Computationally efficient FIR digital filters

Ph.DDOCTOR OF PHILOSOPH

High-speed fir filter design and optimization using artificial intelligence techniques

Ph.DDOCTOR OF PHILOSOPH

FRM-Based FIR filters with minimum coefficient sensitivities

A method for optimizing FRM-based FIR filters with optimum coefficient sensitivity is presented. This technique can be used in conjunction with nonlinear optimization techniques to design very sharp filters that do not only have very sparse coefficient values but also very low coefficient sensitivity

Design of Computationally Efficient Digital FIR Filters and Filter Banks

Ph.DDOCTOR OF PHILOSOPH

Design and implementation of computationally efficient digital filters

Ph.DDOCTOR OF PHILOSOPH

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

Photonic and Phononic Band Gap Engineering for Circuit Quantum Electrodynamics and Quantum Transduction

The ability to pattern materials at the wavelength and sub-wavelength scale has led to the concept of photonic crystals and metamaterials - artificially engineered structures that exhibit electromagnetic properties not found in conventional materials. Such engineered structures offer the ability to slow down and even inhibit the propagation of electromagnetic waves giving rise to a photonic band gap and a sharply varying photonic density of states. Quantum emitters in the presence of an electromagnetic reservoir with varying density of states can undergo a rich set of dynamical behavior. In particular, the reservoir can be tailored to have a memory of past interactions with emitters, in contrast to memory-less Markovian dynamics of typical open systems. In part 1 of this thesis, we investigate the non-Markovian dynamics of a superconducting qubit strongly coupled to a superconducting metamaterial waveguide engineered to have both a sharp spectral variation in its transmission properties and a slowing of light by a factor of 650. Tuning the qubit into the spectral vicinity of the passband of this slow-light waveguide reservoir, we observe a 400-fold change in the emission rate of the qubit, along with oscillatory energy relaxation of the qubit resulting from the beating of bound and radiative dressed qubit-photon states. Further, upon addition of a reflective boundary to one end of the waveguide, we observe revivals in the qubit population on a timescale 30 times longer than the inverse of the qubit’s emission rate, corresponding to the round-trip travel time of an emitted photon. With this superconducting circuit platform, future studies of multi-qubit interactions via highly structured reservoirs and the generation of multi-photon highly entangled states are possible. While microwave frequency superconducting circuits are near ideal testbeds for quantum electrodynamics experiments of the type discussed in part 1, microwave photons are not well suited for transmission of quantum information over long distances due to the presence of a large thermal background at room temperature. Optical photons are ideal for quantum communication applications due to their low propagation loss at room temperature. Coherent transduction of single photons from the microwave to the optical domain has the potential to play a key role in quantum networking and distributed quantum computing. In part 2 of this thesis, we extend the notion of band gap engineering to the optical and acoustic domain and present the design of a piezo-optomechanical quantum transducer where transduction is mediated by a strongly hybridized acoustic mode of a lithium niobate piezoacoustic cavity attached to a silicon optomechanical crystal patterned on a silicon-on-insulator substrate. We estimate an intrinsic transduction efficiency of 29% with &lt;0.5 added noise quanta when our transducer is resonantly coupled to a superconducting transmon qubit and operated in pulsed mode. Our design involves on-chip integration of a superconducting qubit with the piezo-optomechanical transducer. Absorption of stray photons from the optical pump used in the transduction process is known to cause excess decoherence and noise in the superconducting circuit. The recovery time of the superconducting circuit after the optical pulse sets a limit on the transducer repetition rate. We fabricate niobium based superconducting circuits on a silicon substrate and test their response to illumination by a 1550 nm laser. We find a recovery time of ~ 10 μs, indicating that a repetition rate of 10 kHz should be possible. Combined with the expected efficiency and noise metrics of our design, we expect that a transducer in this parameter regime would be suitable to realize probabilistic schemes for remote entanglement of superconducting quantum processors. We conclude by discussing some of the challenges associated with fabricating niobium superconducting qubits and lithium niobate piezoacoustic devices on silicon-on-insulator substrates and provide initial steps towards realizing our transducer design in the lab.</p

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide