Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.

Entwicklung von chiralen- sowie RP-HPLC-Methoden in Verbindung mit hochauflösender MS und deren Anwendung zur Analyse sekundärer organischer Aerosole in der Atmosphäre

Die Erdatmosphäre besteht hauptsächlich aus Stickstoff (78%), Sauerstoff (21%) und Edelga¬sen. Obwohl Partikel weniger als 0,1% ausmachen, spielen sie eine entscheidende Rolle in der Chemie und Physik der Atmosphäre, da sie das Klima der Erde sowohl direkt als auch indirekt beeinflussen. Je nach Art der Bildung unterscheidet man zwischen primären und sekundären Partikeln, wobei primäre Partikel direkt in die Atmosphäre eingetragen werden. Sekundäre Partikel hingegen entstehen durch Kondensation von schwerflüchtigen Verbindungen aus der Gasphase, welche durch Reaktionen von gasförmigen Vorläufersubstanzen (volatile organic compounds, VOCs) mit atmosphärischen Oxidantien wie Ozon oder OH-Radikalen gebildet werden. Da die meisten Vorläufersubstanzen organischer Natur sind, wird das daraus gebil¬dete Aerosol als sekundäres organisches Aerosol (SOA) bezeichnet. Anders als die meisten primären Partikel stammen die VOCs überwiegend aus biogenen Quellen. Es handelt sich da¬bei um ungesättigte Kohlenwasserstoffe, die bei intensiver Sonneneinstrahlung und hohen Temperaturen von Pflanzen emittiert werden. Viele der leichtflüchtigen Vorläufersubstanzen sind chiral, sowohl die Vorläufer als auch die daraus gebildeten Partikel werden aber in den meisten Studien als eine Verbindung betrachtet und gemeinsam analysiert. Die mit Modellen berechneten SOA-Konzentrationen, welche auf dieser traditionellen Vorstellung der SOA-Bil¬dung beruhen, liegen deutlich unterhalb der in der Atmosphäre gefundenen, so dass neben diesem Bildungsweg auch noch andere SOA-Bildungsarten existieren müssen. Aus diesem Grund wird der Fokus der heutigen Forschung vermehrt auf die heterogene Chemie in der Partikelphase gerichtet. Glyoxal als Modellsubstanz kommt hierbei eine wichtige Rolle zu. Es handelt sich bei dieser Verbindung um ein Molekül mit einem hohen Dampfdruck, das auf Grund dieser Eigenschaft nur in der Gasphase zu finden sein sollte. Da es aber über zwei Alde¬hydgruppen verfügt, ist es sehr gut wasserlöslich und kann dadurch in die Partikelphase über¬gehen, wo es heterogenen chemischen Prozessen unterliegt. Unter anderem werden in An¬wesenheit von Ammoniumionen Imidazole gebildet, welche wegen der beiden Stickstoff-He¬teroatome lichtabsorbierende Eigenschaften besitzen. Die Verteilung von Glyoxal zwischen der Gas- und der Partikelphase wird durch das Henrysche Gesetz beschrieben, wobei die Gleichgewichtskonstante die sogenannte Henry-Konstante ist. Diese ist abhängig von der un¬tersuchten organischen Verbindung und den im Partikel vorhandenen anorganischen Salzen. Für die Untersuchung chiraler Verbindungen im SOA wurde zunächst eine Filterextraktions¬methode entwickelt und die erhaltenen Proben anschließend mittels chiraler Hochleistungs-Flüssigchromatographie, welche an ein Elektrospray-Massenspektrometer gekoppelt war, analysiert. Der Fokus lag hierbei auf dem am häufigsten emittierten Monoterpen α-Pinen und seinem Hauptprodukt, der Pinsäure. Da bei der Ozonolyse des α-Pinens das cyclische Grund¬gerüst erhalten bleibt, können trotz der beiden im Molekül vorhanden chiralen Zentren nur zwei Pinsäure Enantiomere gebildet werden. Als Extraktionsmittel wurde eine Mischung aus Methanol/Wasser 9/1 gewählt, mit welcher Extraktionseffizienzen von 65% für Pinsäure Enan¬tiomer 1 und 68% für Pinsäure Enantiomer 2 erreicht werden konnten. Des Weiteren wurden Experimente in einer Atmosphärensimulationskammer durchgeführt, um die Produkte der α-Pinen Ozonolyse eindeutig zu charakterisieren. Enantiomer 1 wurde demnach aus (+)-α-Pinen gebildet und Enantiomer 2 entstand aus (-)-α-Pinen. Auf Filterproben aus dem brasilianischen Regenwald konnte ausschließlich Pinsäure Enantiomer 2 gefunden werden. Enantiomer 1 lag dauerhaft unterhalb der Nachweisgrenze von 18,27 ng/mL. Im borealen Nadelwald war das Verhältnis umgekehrt und Pinsäure Enantiomer 1 überwog vor Pinsäure Enantiomer 2. Das Verhältnis betrug 56% Enantiomer 1 zu 44% Enantiomer 2. Saisonale Verläufe im tropischen Regenwald zeigten, dass die Konzentrationen zur Trockenzeit im August höher waren als wäh¬rend der Regenzeit im Februar. Auch im borealen Nadelwald wurden im Sommer höhere Kon¬zentrationen gemessen als im Winter. Die Verhältnisse der Enantiomere änderten sich nicht im jahreszeitlichen Verlauf. Die Bestimmung der Henry-Konstanten von Glyoxal bei verschiedenen Saataerosolen, nämlich Ammoniumsulfat, Natriumnitrat, Kaliumsulfat, Natriumchlorid und Ammoniumnitrat sowie die irreversible Produktbildung aus Glyoxal in Anwesenheit von Ammoniak waren Forschungs¬gegenstand einer Atmosphärensimulationskammer-Kampagne am Paul-Scherrer-Institut in Villigen, Schweiz. Hierzu wurde zunächst das zu untersuchende Saataerosol in der Kammer vorgelegt und dann aus photochemisch erzeugten OH-Radikalen und Acetylen Glyoxal er¬zeugt. Für die Bestimmung der Glyoxalkonzentration im Kammeraerosol wurde zunächst eine beste¬hende Filterextraktionsmethode modifiziert und die Analyse mittels hochauflösender Mas¬senspektrometrie realisiert. Als Extraktionsmittel kam 100% Acetonitril, ACN zum Einsatz wo¬bei die Extraktionseffizienz bei 85% lag. Für die anschließende Derivatisierung wurde 2,4-Di¬nitrophenylhydrazin, DNPH verwendet. Dieses musste zuvor drei Mal mittels Festphasenex¬traktion gereinigt werden um störende Blindwerte ausreichend zu minimieren. Die gefunde¬nen Henry-Konstanten für Ammoniumsulfat als Saataerosol stimmten gut mit in der Literatur gefundenen Werten überein. Die Werte für Natriumnitrat und Natriumchlorid als Saataerosol waren kleiner als die von Ammoniumsulfat aber größer als der Wert von reinem Wasser. Für Ammoniumnitrat und Kaliumsulfat konnten keine Konstanten berechnet werden. Alle drei Saataerosole führten zu einem „Salting-in“. Das bedeutet, dass bei Erhöhung der Salzmolalität auch die Glyoxalkonzentration im Partikel stieg. Diese Beobachtungen sind auch in der Litera¬tur beschrieben, wobei die Ergebnisse dort nicht auf der Durchführung von Kammerexperi¬menten beruhen, sondern mittels bulk-Experimenten generiert wurden. Für die Trennung der Imidazole wurde eine neue Filterextraktionsmethode entwickelt, wobei sich ein Gemisch aus mit HCl angesäuertem ACN/H2O im Verhältnis 9/1 als optimales Extrak¬tionsmittel herausstellte. Drei verschiedenen Imidazole konnten mit dieser Methode quanti¬fiziert werden, nämlich 1-H-Imidazol-4-carbaldehyd (IC), Imidazol (IM) und 2,2‘-Biimidazol (BI). Die Effizienzen lagen für BI bei 95%, für IC bei 58% und für IM bei 75%. Kammerexperimente unter Zugabe von Ammoniak zeigten höhere Imidazolkonzentrationen als solche ohne. Wurden die Experimente ohne Ammoniak in Anwesenheit von Ammoni¬umsulfat durchgeführt, wurden höhere Imidazol-Konzentrationen gefunden als ohne Ammo¬niumionen. Auch die relative Luftfeuchtigkeit spielte eine wichtige Rolle, da sowohl eine zu hohe als auch eine zu niedrige relative Luftfeuchtigkeit zu einer verminderten Imidazolbildung führte. Durch mit 13C-markiertem Kohlenstoff durchgeführte Experimente konnte eindeutig gezeigt werden, dass es sich bei den gebildeten Imidazolen und Glyoxalprodukte handelte. Außerdem konnte der in der Literatur beschriebene Bildungsmechanismus erfolgreich weiter¬entwickelt werden. Während der CYPHEX Kampagne in Zypern konnten erstmalig Imidazole in Feldproben nach¬gewiesen werden. Das Hauptprodukt IC zeigte einen tageszeitlichen Verlauf mit höheren Kon¬zentrationen während der Nacht und korrelierte signifikant aber schwach mit der Acidität und Ammoniumionenkonzentration des gefundenen Aerosols.

Pupil phase apodization for achromatic imaging of extra-solar planets

Direct imaging of extra-solar planets in the visible and infrared region has generated great interest among scientists and the general public as well. However, this is a challenging problem. Diffculties of detecting a planet (faint source) are caused, mostly, by two factors: sidelobes caused by starlight diffraction from the edge of the pupil and the randomly scattered starlight caused by the phase errors from the imperfections in the optical system. While the latter diffculty can be corrected by high density active deformable mirrors with advanced phase sensing and control technology, the optimized strategy for suppressing the diffraction sidelobes is still an open question. In this thesis, I present a new approach to the sidelobe reduction problem: pupil phase apodization. It is based on a discovery that an anti-symmetric spatial phase modulation pattern imposed over a pupil or a relay plane causes diffracted starlight suppression sufficient for imaging of extra-solar planets. Numerical simulations with specific square pupil (side D) phase functions, such as ... demonstrate annulling in at least one quadrant of the diffraction plane to the contrast level of better than 10^12 with an inner working angle down to 3.5L/D (with a = 3 and e = 10^3). Furthermore, our computer experiments show that phase apodization remains effective throughout a broad spectrum (60% of the central wavelength) covering the entire visible light range. In addition to the specific phase functions that can yield deep sidelobe reduction on one quadrant, we also found that a modified Gerchberg-Saxton algorithm can help to find small sized (101 x 101 element) discrete phase functions if regional sidelobe reduction is desired. Our simulation shows that a 101x101 segmented but gapless active mirror can also generate a dark region with Inner Working Distance about 2.8L/D in one quadrant. Phase-only modulation has the additional appeal of potential implementation via active segmented or deformable mirrors, thereby combining compensation of random phase aberrations and diffraction halo removal in a single optical element.

Contrast sensitivity for complex and random gratings

This thesis studied the effect of (i) the number of grating components and (ii) parameter randomisation on root-mean-square (r.m.s.) contrast sensitivity and spatial integration. The effectiveness of spatial integration without external spatial noise depended on the number of equally spaced orientation components in the sum of gratings. The critical area marking the saturation of spatial integration was found to decrease when the number of components increased from 1 to 5-6 but increased again at 8-16 components. The critical area behaved similarly as a function of the number of grating components when stimuli consisted of 3, 6 or 16 components with different orientations and/or phases embedded in spatial noise. Spatial integration seemed to depend on the global Fourier structure of the stimulus. Spatial integration was similar for sums of two vertical cosine or sine gratings with various Michelson contrasts in noise. The critical area for a grating sum was found to be a sum of logarithmic critical areas for the component gratings weighted by their relative Michelson contrasts. The human visual system was modelled as a simple image processor where the visual stimuli is first low-pass filtered by the optical modulation transfer function of the human eye and secondly high-pass filtered, up to the spatial cut-off frequency determined by the lowest neural sampling density, by the neural modulation transfer function of the visual pathways. The internal noise is then added before signal interpretation occurs in the brain. The detection is mediated by a local spatially windowed matched filter. The model was extended to include complex stimuli and its applicability to the data was found to be successful. The shape of spatial integration function was similar for non-randomised and randomised simple and complex gratings. However, orientation and/or phase randomised reduced r.m.s contrast sensitivity by a factor of 2. The effect of parameter randomisation on spatial integration was modelled under the assumption that human observers change the observer strategy from cross-correlation (i.e., a matched filter) to auto-correlation detection when uncertainty is introduced to the task. The model described the data accurately.

The soft skills of project management : a view from diploma graduates

A research study was conducted in a key area of project management: stakeholder and relationship management through communication - ‘the soft skills’. It was conducted with Diploma of Project Management graduates from one Australian Registered Training Organisation (RTO), the Australian College of Project Management (ACPM). The study was designed to initially identify the qualifications and project management experience of the participants. Further, it identified the respondents’ understanding of and attitude to commonly held principles and literature within the project management field as it relates to the soft skills of projects. This is specifically connected to their project experience and knowledge, approach to project communications, and the stakeholder’s needs. Some of the literature showed that through the management and application of the project soft skills by project managers may actually be a recipe for project success. Hence, an important underpinning of this study was that the project manager can enhance project success (or reduce the impact of failure) by identifying and prioritising stakeholders, developing and implementing strategies for engaging and communicating with them. The use of a positivist approach to this research study allowed for the evaluation and understanding of respondents to the emergent theories of successful projects being delivered through the management of stakeholders, communications, and relationships. Consequently, a quantitative approach to this study was undertaken. The participants were drawn from graduates who completed (graduated) from the ACPM with the Diploma of Project Management between January 2004 and December 2007 only. A list of graduates was collated from this period indicating that a total of 656 graduates have completed and graduated with the qualification. The data collection for this study was done in one phase only. The questionnaire was emailed individually by the researcher directly to the selected potential respondents. Subsequently, a total of 44 responses were received, providing an overall response rate of 43%. Two key factors emerged from the survey questionnaire. Firstly, the need for the soft skills to be incorporated in project management curriculum and education programs, and secondly, that successful projects are delivered through the management and application of the project soft skills. It is expected that the findings of this study be provided across various forums (such as vocational education and training, and project management conferences) and via project management bodies such as the Australian Institute of Project Management (AIPM) to inform learning and provide greater insight into the soft skills of project management. It is the contention of the researcher that this quantitative study of Diploma of Project Management graduates’ views and attitudes highlights the importance of project soft skills and its importance in the delivery of successful projects as well as being part of the competencies of a successful project manager. This study also revealed the value of project experience and knowledge as it pertains to the management and application of the project soft skills.

Breast cancer detection from thermal images using bispectral invariant features

Highly sensitive infrared (IR) cameras provide high-resolution diagnostic images of the temperature and vascular changes of breasts. These images can be processed to emphasize hot spots that exhibit early and subtle changes owing to pathology. The resulting images show clusters that appear random in shape and spatial distribution but carry class dependent information in shape and texture. Automated pattern recognition techniques are challenged because of changes in location, size and orientation of these clusters. Higher order spectral invariant features provide robustness to such transformations and are suited for texture and shape dependent information extraction from noisy images. In this work, the effectiveness of bispectral invariant features in diagnostic classification of breast thermal images into malignant, benign and normal classes is evaluated and a phase-only variant of these features is proposed. High resolution IR images of breasts, captured with measuring accuracy of ±0.4% (full scale) and temperature resolution of 0.1 °C black body, depicting malignant, benign and normal pathologies are used in this study. Breast images are registered using their lower boundaries, automatically extracted using landmark points whose locations are learned during training. Boundaries are extracted using Canny edge detection and elimination of inner edges. Breast images are then segmented using fuzzy c-means clustering and the hottest regions are selected for feature extraction. Bispectral invariant features are extracted from Radon projections of these images. An Adaboost classifier is used to select and fuse the best features during training and then classify unseen test images into malignant, benign and normal classes. A data set comprising 9 malignant, 12 benign and 11 normal cases is used for evaluation of performance. Malignant cases are detected with 95% accuracy. A variant of the features using the normalized bispectrum, which discards all magnitude information, is shown to perform better for classification between benign and normal cases, with 83% accuracy compared to 66% for the original.

Mechanical processing and microstructural control in hot working of hot isostatically pressed P/M IN-100 superalloy

The hot deformation behavior of hot isostatically pressed (HIPd) P/M IN-100 superalloy has been studied in the temperature range 1000-1200 degrees C and strain rate range 0.0003-10 s(-1) using hot compression testing. A processing map has been developed on the basis of these data and using the principles of dynamic materials modelling. The map exhibited three domains: one at 1050 degrees C and 0.01 s(-1), with a peak efficiency of power dissipation of approximate to 32%, the second at 1150 degrees C and 10 s(-1), with a peak efficiency of approximate to 36% and the third at 1200 degrees C and 0.1 s(-1), with a similar efficiency. On the basis of optical and electron microscopic observations, the first domain was interpreted to represent dynamic recovery of the gamma phase, the second domain represents dynamic recrystallization (DRX) of gamma in the presence of softer gamma', while the third domain represents DRX of the gamma phase only. The gamma' phase is stable upto 1150 degrees C, gets deformed below this temperature and the chunky gamma' accumulates dislocations, which at larger strains cause cracking of this phase. At temperatures lower than 1080 degrees C and strain rates higher than 0.1 s(-1), the material exhibits flow instability, manifested in the form of adiabatic shear bands. The material may be subjected to mechanical processing without cracking or instabilities at 1200 degrees C and 0.1 s(-1), which are the conditions for DRX of the gamma phase.

Inertial mass of a vortex in cuprate superconductors

We present here a calculation of the inertial mass of a moving vortex in cuprate superconductors. This is a poorly known basic quantity of obvious interest in vortex dynamics. The motion of a vortex causes a dipolar density distortion and an associated electric field which is screened. The energy cost of the density distortion as well as the related screened electric field contributes to the vortex mass, which is small because of efficient screening. As a preliminary, we present a discussion and calculation of the vortex mass using a microscopically derivable phase-only action functional for the far region which shows that the contribution from the far region is negligible and that most of it arises from the (small) core region of the vortex. A calculation based on a phenomenological Ginzburg-Landau functional is performed in the core region. Unfortunately such a calculation is unreliable; the reasons for it are discussed. A credible calculation of the vortex mass thus requires a fully microscopic non-coarse-grained theory. This is developed, and results are presented for an s-wave BCS-like gap, with parameters appropriate to the cuprates. The mass, about 0.5m(e) per layer, for a magnetic field along the c axis arises from deformation of quasiparticle states bound in the core and screening effects mentioned above. We discuss earlier results, possible extensions to d-wave symmetry, and observability of effects dependent on the inertial mass. [S0163-1829(97)05534-3].

Compact AM Signals for Maximum Clutter Rejection

The transmitted signal is assumed to consist of a close succession of rectangular pulses of equal width. A matched filter scheme is employed and a theory is developed for a computer-aided optimization of the envelope of monotone compact signals for maximum rejection of dense clutter of any given distribution in range. Specific results are presented and indeterminate cases are discussed.

BER-optimized linear parallel interference cancellers for multicarrier DS-CDMA systems

In this paper, we consider the design and bit-error performance analysis of linear parallel interference cancellers (LPIC) for multicarrier (MC) direct-sequence code division multiple access (DS-CDMA) systems. We propose an LPIC scheme where we estimate and cancel the multiple access interference (MAT) based on the soft decision outputs on individual subcarriers, and the interference cancelled outputs on different subcarriers are combined to form the final decision statistic. We scale the MAI estimate on individual subcarriers by a weight before cancellation. In order to choose these weights optimally, we derive exact closed-form expressions for the bit-error rate (BER) at the output of different stages of the LPIC, which we minimize to obtain the optimum weights for the different stages. In addition, using an alternate approach involving the characteristic function of the decision variable, we derive BER expressions for the weighted LPIC scheme, matched filter (MF) detector, decorrelating detector, and minimum mean square error (MMSE) detector for the considered multicarrier DS-CDMA system. We show that the proposed BER-optimized weighted LPIC scheme performs better than the MF detector and the conventional LPIC scheme (where the weights are taken to be unity), and close to the decorrelating and MMSE detectors.

Performance analysis of a suprathreshold, stochastic resonance based nonlinear detector

In this paper we introduce a nonlinear detector based on the phenomenon of suprathreshold stochastic resonance (SSR). We first present a model (an array of 1-bit quantizers) that demonstrates the SSR phenomenon. We then use this as a pre-processor to the conventional matched filter. We employ the Neyman-Pearson(NP) detection strategy and compare the performances of the matched filter, the SSR-based detector and the optimal detector. Although the proposed detector is non-optimal, for non-Gaussian noises with heavy tails (leptokurtic) it shows better performance than the matched filter. In situations where the noise is known to be leptokurtic without the availability of the exact knowledge of its distribution, the proposed detector turns out to be a better choice than the matched filter.

Transient signal detection using wigner-ville distribution and wavelet denoising

The problem of detecting an unknown transient signal in noise is considered. The SNR of the observed data is first enhanced using wavelet domain filter The output of the wavelet domain filter is then transformed using a Wigner-Ville transform,which separates the spectrum of the observed signal into narrow frequency bands. Each subband signal at the output of the Wigner-ville block is subjected kto wavelet based level dependent denoising (WBLDD)to supress colored noise A weighted sum of the absolute value of outputs of WBLDD is passed through an energy detector, whose output is used as test statistic to take the final decision. By assigning weights proportional to the energy of the corresponding subband signals, the proposed detector approximates a frequency domain matched filter Simulation results are presented to show that the performance of the proposed detector is better than that of the wavelet packet transform based detector.

Importance of local heating in the compaction of thermally sensitive solids

Local heating is an important parameter in compaction of thermally sensitive solids since local hot spots could conceivably raise the temperature of the system by several hundred degrees. To understand the importance of local hot spots, 20 g of ammonium perchlorate (AP) and potassium perchlorate (KP) were pressed together at 1500 kg cm−2 for 5 min. The surface structural examination of the compact revealed a secondary phase at the interfaces between the grains in the compositions ranging from 50% AP-50% KP to 10% AP-90% KP. The observation of the secondary phase only at the interfaces has been attributed to the short life times of temperature pulses present during the compaction. An interesting aspect of the investigation is the formation of a series of solid solutions of AP-KP.

BER Analysis of Weighted Interference Cancellation in Multicarrier DS-CDMA Systems

In this paper, we present the design and bit error performance analysis of weighted linear parallel interference cancellers (LPIC) for multicarrier (MC) DS-CDMA systems. We propose an LPIC scheme where we estimate (and cancel) the multiple access interference (MAI) based on the soft outputs on individual subcarriers, and the interference cancelled outputs on different subcarriers are combined to form the final decision statistic. We scale the MAI estimate on individual subcarriers by a weight before cancellation; these weights are so chosen to maximize the signal-to-interference ratios at the individual subcarrier outputs. For this weighted LPIC scheme, using an approach involving the characteristic function of the decision variable, we derive exact bit error rate (BER) expressions for different cancellation stages. Using the same approach, we also derive exact BER expressions for the matched filter (MF) and decorrelating detectors for the considered MC DS-CDMA system. We show that the proposed weighted LPIC scheme performs better than the MF detector and the conventional LPIC (where the weights are taken to be unity), and close to the decorrelating detector.

A novel property of an Auto-Correlation Sequence and some Applications

In this article, we use some spectral properties of polynomials presented in 1] and map an auto-correlation sequence to a set of Line Spectral Frequencies(LSFs) and reflection coefficients. This novel characterization of an auto-correlation sequence is used to obtain a lattice structure of a Linear-Phase(LP) FIR filter.