A Compact Digital Gamma-tone Filter Processor

Area consumption is one of the most important design constrains in the development of compact digital systems. Several authors have proposed making compact Cochlear Implant processors using Gamma-tone filter banks. These model aspects of the cochlea spectral filtering. A good area-efficient design of the Gamma-tone Filter Bank could reduce the amount of circuitry allowing patients to wear these cochlear implants more easily. In consequence, many authors have reduced the area by using the minimum number of registers when implementing this type of filter. However, critical paths limit their performance. Here a compact Gamma-tone Filter processor, formulated using the impulse invariant transformation together with a normalization method, is presented. The normalization method in the model guarantees the same precision for any filter order. In addition, area resources are kept low due to the implementation of a single Second Order Section (SOS) IIR stage for processing several SOS IIR stages and several channels at different times. Results show that the combination of the properties of the model and the implementation techniques generate a processor with high processing speed, expending less resources than reported in the literature.Collaboration with Sanchez-Rivera, related to, but not funded by, EPSRC grant EP/G062609/

Use of frequency response masking technique in designing A/D converter for SDR.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2005.Analog-to-digital converters (ADCs) are required in almost all signal processing and communication systems. They are often the most critical components, since they tend to determine the overall system performance. Hence, it is important to determine their performance limitations and develop improved realizations. One of the most challenging tasks for realizing software defined radio (SDR) is to move ND conversion as close to the antenna as possible, this implies that the ADC has to sample the incoming signal with a very high sample rate (over 100 MSample/s) and with a very high resolution (14 -to -16 bits). To design and implement AID converters with such high performance, it is necessary to investigate new designing techniques. The focus in this work is on a particular type of potentially high-performance (high-resolution and highspeed) analog-to-digital conversion technique, utilizing filter banks, where two or more ADCs are used in the converter array in parallel together with asymmetric filter banks. The hybrid filter bank analog-todigital converter (HFB ADC) utilizes analog filters (analysis filters) to allocate a frequency band to each ADC in a converter array and digital synthesis filters to reconstruct the digitized signal. The HFB improves the speed and resolution of the conversion, in comparison to the standard time-interleaving technique by attenuating the effect of gain and phase mismatches between the ADCs. Many of the designs available in the literature are compromising between some metrics: design complexity, order of the filter bank (computation time) and the sharpness of the frequency response rolloff (the transition from the pass band to the stop band). In this dissertation, five different classes of near perfect magnitude reconstruction (NPMR) continuoustime hybrid filter banks (CT HFBs) are proposed. In each of the five cases, two filter banks are designed; analysis filter bank and synthesis filter bank. Since the systems are hybrid, continuous time IlR filter are used to implement the analysis filter bank and digital filters are used for the synthesis filter bank. To optimize the system, we used a new technique, known in the literature as frequency response masking (FRM), to design the synthesis filter bank. In this technique, the sharp roll-off characteristics can be achieved while keeping the complexity of the filter within practical range, this is done by splitting the filter into two filters in cascade; model filter with relaxed roll-off characteristics followed by a masking filter. One of the main factors controlling the overall complexity of the filter is the way of designing the model filter and that of designing the masking filter. The dissertation proposes three combinations: use of HR model filter and IlR masking filter, HR model filter/FIR masking filter and FIR model filter/FIR masking filter. To show the advantages of our designs, we considered the cases of designing the synthesis filter as one filter, either FIR or IlR. These two filters are used as base for comparison with our proposed designs (the use of masking response filter). The results showed the following: 1. Asymmetric hybrid filter banks alone are not sufficient for filters with sharp frequency response roll-off especially for HR/FIR class. 2. All classes that utilize FRM in their synthesis filter banks gave a good performance in general in comparison to conventional classes, such as the reduction of the order of filters 3. HR/HR FRM gave better performance than HR/FIR FRM. 4. Comparing HR/HR FRM using FIR masking filters and HR/IIR FRM using IIR masking filters, the latter gave better performance (the performance is generally measured in terms of reduced filter order). 5. All classes that use the FRM approach have a very low complexity, in terms of reduced filter order. Our target was to design a system with the following overall characteristics: pass band ripple of -0.01 dB, stop band minimum attenuation of - 40 dB and of response roll-off of 0.002. Our calculations showed that the order of the conventional IIR/FIR filter that achieves such characteristics is aboutN =2000. Using the FRM technique, the order N reduced to aboutN = 244, N = 179 for IIRJFIR and IIR/IIR classes, respectively. This shows that the technique is very effective in reducing the filter complexity. 6. The magnitude distortion and the aliasing noise are calculated for each design proposal and compared with the theoretical values. The comparisons show that all our proposals result in approximately perfect magnitude reconstruction (NPMR). In conclusion, our proposal of using frequency-response masking technique to design the synthesis filter bank can, to large extent, reduce the complexity of the system. The design of the system as a whole is simplified by designing the synthesis filter bank separately from the design of the analysis filter bank. In this case each bank is optimized separately. This implies that for SDR applications we are proposing the use of the continuous-time HFB ADC (CT HFB ADC) structure utilizing FRM for digital filters

A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters

Passive cascaded-lattice structures for low-sensitivity FIR filter design, with applications to filter banks

A class of nonrecursive cascaded-lattice structures is derived, for the implementation of finite-impulse response (FIR) digital filters. The building blocks are lossless and the transfer function can be implemented as a sequence of planar rotations. The structures can be used for the synthesis of any scalar FIR transfer function H(z) with no restriction on the location of zeros; at the same time, all the lattice coefficients have magnitude bounded above by unity. The structures have excellent passband sensitivity because of inherent passivity, and are automatically internally scaled, in an L_2 sense. The ideas are also extended for the realization of a bank of MFIR transfer functions as a cascaded lattice. Applications of these structures in subband coding and in multirate signal processing are outlined. Numerical design examples are included

Optimum low cost two channel IIR orthonormal filter bank

In this paper, we statistically optimize a well known class of IIR two channel orthonormal filter banks parameterized by a single coefficient when subband quantizers are present. The optimization procedure is extremely simple and very fast compared for example to the linear programming method used in the FIR case to achieve similar compaction (coding) gains. The special form of the filters assure the existence of a zero at π which can be important for some wavelet applications and eliminate some of the major concerns that arise in the FIR design case. Finally, the compaction gain obtained is high and numerically very close to two (ideal case) for low pass spectra, high pass spectra and certain cases of multiband spectra. For these cases, the use of higher order IIR filters does not increase the compaction (coding) gain

Implementation of a Two-Channel Maximally Decimated Filter Bank using Switched Capacitor Circuits

The aim of this paper is to describe the implementation of a two-channel filter bank (FB) using the switched capacitor (SC) technique considering real properties of operational amplifiers (OpAmps). The design procedure is presented and key recommendations for the implementation are given. The implementation procedure describes the design of two-channel filter bank using an IIR Cauer filter, conversion of IIR into the SC filters and the final implementation of the SC filters. The whole design and an SC circuit implementation is performed by a PraCAn package in Maple. To verify the whole filter bank, resulting real property circuit structures are completely simulated by WinSpice and ELDO simulators. The results confirm that perfect reconstruction conditions can be almost accepted for the filter bank implemented by the SC circuits. The phase response of the SC filter bank is not strictly linear due to the IIR filters. However, the final ripple of a magnitude frequency response in the passband is almost constant, app. 0.5 dB for a real circuit analysis

Chromatic Dispersion Compensation Using Filter Bank Based Complex-Valued All-Pass Filter

A long-haul transmission of 100 Gb/s without optical chromatic-dispersion (CD) compensation provides a range of benefits regarding cost effectiveness, power budget, and nonlinearity tolerance. The channel memory is largely dominated by CD in this case with an intersymbol-interference spread of more than 100 symbol durations. In this paper, we propose CD equalization technique based on nonmaximally decimated discrete Fourier transform (NMDFT) filter bank (FB) with non-trivial prototype filter and complex-valued infinite impulse response (IIR) all-pass filter per sub-band. The design of the sub-band IIR all-pass filter is based on minimizing the mean square error (MSE) in group delay and phase cost functions in an optimization framework. Necessary conditions are derived and incorporated in a multi-step and multi-band optimization framework to ensure the stability of the resulting IIR filter. It is shown that the complexity of the proposed method grows logarithmically with the channel memory, therefore, larger CD values can be tolerated with our approach

Design of doubly-complementary IIR digital filters using a single complex allpass filter, with multirate applications

It is shown that a large class of real-coefficient doubly-complementary IIR transfer function pairs can be implemented by means of a single complex allpass filter. For a real input sequence, the real part of the output sequence corresponds to the output of one of the transfer functions G(z) (for example, lowpass), whereas the imaginary part of the output sequence corresponds to its "complementary" filter H(z)(for example, highpass). The resulting implementation is structurally lossless, and hence the implementations of G(z) and H(z) have very low passband sensitivity. Numerical design examples are included, and a typical numerical example shows that the new implementation with 4 bits per multiplier is considerably better than a direct form implementation with 9 bits per multiplier. Multirate filter bank applications (quadrature mirror filtering) are outlined

Summed Parallel Infinite Impulse Response (SPIIR) Filters For Low-Latency Gravitational Wave Detection

With the upgrade of current gravitational wave detectors, the first detection of gravitational wave signals is expected to occur in the next decade. Low-latency gravitational wave triggers will be necessary to make fast follow-up electromagnetic observations of events related to their source, e.g., prompt optical emission associated with short gamma-ray bursts. In this paper we present a new time-domain low-latency algorithm for identifying the presence of gravitational waves produced by compact binary coalescence events in noisy detector data. Our method calculates the signal to noise ratio from the summation of a bank of parallel infinite impulse response (IIR) filters. We show that our summed parallel infinite impulse response (SPIIR) method can retrieve the signal to noise ratio to greater than 99% of that produced from the optimal matched filter. We emphasise the benefits of the SPIIR method for advanced detectors, which will require larger template banks.Comment: 9 pages, 6 figures, for PR

Theory and design of uniform DFT, parallel, quadrature mirror filter banks

In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signalx(n), are also derived using this concept. In general, the reconstructed. signalhat{x}(n)suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, andhat{x}(n)is equal to a delayed version ofx(n))of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general, once aliasing is canceled, the other distortions can be minimized rather than completely eliminated. Algorithms for this are presented. The properties of FIR filter banks are then investigated. Several aspects of IIR filter banks are also studied using the same framework