Practical considerations on optimising multistage decimation and interpolation processes

Multistage filter design is a complex multidimensional optimisation problem. The formulae for optimal design generally yield non-integer real numbers for the sample-rate-changing factors of multiple stages. Approaches yielding useful integer results have high computational cost and do not consider important multistage filter design properties. We have developed a simplified algorithm for directly searching the optimal integer results. Considering the most useful practical design parameters, optimal results can be approximated with a limited number of sets for any designs satisfying certain constraints, with negligible costs. This vastly simplifies the complexity of the problem

A Scalable Correlator Architecture Based on Modular FPGA Hardware, Reuseable Gateware, and Data Packetization

A new generation of radio telescopes is achieving unprecedented levels of sensitivity and resolution, as well as increased agility and field-of-view, by employing high-performance digital signal processing hardware to phase and correlate large numbers of antennas. The computational demands of these imaging systems scale in proportion to BMN^2, where B is the signal bandwidth, M is the number of independent beams, and N is the number of antennas. The specifications of many new arrays lead to demands in excess of tens of PetaOps per second. To meet this challenge, we have developed a general purpose correlator architecture using standard 10-Gbit Ethernet switches to pass data between flexible hardware modules containing Field Programmable Gate Array (FPGA) chips. These chips are programmed using open-source signal processing libraries we have developed to be flexible, scalable, and chip-independent. This work reduces the time and cost of implementing a wide range of signal processing systems, with correlators foremost among them,and facilitates upgrading to new generations of processing technology. We present several correlator deployments, including a 16-antenna, 200-MHz bandwidth, 4-bit, full Stokes parameter application deployed on the Precision Array for Probing the Epoch of Reionization.Comment: Accepted to Publications of the Astronomy Society of the Pacific. 31 pages. v2: corrected typo, v3: corrected Fig. 1

Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This includes design of decimation and interpolation filters, analysis/synthesis filter banks (also called quadrature mirror filters, or QMFJ, and the development of new sampling theorems. First, the basic concepts and building blocks in multirate digital signal processing (DSPJ, including the digital polyphase representation, are reviewed. Next, recent progress as reported by several authors in this area is discussed. Several applications are described, including the following: subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrow-band filter coefficients. The M-band QMF bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, based on a pseudo-circulant matrix framework, is covered. Unconventional applications of the polyphase concept are discussed

Design and implementation of a wideband sigma delta ADC

Abstract. High-speed and wideband ADCs have become increasingly important in response to the growing demand for high-speed wireless communication services. Continuous time sigma delta modulators (CTƩ∆M), well-known for their oversampling and noise shaping properties, offer a promising solution for low-power and high-speed design in wireless applications. The objective of this thesis is to design and implement a wideband CTƩ∆M for a global navigation satellite system(GNSS) receiver. The targeted modulator architecture is a 3rdorder single-bit CTƩ∆M, specifically designed to operate within a 15 MHz signal bandwidth. With an oversampling ratio of 25, the ADC’s sampling frequency is set at 768 MHz. The design goal is to achieve a theoretical signal to noise ratio (SNR) of 55 dB. This thesis focuses on the design and implementation of the CTƩ∆M, building upon the principles of a discrete time Ʃ∆ modulator, and leveraging system-level simulation and formulations. A detailed explanation of the coefficient calculation procedure specific to CTƩ∆ modulators is provided, along with a "top-down" design approach that ensures the specified requirements are met. MATLAB scripts for coefficient calculation are also included. To overcome the challenges associated with the implementation of CTƩ∆ modulators, particularly excess loop delay and clock jitter sensitivity, this thesis explores two key strategies: the introduction of a delay compensation path and the utilization of a finite impulse response (FIR) feedback DAC. By incorporating a delay compensation path, the stability of the modulator can be ensured and its noise transfer function (NTF) can be restored. Additionally, the integration of an FIR feedback DAC addresses the issue of clock jitter sensitivity, enhancing the overall performance and robustness of the CTƩ∆M. The CTƩ∆Ms employ the cascade of integrators with feed forward (CIFF) and cascade of integrators with feedforward and feedback (CIFF-B) topologies, with a particular emphasis on the CIFF-B configuration using 22nm CMOS technology node and a supply voltage of 0.8 V. Various simulations are performed to validate the modulator’s performance. The simulation results demonstrate an achievable SNR of 55 dB with a power consumption of 1.36 mW. Furthermore, the adoption of NTF zero optimization techniques enhances the SNR to 62 dB.Laajakaistaisen jatkuva-aikaisen sigma delta-AD-muuntimen suunnittelu ja toteutus. Tiivistelmä. Nopeat ja laajakaistaiset AD-muuntimet ovat tulleet entistä tärkeämmiksi nopeiden langattomien kommunikaatiopalvelujen kysynnän kasvaessa. Jatkuva-aikaiset sigma delta -modulaattorit (CTƩ∆M), joissa käytetään ylinäytteistystä ja kohinanmuokkausta, tarjoavat lupaavan ratkaisun matalan tehonkulutuksen ja nopeiden langattomien sovellusten suunnitteluun. Tämän työn tarkoituksena on suunnitella ja toteuttaa laajakaistainen jatkuva -aikainen sigma delta -modulaattori satelliittipaikannusjärjestelmien (GNSS) vastaanottimeen. Arkkitehtuuriltaan modulaattori on kolmannen asteen 1-bittinen CTƩ∆M, jolla on 15MHz:n signaalikaistanleveys. Ylinäytteistyssuhde on 25 ja AD muuntimen näytteistystaajuus 768 MHz. Tavoitteena on saavuttaa teoreettinen 55 dB signaalikohinasuhde (SNR). Tämä työ keskittyy jatkuva-aikaisen sigma delta -modulaattorin suunnitteluun ja toteutukseen, perustuen diskreettiaikaisen Ʃ∆-modulaattorin periaatteisiin ja systeemitason simulointiin ja mallitukseen. Jatkuva-aikaisen sigma delta -modulaattorin kertoimien laskentamenetelmä esitetään yksityiskohtaisesti, ja vaatimusten täyttyminen varmistetaan “top-down” -suunnitteluperiaatteella. Liitteenä on kertoimien laskemiseen käytetty MATLAB-koodi. Jatkuva-aikaisten sigma delta -modulaattoreiden erityishaasteiden, liian pitkän silmukkaviiveen ja kellojitterin herkkyyden, voittamiseksi tutkitaan kahta strategiaa, viiveen kompensointipolkua ja FIR takaisinkytkentä -DA muunninta. Viivekompensointipolkua käyttämällä modulaattorin stabiilisuus ja kohinansuodatusfunktio saadaan varmistettua ja korjattua. Lisäksi FIR takaisinkytkentä -DA-muuntimen käyttö pienentää kellojitteriherkkyyttä, parantaen jatkuva aikaisen sigma delta -modulaattorin kokonaissuorituskykyä ja luotettavuutta. Toteutetuissa jatkuva-aikaisissa sigma delta -modulaattoreissa on kytketty peräkkäin integraattoreita myötäkytkentärakenteella (CIFF) ja toisessa sekä myötä- että takaisinkytkentärakenteella (CIFF-B). Päähuomio on CIFF-B rakenteessa, joka toteutetaan 22nm CMOS prosessissa käyttäen 0.8 voltin käyttöjännitettä. Suorityskyky varmistetaan erilaisilla simuloinneilla, joiden perusteella 55 dB SNR saavutetaan 1.36 mW tehonkulutuksella. Lisäksi kohinanmuokkausfunktion optimoinnilla SNR saadaan nostettua 62 desibeliin

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

Digital instrumentation for the measurement of high spectral purity signals

Improvements on electronic technology in recent years have allowed the application of digital techniques in time and frequency metrology where low noise and high accuracy are required, yielding flexibility in systems implementation and setup. This results in measurement systems with extended capabilities, additional functionalities and ease of use. The Analog to Digital Converters (ADCs) and Digital to Analog Converters (DACs), as the system front-end, set the ultimate performance of the system in terms of noise. The noise characterization of these components will allow performing punctual considerations on the study of the implementation feasibility of new techniques and for the selection of proper components according to the application requirements. Moreover, most commercial platforms based on FPGA are clocked by quartz oscillators whose accuracy and frequency stability are not suitable for many time and frequency applications. In this case, it is possible to take advantage of the internal Phase Locked Loop (PLL) for generating the internal clock from an external frequency reference. However, the PLL phase noise could degrade the oscillator stability thereby limiting the entire system performance becoming a critical component for digital instrumentation. The information available currently in literature, describes in depth the features of these devices at frequency offsets far from the carrier. However, the information close to the carrier is a more important concern for time and frequency applications. In this frame, my PhD work is focused on understanding the limitations of the critical blocks of digital instrumentation for time and frequency metrology. The aim is to characterize the noise introduced by these blocks and in this manner to be able to predict their effects on a specific application. This is done by modeling the noise introduced by each component and by describing them in terms of general and technical parameters. The parameters of the models are identified and extracted through the corresponding method proposed accordingly to the component operation. This work was validated by characterizing a commercially available platform, Red Pitaya. This platform is an open source embedded system whose resolution and speed (14 bit, 125 MSps) are reasonably close to the state of the art of ADCs and DACs (16 bit, 350 MSps or 14 bit, 1 GSps/3GSPs) and it is potentially sufficient for the implementation of a complete instrument. The characterization results lead to the noise limitations of the platform and give a guideline for instrumentation design techniques. Based on the results obtained from the noise characterization, the implementation of a digital instrument for frequency transfer using fiber link was performed on the Red Pitaya platform. In this project, a digital implementation for the detection and compensation of the phase noise induced by the fiber is proposed. The beat note, representing the fiber length variations, is acquired directly with a high speed ADC followed by a fully digital phase detector. Based on the characterization results, it was expected a limitation in the phase noise measurement given by the PLL. First measurements of this implementation were performed using the 150 km-long buried fibers, placed in the same cables between INRiM and the Laboratoire Souterrain de Modane (LSM) on the Italy-France border. The two fibers are joined together at LSM to obtain a 300 km loop with both ends at INRiM. From these results the noise introduced by the digital system was verified in agreement with characterization results. Further test and improvements will be performed for having a finished system which is intended to be used on the Italian Link for Frequency and Time from Turin to Florence that is 642-km long and to its extension in the rest of Italy that is foreseen in the next future. Currently, a higher performance platform is under assessment by applying the tools and concepts developed along the PhD. The purpose of this project is the implementation of a state of the art phasemeter whose architecture is based on the DAC. In order to estimate the ultimate performance of the instrument, the DAC characterization is under development and preliminary measurements are also reported here

Digital electronic predistortion for optical communications

The distortion of optical signals has long been an issue limiting the performance of communication systems. With the increase of transmission speeds the effects of distortion are becoming more prominent. Because of this, the use of methods known from digital signal processing (DSP) are being introduced to compensate for them. Applying DSP to improve optical signals has been limited by a discrepancy in digital signal processing speeds and optical transmission speeds. However high speed Field Programmable Gate Arrays (FPGA) which are sufficiently fast have now become available making DSP experiments without costly ASIC implementation possible for optical transmission experiments. This thesis focuses on Look Up Table (LUT) based digital Electronic Predistortion (EPD) for optical transmission. Because it is only one out of many possible implementations of EPD, it has to be placed in context with other EPD techniques and other distortion combating techniques in general, especially since it is possible to combine the different techniques. Building an actual transmitter means that compromises and decisions have to be made in the design and implementation of an EPD based system. These are based on balancing the desire to achieve optimal performance with technological and economic limitations. This is partly done using optical simulations to asses the performance. This thesis describes a novel experimental transmitter that has been built as part of this research applying LUT based EPD to an optical signal. The experimental transmitter consists of a digital design (using a hardware description language) for a pair of FPGAs and an analogue optical/electronic setup including two standard DAC integrated circuits. The DSP in the transmitter compensated for both chromatic dispersion and self phase modulation. We achieved transmission of 10.7 Gb/s non-return-to-zero (NRZ) signals with a +4 dBm launch power over 450 km keeping the required optical-signal-to-noise-ratio (OSNR) for a bit-error-rate of 2x10^{-3} below 11 dB. In doing so we showed experimentally, for the first time, that nonlinear effects can be compensated with this approach and that the combination of FPGA-DAC is a viable approach for an experimental setup