synthesis of musical instruments.

Splitting the unit delay [FIR/all pass filters design]

Digital calibration using adaptive signal processing corrects for offset mismatch, gain mismatch, and sample-time error between time-interleaved channels in a 10-b 120-Msample/s pipelined analog-to-digital converter (ADC). Offset mismatch between channels is overcome with a random chopper-based offset calibration. Gain mismatch and sample-time error are overcome with correlation-based algorithms, which drive the correlation between a signal and its chopped image or its chopped and delayed image to zero. Test results show that, with a 0.99-MHz sinusoidal input, the ADC achieves a peak signal-to-noise-and-distortion ratio (SNDR) of 56.8 dB, a peak integral nonlinearity of 0.88 least significant bit (LSB), and a peak differential nonlinearity of 0.44 LSB. For a 39.9-MHz sinusoidal input, the ADC achieves a peak SNDR of 50.2 dB. The active area is 5.2 mm/sup 2/, and the power dissipation is 234 mW from a 3.3-V supply.

A 10b 120MSample/s time-interleaved analog-to-digital converter with digital background calibration

This paper puts forth the notion that explicitly specified transition bands have been introduced in the filter design literature in part as an indirect approach for dealing with discontinuities in the desired frequency response. We suggest that the use of explicitly specified transition bands is sometimes inappropriate because to satisfy a meaningful optimality criterion, their use implicitly assumes a possibly unrealistic assumption on the class of input signals. This paper also presents an algorithm for the design of peak constrained lowpass FIR filters according to an integral square error criterion that does not require the use of specified transition bands. This rapidly converging, robust, simple multiple exchange algorithm uses Lagrange multipliers and the Kuhn-Tucker conditions on each iteration. The algorithm will design linear- and minimum-phase FIR filters and gives the best L/sub 2/ filter and a continuum of Chebyshev filters as special cases. It is distinct from many other filter design methods because it does not exclude from the integral square error a region around the cut-off frequency, and yet, it overcomes the Gibbs' phenomenon without resorting to windowing or 'smoothing out' the discontinuity of the ideal lowpass filter.

Constrained least square design of FIR filters without specified transition bands

Master the basic concepts and methodologies of digital signal processing with this systematic introduction, without the need for an extensive mathematical background The authors lead the reader through the fundamental mathematical principles underlying the operation of key signal processing techniques, providing simple arguments and cases rather than detailed general proofs Coverage of practical implementation, discussion of the limitations of particular methods and plentiful MATLAB illustrations allow readers to better connect theory and practice A focus on algorithms that are of theoretical importance or useful in real-world applications ensures that students cover material relevant to engineering practice, and equips students and practitioners alike with the basic principles necessary to apply DSP techniques to a variety of applications Chapters include worked examples, problems and computer experiments, helping students to absorb the material they have just read Lecture slides for all figures and solutions to the numerous problems are available to instructors

Applied Digital Signal Processing: Theory and Practice

An 11-bit 160-MS/s four-channel time-interleaved double-sampled pipelined ADC implemented in a 0.35-μm CMOS process is described. Digital calibration is used to correct mismatch errors between channels as well as the memory errors that arise from the use of double sampling. The signal-to-noise-and-distortion ratio is improved from 45 to 62 dB after calibration with an 8.7-MHz input. The spurious-free dynamic range is increased from 47 dB to 79 dB.

A Four-Channel Time-Interleaved ADC With Digital Calibration of Interchannel Timing and Memory Errors

The authors propose the use of transition bands and transition functions in the ideal amplitude frequency response to allow the analytical design of optimal least-squared-error FIR digital filters with an explicit control of the transition band edges. Design formulas are derived for approximations to ideal frequency responses which use pth-order spline transition functions. A mixed analytical and numerical method for zero-error weight in the transition bands and passband and stopband error weighting functions with an integral squared error approximation are derived. A variable-order spline transition function is developed, and a method for choosing the optimal order to minimize the integral squared approximation error is given. >

Least squared error FIR filter design with transition bands

The authors propose the use of transition bands and transition functions in the ideal amplitude frequency response of a linear finite impulse response phase (FIR) digital filter to allow the analytical design of optimal least integral squared error filters with an explicit control of the transition band edges. Design formulas for approximations to ideal frequency responses which use a pth-order spline transition function are derived and analyzed. A variable-order spline is used with a method for optimally choosing the order. The results of this method are compared with those of other optimal methods. >

A.W. Soewito

Papers

Least squared error FIR filter design with transition bands

Least squared error FIR filter design with spline transition functions