Tree-structured complementary filter banks using all-pass sections

Tree-structured complementary filter banks are developed with transfer functions that are simultaneously all-pass complementary and power complementary. Using a formulation based on unitary transforms and all-pass functions, we obtain analysis and synthesis filter banks which are related through a transposition operation, such that the cascade of analysis and synthesis filter banks achieves an all-pass function. The simplest structure is obtained using a Hadamard transform, which is shown to correspond to a binary tree structure. Tree structures can be generated for a variety of other unitary transforms as well. In addition, given a tree-structured filter bank where the number of bands is a power of two, simple methods are developed to generate complementary filter banks with an arbitrary number of channels, which retain the transpose relationship between analysis and synthesis banks, and allow for any combination of bandwidths. The structural properties of the filter banks are illustrated with design examples, and multirate applications are outlined

Optimal cosine modulated nonuniform linear phase FIR filter bank design via stretching and shifting frequency response of prototype filter

This paper proposes an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank design. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of the prototype filter. The total aliasing error of the filter bank is minimized subject to a specification on the maximum amplitude distortion of the filter bank as well as specifications on both the maximum passband ripple magnitude and the maximum stopband ripple magnitude of the prototype filter. This filter bank design problem is actually a functional inequality constrained optimization problem. Our recently developed integration approach is employed for solving the problem. Computer numerical simulation results show that our proposed design method outperforms existing design methods

Optimum nonuniform transmultiplexer design

This paper considers an optimum nonuniform FIR transmultiplexer design subject to specifications in the frequency domain. Our objective is to minimize the sum of the ripple energy for all the individual filters, subject to the specifications on amplitude and aliasing distortions, and to the passband and stopband specifications for the individual filters. This optimum nonuniform transmultiplexer design problem can be formulated as a quadratic semi-infinite programming problem. The dual parametrization algorithm is extended to the design of this nonuniform transmultiplexer problem. If the lengths of the filters are sufficiently long and the set of decimation integers is compatible, then our algorithm guarantees that the solution obtained will give rise to the global minimum, and the required specifications are satisfied

Application of multirate digital filter banks to wideband all-digital phase-locked loops design

A new class of architecture for all-digital phase-locked loops (DPLL's) is presented in this article. These architectures, referred to as parallel DPLL (PDPLL), employ multirate digital filter banks (DFB's) to track signals with a lower processing rate than the Nyquist rate, without reducing the input (Nyquist) bandwidth. The PDPLL basically trades complexity for hardware-processing speed by introducing parallel processing in the receiver. It is demonstrated here that the DPLL performance is identical to that of a PDPLL for both steady-state and transient behavior. A test signal with a time-varying Doppler characteristic is used to compare the performance of both the DPLL and the PDPLL

Optimal design of nonuniform FIR transmultiplexer using semi-infinite programming

This paper considers an optimum nonuniform FIR transmultiplexer design problem subject to specifications in the frequency domain. Our objective is to minimize the sum of the ripple energy for all the individual filters, subject to the specifications on amplitude and aliasing distortions, and to the passband and stopband specifications for the individual filters. This optimum nonuniform transmultiplexer design problem can be formulated as a quadratic semi-infinite programming problem. The dual parametrization algorithm is extended to this nonuniform transmultiplexer design problem. If the lengths of the filters are sufficiently long and the set of decimation integers is compatible, then a solution exists. Since the problem is formulated as a convex problem, if a solution exists, then the solution obtained is unique and the local solution is a global minimum

Design of nonuniform near allpass complementary FIR filters via a semi-infinite programming technique

In this paper, we consider the problem of designing a set of nonuniform near allpass complementary FIR filters. This problem can be formulated as a quadratic semi-infinite programming problem, where the objective is to minimize the sum of the ripple energy for the individual filters, subject to the passband and stopband specifications as well as to the allpass complementary specification. The dual parameterization method is used for solving the linear quadratic semi-infinite programming problem

Efficient TV white space filter bank transceiver

Future devices operating in the TV white space (TVWS) spectrum will require to access different bands at different locations and times in order to avoid interference to incumbent users, requiring agility and sufficient spectral masks to satisfy regulators. Further, with very high-speed ADCs and DACs becoming reality, the purpose of this paper is to present a transceiver front-end capable of simultaneously up- and downconverting a significant portion of the UHF band. The proposed approach takes a two-stage filter-bank conversion for implementation on state-of-the-art FPGAs. We present three different parameterisations, which are compatible with the 40 TVWS channels between 470 and 790MHz in Europe, and compare them in terms of complexity and latency

Generalizations of the sampling theorem: Seven decades after Nyquist

The sampling theorem is one of the most basic and fascinating topics in engineering sciences. The most well-known form is Shannon's uniform-sampling theorem for bandlimited signals. Extensions of this to bandpass signals and multiband signals, and to nonuniform sampling are also well-known. The connection between such extensions and the theory of filter banks in DSP has been well established. This paper presents some of the less known aspects of sampling, with special emphasis on non bandlimited signals, pointwise stability of reconstruction, and reconstruction from nonuniform samples. Applications in multiresolution computation and in digital spline interpolation are also reviewed

A Binaural Neuromorphic Auditory Sensor for FPGA: A Spike Signal Processing Approach

This paper presents a new architecture, design flow, and field-programmable gate array (FPGA) implementation analysis of a neuromorphic binaural auditory sensor, designed completely in the spike domain. Unlike digital cochleae that decompose audio signals using classical digital signal processing techniques, the model presented in this paper processes information directly encoded as spikes using pulse frequency modulation and provides a set of frequency-decomposed audio information using an address-event representation interface. In this case, a systematic approach to design led to a generic process for building, tuning, and implementing audio frequency decomposers with different features, facilitating synthesis with custom features. This allows researchers to implement their own parameterized neuromorphic auditory systems in a low-cost FPGA in order to study the audio processing and learning activity that takes place in the brain. In this paper, we present a 64-channel binaural neuromorphic auditory system implemented in a Virtex-5 FPGA using a commercial development board. The system was excited with a diverse set of audio signals in order to analyze its response and characterize its features. The neuromorphic auditory system response times and frequencies are reported. The experimental results of the proposed system implementation with 64-channel stereo are: a frequency range between 9.6 Hz and 14.6 kHz (adjustable), a maximum output event rate of 2.19 Mevents/s, a power consumption of 29.7 mW, the slices requirements of 11 141, and a system clock frequency of 27 MHz.Ministerio de Economía y Competitividad TEC2012-37868-C04-02Junta de Andalucía P12-TIC-130