Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

BICEP2 II: Experiment and Three-Year Data Set

We report on the design and performance of the BICEP2 instrument and on its three-year data set. BICEP2 was designed to measure the polarization of the cosmic microwave background (CMB) on angular scales of 1 to 5 degrees ($\ell$=40-200), near the expected peak of the B-mode polarization signature of primordial gravitational waves from cosmic inflation. Measuring B-modes requires dramatic improvements in sensitivity combined with exquisite control of systematics. The BICEP2 telescope observed from the South Pole with a 26~cm aperture and cold, on-axis, refractive optics. BICEP2 also adopted a new detector design in which beam-defining slot antenna arrays couple to transition-edge sensor (TES) bolometers, all fabricated on a common substrate. The antenna-coupled TES detectors supported scalable fabrication and multiplexed readout that allowed BICEP2 to achieve a high detector count of 500 bolometers at 150 GHz, giving unprecedented sensitivity to B-modes at degree angular scales. After optimization of detector and readout parameters, BICEP2 achieved an instrument noise-equivalent temperature of 15.8 $\mu$K sqrt(s). The full data set reached Stokes Q and U map depths of 87.2 nK in square-degree pixels (5.2 $\mu$K arcmin) over an effective area of 384 square degrees within a 1000 square degree field. These are the deepest CMB polarization maps at degree angular scales to date. The power spectrum analysis presented in a companion paper has resulted in a significant detection of B-mode polarization at degree scales.Comment: 30 pages, 24 figure

(SI10-068) Performance Analysis of Cosine Window Function

This paper reviews the mathematical functions called the window functions which are employed in the Finite Impulse Response (FIR) filter design applications as well as spectral analysis for the detection of weak signals. The characteristic properties of the window functions are analyzed and parameters are compared among the known conventional cosine window (CW) functions (Rectangular, Hamming, Hanning, and Blackman) and the variable Kaiser window function. The window function expressed in the time domain can be transformed into the frequency domain by taking the Discrete Fourier Transform (DFT) of the time domain window function. The frequency response of the window function so obtained has main lobe, side lobes, and roll-off rate of side lobes. The main lobe width (MLW) expressed in 3dB bandwidth (BW), highest side lobe level (HSLL), and side lobe roll-off rate (SLROR) of the conventional window function and variable Kaiser window is then evaluated from the frequency response and compared to find out the appropriate window for employed applications

Tunable far infrared laser spectrometers

The state of the art in far infrared (FIR) spectroscopy is reviewed. The development of tunable, coherent FIR radiation sources is discussed. Applications of tunable FIR laser spectrometers for measurement of rotational spectra and dipole moments of molecular ions and free radicals, vibration-rotation-tunneling (VRT) spectra of weakly bound complexes, and vibration-rotation spectra of linear carbon clusters are presented. A detailed description of the Berkeley tunable FIR laser spectrometers is presented in the following article

Tunable complex-valued multi-tap microwave photonic filter based on single silicon-oninsulator microring resonator

This paper was published in OPTICS EXPRESS and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/OE.19.012402. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under lawA complex-valued multi-tap tunable microwave photonic filter based on single silicon-on-insulator microring resonator is presented. The degree of tunability of the approach involving two, three and four taps is theoretical and experimentally characterized, respectively. The constraints of exploiting the optical phase transfer function of a microring resonator aiming at implementing complex-valued multi-tap filtering schemes are also reported. The trade-off between the degree of tunability without changing the free spectral range and the number of taps is studied in-depth. Different window based scenarios are evaluated for improving the filter performance in terms of the side-lobe level. (C) 2011 Optical Society of AmericaThe authors wish to acknowledge the technical support given by Prof. Pascual Munoz and David Domenech, as well as the financial support of the European Commission Seventh Framework Programme (FP 7) project GOSPEL; the Generalitat Valenciana through the Microwave Photonics research Excellency award programme GVA PROMETEO 2008/092 and also the Plan Nacional I + D TEC2007-68065-C03-01 and TEC2008-06145.Lloret Soler, JA.; Sancho Durá, J.; Pu, M.; Gasulla Mestre, I.; Yvind, K.; Sales Maicas, S.; Capmany Francoy, J. (2011). Tunable complex-valued multi-tap microwave photonic filter based on single silicon-on-insulator microring resonator. Optics Express. 19(13):12402-12407. https://doi.org/10.1364/OE.19.012402S1240212407191

Hardward and algorithm architectures for real-time additive synthesis

Additive synthesis is a fundamental computer music synthesis paradigm tracing its origins to the work of Fourier and Helmholtz. Rudimentary implementation linearly combines harmonic sinusoids (or partials) to generate tones whose perceived timbral characteristics are a strong function of the partial amplitude spectrum. Having evolved over time, additive synthesis describes a collection of algorithms each characterised by the time-varying linear combination of basis components to generate temporal evolution of timbre. Basis components include exactly harmonic partials, inharmonic partials with time-varying frequency or non-sinusoidal waveforms each with distinct spectral characteristics. Additive synthesis of polyphonic musical instrument tones requires a large number of independently controlled partials incurring a large computational overhead whose investigation and reduction is a key motivator for this work. The thesis begins with a review of prevalent synthesis techniques setting additive synthesis in context and introducing the spectrum modelling paradigm which provides baseline spectral data to the additive synthesis process obtained from the analysis of natural sounds. We proceed to investigate recursive and phase accumulating digital sinusoidal oscillator algorithms, defining specific metrics to quantify relative performance. The concepts of phase accumulation, table lookup phase-amplitude mapping and interpolated fractional addressing are introduced and developed and shown to underpin an additive synthesis subclass - wavetable lookup synthesis (WLS). WLS performance is simulated against specific metrics and parameter conditions peculiar to computer music requirements. We conclude by presenting processing architectures which accelerate computational throughput of specific WLS operations and the sinusoidal additive synthesis model. In particular, we introduce and investigate the concept of phase domain processing and present several “pipeline friendly” arithmetic architectures using this technique which implement the additive synthesis of sinusoidal partials

Spektralna analiza poopćene trokutaste i Welchove prozorske funkcije korištenjem frakcijske Fourierove transformacije

The paper presents a new closed-form expression for the fractional Fourier transform of generalized Triangular and Welch window functions. Fractional Fourier Transform (FrFT) is a parameterized transform having an adjustable transform parameter which makes it more flexible and superior over ordinary Fourier transform in several applications. It is an important tool used in signal processing for spectral analysis. The analysis of generalized Triangular and Welch window functions in fractional Fourier domain establishes a direct relationship between their FrFTs and fractional angle. Based on the mathematical model obtained, it is observed that adjustable spectral parameters of these functions can be obtained by modifying the fractional angle. The various values of spectral parameters such as half main-lobe width, side lobe fall-off rate and maximum side-lobe level with change in order of fractional Fourier transform are also obtained for these functions.U radu je prikazan novi izraz za zatvoreni oblik frakcijske Fourierove transformacije poopćene trokutaste i Welchove prozorske funkcije. Frakcijska Fourierova transformacija (FrFT) parametrizirana je transformacija s podesivim parametrom transformacije koja je u određenim primjenama fleksibilnija i superiornija u odnosu na uobičajenu Fourierovu transformaciju. Ističe se kao važan alat u obradi signala i spektralnoj analizi. Analiza poopćene trokutaste i Welchove prozorske funkcije u području frkacijske Fourierove transformacije uspostavlja izravni odnos između FrFT-a i frakcijskog kuta. Koristeći dobiveni matematički model, uočeno je da se podesivi spektralni parametri ovih funkcija mogu izvesti mijenjanjem frakcijskog kuta. Različite vrijednosti spektralnih parametara, kao što su polovica širine spektralnog vrha, stopa snižavanja amplituda viših harmonika ili najveća amplituda viših harmonika, odnosno njihova ovisnost u odnosu na red frakcijske Fourierove transformacije, također se mogu odrediti upotrebom ovih funkcija

Efficient Fast-Convolution-Based Waveform Processing for 5G Physical Layer

This paper investigates the application of fast-convolution (FC) filtering schemes for flexible and effective waveform generation and processing in the fifth generation (5G) systems. FC-based filtering is presented as a generic multimode waveform processing engine while, following the progress of 5G new radio standardization in the Third-Generation Partnership Project, the main focus is on efficient generation and processing of subband-filtered cyclic prefix orthogonal frequency-division multiplexing (CP-OFDM) signals. First, a matrix model for analyzing FC filter processing responses is presented and used for designing optimized multiplexing of filtered groups of CP-OFDM physical resource blocks (PRBs) in a spectrally well-localized manner, i.e., with narrow guardbands. Subband filtering is able to suppress interference leakage between adjacent subbands, thus supporting independent waveform parametrization and different numerologies for different groups of PRBs, as well as asynchronous multiuser operation in uplink. These are central ingredients in the 5G waveform developments, particularly at sub-6-GHz bands. The FC filter optimization criterion is passband error vector magnitude minimization subject to a given subband band-limitation constraint. Optimized designs with different guardband widths, PRB group sizes, and essential design parameters are compared in terms of interference levels and implementation complexity. Finally, extensive coded 5G radio link simulation results are presented to compare the proposed approach with other subband-filtered CP-OFDM schemes and time-domain windowing methods, considering cases with different numerologies or asynchronous transmissions in adjacent subbands. Also the feasibility of using independent transmitter and receiver processing for CP-OFDM spectrum control is demonstrated