Optimal digital filter design for dispersed signal equalization

Any signal a satellite receives from Earth has traveled through the ionosphere. Transmission through the ionosphere results in a frequency dependent time-delay of the signal frequency components. This effect of the medium on the signal is termed dispersion, and it increases the difficulty of pulse detection. A system capable of compensating for the dispersion would be desirable, as pulsed signals would be more readily detected after compression. In this thesis, we investigate the derivation of a digital filter to compensate for the dispersion caused by the ionosphere. A transfer function model for the analysis of the ionosphere as a system is introduced. Based on the signal model, a matched filter response is derived. The problem is formulated as a group delay compensation effort. The Abel-Smith algorithm is employed for the synthesis of a cascaded allpass filter bank with desired group delay characteristics. Extending this work, an optimized allpass filter is then derived using a pole location approach. A mean-square error metric shows that the optimized filter can reproduce, and even improve upon, the results of the Abel-Smith design with a significantly lower order filter. When compared against digital filters produced with the least p-th minimax algorithm, we find that the new method exhibits significantly lower error in the band of interest, as well as lower mean squared error overall. The result is a simple optimized equalization filter that is stable, robust against cascading difficulties, and applicable to arbitrary waveforms. This filter is the cornerstone to a new all-digital electromagnetic pulse detection system

Simultaneous Digital Demodulation and RDS Extraction of FM Radio Signals

FM radio plays a large part in many peoples\u27 lives. A digital stream of information known as the Radio Data System (RDS) can be transmitted alongside the audio signal in an FM radio broadcast. This digital signal may contain information such as the current song, traffic alerts, and emergency notices. Using MATLAB, a method is presented by which the RDS data may be digitally extracted from multiple FM broadcasts simultaneously. This method\u27s parallel nature makes Digital Signal Processing (DSP) technology, such as a Field Programmable Gate Array (FPGA), an ideal platform for implementation

On the Equivalence of the Digital Waveguide and Finite Difference Time Domain Schemes

It is known that the digital waveguide (DW) method for solving the wave equation numerically on a grid can be manipulated into the form of the standard finite-difference time-domain (FDTD) method (also known as the ``leapfrog'' recursion). This paper derives a simple rule for going in the other direction, that is, converting the state variables of the FDTD recursion to corresponding wave variables in a DW simulation. Since boundary conditions and initial values are more intuitively transparent in the DW formulation, the simple means of converting back and forth can be useful in initializing and constructing boundaries for FDTD simulations.Comment: v1: 6 pages; v2: 7 pages, generally more polished, more examples, expanded discussion; v3: 15 pages, added state space formulation, analysis of inputs and boundary conditions, translation of passive boundary conditions; v4: various typos fixe

Minimal structures for the implementation of digital rational lossless systems

Digital lossless transfer matrices and vectors (power-complementary vectors) are discussed for applications in digital filter bank systems, both single rate and multirate. Two structures for the implementation of rational lossless systems are presented. The first structure represents a characterization of single-input, multioutput lossless systems in terms of complex planar rotations, whereas the second structure offers a representation of M-input, M-output lossless systems in terms of unit-norm vectors. This property makes the second structure desirable in applications that involve optimization of the parameters. Modifications of the second structure for implementing single-input, multioutput, and lossless bounded real (LBR) systems are also included. The main importance of the structures is that they are completely general, i.e. they span the entire set of M×1 and M×M lossless systems. This is demonstrated by showing that any such system can be synthesized using these structures. The structures are also minimal in the sense that they use the smallest number of scalar delays and parameters to implement a lossless system of given degree and dimensions. A design example to demonstrate the main results is included

Suprajohtavien kvantti-inferferenssilaitteiden älykäs digitaalinen ohjaus ultramatalan kentän magneettikuvauksessa

Ultra-low-field magnetic resonance imaging (ULF MRI) studies the inner structure of matter by exciting nuclear spins using microtesla-range magnetic fields. The weak spin-induced magnetic signals are received with highly sensitive superconducting-quantum-interference-device-based (SQUID) sensors that act as flux-to-voltage converters. Because of the physical nature of the SQUID, its response to magnetic flux is periodic. To make the measurements easier, the response is linearized with a special feedback scheme. In the measurement setup used in this work, the SQUID feedback is realized with digital signal processors so that the response of the system can be manipulated using computer software. The software is designed for magnetoencephalography, which measures magnetic signals generated by the neuronal currents. These signals are in both amplitude and frequency smaller than those encountered in ULF MRI. In this thesis, new software for the needs of ULF MRI was developed. For example, a method to measure the feedback-to-input response and a new feedback reset algorithm tailored for ULF MRI were designed and implemented. The reset algorithm was designed to reactivate the flux dams in the SQUID input circuits and to reduce the signal transient after the reset. The feedback-to-input response measurements revealed a notable delay in the feedback, which degrades the frequency response of the whole system. It was shown that the frequency response can be improved by an additional digital compensation based on the measured feedback-to-input response.Ultramatalan kentän magneettikuvauksessa tutkitaan aineen rakennetta virittämällä atomiytimien spinejä mikroteslaluokan magneettikentillä. Spinien tuottamat heikot magneettiset signaalit vastaanotetaan erittäin herkillä suprajohtaviin kvantti-interferenssilaitteisiin (SQUID) perustuvilla antureilla, jotka muuntavat magneettivuon jännitteeksi. SQUIDin vaste magneettivuohon on luonnostaan periodinen. Mittausten helpottamiseksi se linearisoidaan kytkemällä mitattu signaali takaisin SQUIDiin. Tässä työssä käytetyssä mittausjärjestelmässä SQUIDien takaisinkytkentä on toteutettu digitaalisten signaaliprosessoreiden avulla, minkä ansiosta systeemin vastetta voidaan muokata tietokoneohjelmistolla. Ohjelmisto on kuitenkin suunniteltu magnetoenkefalografiaa varten. Magnetoenkefalografiassa mitatut signaalit ovat niin taajuudeltaan kuin amplitudiltaan huomattavan pieniä verattuna magneettikuvaukseen. Tämän diplomityön tarkoituksena oli kehittää uutta ohjelmistoa ultramatalan kentän magneettikuvauksen tarpeisiin. Ohjelmistoa kehitettiin esimerkiksi mittaamaan takaisinkytkentävasteita sekä kontrolloimaan vuosignaalia uudella tavalla takaisinkytkennän resetoinnin aikana. Uusi resetointialgoritmi pyrkii ohjaamaan SQUIDien vastaanottopiirien vuopatoja suprajohtavaan tilaan sekä vähentämään signaalitransienttia takaisinkytkennän resetoinnin jälkeen. Takaisinkytkennässä havaittiin viivettä, joka heikentää koko systeemin taajuusvastetta. Taajuusvasteen osoitettiin kohentuvan, kun signaalia kompensoitiin digitaalisesti hyödyntäen tietoa mitatusta takaisinkytkentävasteesta

AUDIO PROCESSING ANALYZER

The project emphasizes simulation of various DSP effects using elementary phenomenon of audio processing, and by manipulating audio using various filters in order to enhance the quality. There are many commercially available systems, which provide facilities such as channel equalizers, karaoke systems, and a few audio processors based on Digital Signal Processing. Software systems are also available which provide a fairly good and cost effective solution to audio enhancement. Yet they are limited due to resources issues and thus make a trade-off between performance and quality. The project at first studies and analyses proceeds as study and analysis of audio processing phenomena and various effects involved in it. In the second phase algorithms have been developed for these phenomena and their simulation in MATLAB.

A fast-initializing digital equalizer with on-line tracking for data communications

A theory is developed for a digital equalizer for use in reducing intersymbol interference (ISI) on high speed data communications channels. The equalizer is initialized with a single isolated transmitter pulse, provided the signal-to-noise ratio (SNR) is not unusually low, then switches to a decision directed, on-line mode of operation that allows tracking of channel variations. Conditions for optimal tap-gain settings are obtained first for a transversal equalizer structure by using a mean squared error (MSE) criterion, a first order gradient algorithm to determine the adjustable equalizer tap-gains, and a sequence of isolated initializing pulses. Since the rate of tap-gain convergence depends on the eigenvalues of a channel output correlation matrix, convergence can be improved by making a linear transformation on to obtain a new correlation matrix