A Proposal for Concurrent Estimation of Static and Dynamic Nonlinearity of ADC

Despite great advances in very large scale integrated-circuit design and manufacturing, performance of even the best available high-speed, high-resolution analog-to-digital converter (ADC) is known to deteriorate while acquiring fast-rising, high-frequency, and nonrepetitive waveforms. Waveform digitizers (ADCs) used in high-voltage impulse recordings and measurements are invariably subjected to such waveforms. Errors resulting from a lowered ADC performance can be unacceptably high, especially when higher accuracies have to be achieved (e.g., when part of a reference measuring system). Static and dynamic nonlinearities (estimated independently) are vital indices for evaluating performance and suitability of ADCs to be used in such environments. Typically, the estimation of static nonlinearity involves 10-12 h of time or more (for a 12-b ADC) and the acquisition of millions of samples at high input frequencies for dynamic characterization. ADCs with even higher resolution and faster sampling speeds will soon become available. So, there is a need to reduce testing time for evaluating these parameters. This paper proposes a novel and time-efficient method for the simultaneous estimation of static and dynamic nonlinearity from a single test. This is achieved by conceiving a test signal, comprised of a high-frequency sinusoid (which addresses dynamic assessment) modulated by a low-frequency ramp (relevant to the static part). Details of implementation and results on two digitizers are presented and compared with nonlinearities determined by the existing standardized approaches. Good agreement in results and time savings achievable indicates its suitability.

A Proposal for Concurrent Estimation of Static and Dynamic Nonlinearity of ADC

Despite great advances in very large scale integrated-circuit design and manufacturing, performance of even the best available high-speed, high-resolution analog-to-digital converter (ADC) is known to deteriorate while acquiring fast-rising, high-frequency, and nonrepetitive waveforms. Waveform digitizers (ADCs) used in high-voltage impulse recordings and measurements are invariably subjected to such waveforms. Errors resulting from a lowered ADC performance can be unacceptably high, especially when higher accuracies have to be achieved (e.g., when part of a reference measuring system). Static and dynamic nonlinearities (estimated independently) are vital indices for evaluating performance and suitability of ADCs to be used in such environments. Typically, the estimation of static nonlinearity involves 10-12 h of time or more (for a 12-b ADC) and the acquisition of millions of samples at high input frequencies for dynamic characterization. ADCs with even higher resolution and faster sampling speeds will soon become available. So, there is a need to reduce testing time for evaluating these parameters. This paper proposes a novel and time-efficient method for the simultaneous estimation of static and dynamic nonlinearity from a single test. This is achieved by conceiving a test signal, comprised of a high-frequency sinusoid (which addresses dynamic assessment) modulated by a low-frequency ramp (relevant to the static part). Details of implementation and results on two digitizers are presented and compared with nonlinearities determined by the existing standardized approaches. Good agreement in results and time savings achievable indicates its suitability.

Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.

Impact of the Human Bacterial Environment on Mycobacteriosis and Allergy

My work describes two sectors of the human bacterial environment: 1. The sources of exposure to infectious non-tuberculous mycobacteria. 2. Bacteria in dust, reflecting the airborne bacterial exposure in environments protecting from or predisposing to allergic disorders. Non-tuberculous mycobacteria (NTM) transmit to humans and animals from the environment. Infection by NTM in Finland has increased during the past decade beyond that by Mycobacterium tuberculosis. Among the farm animals, porcine mycobacteriosis is the predominant NTM disease in Finland. Symptoms of mycobacteriosis are found in 0.34 % of slaughtered pigs. Soil and drinking water are suspected as sources for humans and bedding materials for pigs. To achieve quantitative data on the sources of human and porcine NTM exposure, methods for quantitation of environmental NTM are needed. We developed a quantitative real-time PCR method, utilizing primers targeted at the 16S rRNA gene of the genus of Mycobacterium. With this method, I found in Finnish sphagnum peat, sandy soils and mud high contents of mycobacterial DNA, 106 to 107 genome equivalents per gram. A similar result was obtained by a method based on the Mycobacterium-specific hybridization of 16S rRNA. Since rRNA is found mainly in live cells, this result shows that the DNA detected by qPCR mainly represented live mycobacteria. Next, I investigated the occurrence of environmental mycobacteria in the bedding materials obtained from 5 pig farms with high prevalence (>4 %) of mycobacteriosis. When I used for quantification the same qPCR methods as for the soils, I found that piggery samples contained non-mycobacterial DNA that was amplified in spite of several mismatches with the primers. I therefore improved the qPCR assay by designing Mycobacterium-specific detection probes. Using the probe qPCR assay, I found 105 to 107 genome equivalents of mycobacterial DNA in unused bedding materials and up to 1000 fold more in the bedding collected after use in the piggery. This result shows that there was a source of mycobacteria in the bedding materials purchased by the piggery and that mycobacteria increased in the bedding materials during use in the piggery. Allergic diseases have reached epidemic proportions in urbanized countries. At the same time, childhood in rural environment or simple living conditions appears to protect against allergic disorders. Exposure to immunoreactive microbial components in rural environments seems to prevent allergies. I searched for differences in the bacterial communities of two indoor dusts, an urban house dust shown to possess immunoreactivity of the TH2-type and a farm barn dust with TH1-activity. The immunoreactivities of the dusts were revealed by my collaborators, in vitro in human dendritic cells and in vivo in mouse. The dusts accumulated >10 years in the respiratory zone (>1.5 m above floor), thus reflecting the long-term content of airborne bacteria at the two sites. I investigated these dusts by cloning and sequencing of bacterial 16S rRNA genes from dust contained DNA. From the TH2-active urban house dust, I isolated 139 16S rRNA gene clones. The most prevalent genera among the clones were Corynebacterium (5 species, 34 clones), Streptococcus (8 species, 33 clones), Staphylococcus (5 species, 9 clones) and Finegoldia (1 species, 9 clones). Almost all of these species are known as colonizers of the human skin and oral cavity. Species of Corynebacterium and Streptococcus have been reported to contain anti-inflammatory lipoarabinomannans and immunmoreactive beta-glucans respectively. Streptococcus mitis, found in the urban house dust is known as an inducer of TH2 polarized immunity, characteristic of allergic disorders. I isolated 152 DNA clones from the TH1-active farm barn dust and found species quite different from those found from the urban house dust. Among others, I found DNA clones representing Bacillus licheniformis, Acinetobacter lwoffii and Lactobacillus each of which was recently reported to possess anti-allergy immunoreactivity. Moreover, the farm barn dust contained dramatically higher bacterial diversity than the urban house dust. Exposure to this dust thus stimulated the human dendritic cells by multiple microbial components. Such stimulation was reported to promote TH1 immunity. The biodiversity in dust may thus be connected to its immunoreactivity. Furthermore, the bacterial biomass in the farm barn dust consisted of live intact bacteria mainly. In the urban house dust only ~1 % of the biomass appeared as intact bacteria, as judged by microscoping. Fragmented microbes may possess bioactivity different from that of intact cells. This was recently shown for moulds. If this is also valid for bacteria, the different immunoreactivities of the two dusts may be explained by the intactness of dustborne bacteria. Based on these results, we offer three factors potentially contributing to the polarized immunoreactivities of the two dusts: (i) the species-composition, (ii) the biodiversity and (iii) the intactness of the dustborne bacterial biomass. The risk of childhood atopic diseases is 4-fold lower in the Russian compared with the Finnish Karelia. This difference across the country border is not explainable by different geo-climatic factors or genetic susceptibilities of the two populations. Instead, the explanation must be lifestyle-related. It has already been reported that the microbiological quality of drinking water differs on the two sides of the borders. In collaboration with allergists, I investigated dusts collected from homes in the Russian Karelia and in the Finnish Karelia. I found that bacterial 16S rRNA genes cloned from the Russian Karelian dusts (10 homes, 234 clones) predominantly represented Gram-positive taxa (the phyla Actinobacteria and Firmicutes, 67%). The Russian Karelian dusts contained nine-fold more of muramic acid (60 to 70 ng mg-1) than the Finnish Karelian dusts (3 to 11 ng mg-1). Among the DNA clones isolated from the Finnish side (n=231), Gram-negative taxa (40%) outnumbered the Gram-positives (34%). Out of the 465 DNA clones isolated from the Karelian dusts, 242 were assigned to cultured validly described bacterial species. In Russian Karelia, animal-associated species e.g. Staphylococcus and Macrococcus were numerous (27 clones, 14 unique species). This finding may connect to the difference in the prevalence of allergy, as childhood contacts with pets and farm animals have been connected with low allergy risk. Plant-associated bacteria and plant-borne 16S rRNA genes (chloroplast) were frequent among the DNA clones isolated from the Finnish Karelia, indicating components originating from plants. In conclusion, my work revealed three major differences between the bacterial communtites in the Russian and in the Finnish Karelian homes: (i) the high prevalence of Gram-positive bacteria on the Russian side and of Gram-negative bacteria on the Finnish side and (ii) the rich presence of animal-associated bacteria on the Russian side whereas (iii) plant-associated bacteria prevailed on the Finnish side. One or several of these factors may connect to the differences in the prevalence of allergy.

Welfare outcomes for 3- and 6-month-old beef calves in a tropical environment castrated surgically or by applying rubber rings

Castration of cattle using rubber rings is becoming increasingly popular due to the perceived ease of the procedure and greater operator safety when compared with surgical castration. Few comparative studies have investigated the effects of different castration methods and calf age on welfare outcomes, particularly in a tropical environment. Thirty Belmont Red (a tropically adapted breed), 3-month-old (liveweight 71–119 kg) and 30, 6-month-old (liveweight 141–189 kg) calves were assigned to a two age × three castration (surgical, ring and sham) treatment factorial study (Surg3, Surg6, Ring3, Ring6, Sham3 and Sham6, n = 10 for each treatment group). Welfare outcomes were assessed post-castration using: behaviour for 2 weeks; blood parameters (cortisol and haptoglobin concentrations) to 4 weeks; wound healing to 5 weeks; and liveweights to 6 weeks. More Surg calves struggled during castration compared with Sham and Ring (P < 0.05, 90 ± 7% vs. 20 ± 9% and 24 ± 10%) and performed more struggles (1.9 ± 0.2, 1.1 ± 0.3 and 1.1 ± 0.3 for Surg, Sham and Ring, respectively), suggesting that surgical castration caused most pain during performance of the procedure. A significant (P < 0.05) time × castration method × age interaction for plasma cortisol revealed that concentrations decreased most rapidly in Sham; the Ring6 calves failed to show reduced cortisol concentrations at 2 h post-castration, unlike other treatment groups. By 7 h post-castration, all treatment groups had similar concentrations. A significant (P < 0.01) interaction between time and castration method showed that haptoglobin concentrations increased slightly to 0.89 and 0.84 mg/mL for Surg and Ring, respectively over the first 3 days post-castration. Concentrations for Surg then decreased to levels similar to Sham by day 21 and, although concentrations for Ring decreased on day 7 to 0.76 mg/mL, they increased significantly on day 14 to 0.97 mg/mL before reducing to concentrations similar to the other groups (0.66 mg/mL) by day 21. Significantly (P < 0.05) more of the wounds of the 3-month compared with the 6-month calves scored as ‘healed’ at day 7 (74% vs. 39%), while more (P = 0.062) of the Surg than Ring scored as ‘healed’ at day 21 (60% vs. 29%). At day 14 there were significantly (P < 0.05) fewer healed wounds in Ring6 compared with other treatment groups (13% vs. 40–60%). Liveweight gain was significantly (P < 0.05) greater in 3-month (0.53 kg/day) than in 6-month calves (0.44 kg/day) and in Sham calves (P < 0.001, 0.54 kg/day), than in Ring (0.44 kg/day) and Surg (0.48 kg/day) calves. Overall, welfare outcomes were slightly better for Surg than Ring calves due to reduced inflammation and faster wound healing, with little difference between age groups.

Welfare outcomes for 3- and 6-month-old beef calves in a tropical environment castrated surgically or by applying rubber rings

Castration of cattle using rubber rings is becoming increasingly popular due to the perceived ease of the procedure and greater operator safety when compared with surgical castration. Few comparative studies have investigated the effects of different castration methods and calf age on welfare outcomes, particularly in a tropical environment. Thirty Belmont Red (a tropically adapted breed), 3-month-old (liveweight 71–119 kg) and 30, 6-month-old (liveweight 141–189 kg) calves were assigned to a two age × three castration (surgical, ring and sham) treatment factorial study (Surg3, Surg6, Ring3, Ring6, Sham3 and Sham6, n = 10 for each treatment group). Welfare outcomes were assessed post-castration using: behaviour for 2 weeks; blood parameters (cortisol and haptoglobin concentrations) to 4 weeks; wound healing to 5 weeks; and liveweights to 6 weeks. More Surg calves struggled during castration compared with Sham and Ring (P < 0.05, 90 ± 7% vs. 20 ± 9% and 24 ± 10%) and performed more struggles (1.9 ± 0.2, 1.1 ± 0.3 and 1.1 ± 0.3 for Surg, Sham and Ring, respectively), suggesting that surgical castration caused most pain during performance of the procedure. A significant (P < 0.05) time × castration method × age interaction for plasma cortisol revealed that concentrations decreased most rapidly in Sham; the Ring6 calves failed to show reduced cortisol concentrations at 2 h post-castration, unlike other treatment groups. By 7 h post-castration, all treatment groups had similar concentrations. A significant (P < 0.01) interaction between time and castration method showed that haptoglobin concentrations increased slightly to 0.89 and 0.84 mg/mL for Surg and Ring, respectively over the first 3 days post-castration. Concentrations for Surg then decreased to levels similar to Sham by day 21 and, although concentrations for Ring decreased on day 7 to 0.76 mg/mL, they increased significantly on day 14 to 0.97 mg/mL before reducing to concentrations similar to the other groups (0.66 mg/mL) by day 21. Significantly (P < 0.05) more of the wounds of the 3-month compared with the 6-month calves scored as ‘healed’ at day 7 (74% vs. 39%), while more (P = 0.062) of the Surg than Ring scored as ‘healed’ at day 21 (60% vs. 29%). At day 14 there were significantly (P < 0.05) fewer healed wounds in Ring6 compared with other treatment groups (13% vs. 40–60%). Liveweight gain was significantly (P < 0.05) greater in 3-month (0.53 kg/day) than in 6-month calves (0.44 kg/day) and in Sham calves (P < 0.001, 0.54 kg/day), than in Ring (0.44 kg/day) and Surg (0.48 kg/day) calves. Overall, welfare outcomes were slightly better for Surg than Ring calves due to reduced inflammation and faster wound healing, with little difference between age groups.

Use of semi-active dampers in seismic mitigation of building structures

This research provides information for providing the required seismic mitigation in building structures through the use of semi active and passive dampers. The Magneto-Rheological (MR) semi-active damper model was developed using control algorithms and integrated into seismically excited structures as a time domain function. Linear and nonlinear structure models are evaluated in real time scenarios. Research information can be used for the design and construction of earthquake safe buildings with optimally employed MR dampers and MR-passive damper combinations.

Vallankumous kotona! : Arkielämän visuaalinen murros 1960-luvun lopussa ja 1970-luvun alussa

Revolution at home! Visual Changes in Everyday Life in Finland in the Late 1960s and Early 1970s The purpose of my research was to investigate the visual changes in private homes in Finland during the 1960s and 1970s. The 1960s is often described as a turning point in Finnish life, a time when the society's previous agricultural orientation began to give way first to an industrial orientation and then, by the end of the 1970s, to a service orientation. My title refers to three elements in the transition period: the question of daily life; the timeframe; and the visual changes observable in private homes, which in retrospect signalled a kind of revolution in the social orientation. Those changes appeared not only in colours and designs but also in the forms and materials of household objects. My premise is that analysing interiors from a historical perspective can reveal valuable information about Finnish society and social attitudes, information that might easily escape attention otherwise. I have used the time-honoured method of collecting narratives. As far back as Aristotle, formulating narratives has been a means of gaining knowledge. By collecting and classifying narratives about the 1960s and 1970s, it is possible to gain new insight into these important decades. The archetypal 1960s narrative, involving student demonstrations and young people's efforts to improve society, is well known. Less well known is the narrative that relates the changes going on in daily life. Substantially the study focuses mainly on fabrics, porcelain ware and the use of plastics. Marimekko's style is especially important when following innovations in the 1950s, 1960s and 1970s. Porcelain production at the Arabia factory was another element that had a great influence on the look of Finnish homes and kitchens; and a further widespread phenomenon of the late 1960s and early 1970s was the use of plastics in many different forms. Further evidence was sought in Anttila department store mail catalogues, which displayed products that were marketed on a large scale, as well as in magazines such as Avotakka. The terminal point of the visual evolution is the real homes, as seen in the questionnaire "Homemade". I have used the 800 pages of the oral history text that respondents of the Finnish Literature Society have written about their first home in the 1960s. I also used archival material on actual homes in Helsinki from the archives of the Helsinki City Museum. The basic story is the elite narrative, which was produced by students in the 1960s. My main narrative from the same time is visual change in everyday life in the late 1960s and early 1970s. I have classified the main narrative of visual change into four subcategories: the narrative of national ideas, the narrative of a better standard of living, the narrative of objects in the culture of everyday life and the narrative of changing colour and form.

Large Low-Frequency Fluctuations in the Velocity of a Driven Vortex Lattice in a Single Crystal of 2H-NbSe2 Superconductor

The driven state of a well-ordered flux line lattice in a single crystal of 2H-NbSe2 in the time domain has revealed the presence of substantial fluctuations in velocity, with large and distinct time periods (similar to seconds). A superposition of a periodic drive in the driven vortex lattice causes distinct changes in these fluctuations. We propose that prior to the onset of the peak effect there exists a heretofore unexplored regime of coherent dynamics, with unexpected behavior in velocity fluctuations.

Contribution of geophysical surveys to groundwater modelling of a porous aquifer in semiarid Niger: An overview

Subsurface geophysical surveys were carried out using a large range of methods in an unconfined sandstone aquifer in semiarid south-western Niger for improving both the conceptual model of water flow through the unsaturated zone and the parameterization of numerical a groundwater model of the aquifer. Methods included: electromagnetic mapping, electrical resistivity tomography (ERT), resistivity logging, time domain electromagnetic sounding (TDEM), and magnetic resonance sounding (MRS). Analyses of electrical conductivities, complemented by geochemical measurements, allowed us to identify preferential pathways for infiltration and drainage beneath gullies and alluvial fans. The mean water content estimated by MRS (13%) was used for computing the regional groundwater recharge from long-term change in the water table. The ranges in permeability and water content obtained with MRS allowed a reduction of the degree of freedom of aquifer parameters used in groundwater modelling.

Vave propagation and bandgaps in a parametrically modulated composite laminate

Wave propagation and its frequency bandgaps in a parametrically modulated composite laminate are reported in this paper. The modulated properties under considerations are due to periodic microstructure, for example honeycomb core sandwich composite, which can be parameterized and homogenized in a suitable scale. Wave equations are derived by assuming a third-order shear deformation theory. Homogenization of the wave equations is carried out in the scale of wavelength. In-plane wave and flexural-shear wave dispersions are obtained for a range of values of a stiffness modulation coefficient (alpha). A clear pattern of stop-bands is observed for alpha >= 4. To validate the band-gap phenomena, we take recourse to time domain response obtained from finite element simulation. As predicted by the proposed analytical technique, a distinct correlation between the chosen frequency band and the simulated wave arrival time and amplitude reduction is found. This promises practical applications of the proposed analytical technique to designing parametrically modulated composite laminate for wave suppression. (C) 2009 Elsevier B.V. All rights reserved.

Electromagnetic signatures of lightning near the HF frequency band

The dissertation deals with remote narrowband measurements of the electromagnetic radiation emitted by lightning flashes. A lightning flash consists of a number of sub-processes. The return stroke, which transfers electrical charge from the thundercloud to to the ground, is electromagnetically an impulsive wideband process; that is, it emits radiation at most frequencies in the electromagnetic spectrum, but its duration is only some tens of microseconds. Before and after the return stroke, multiple sub-processes redistribute electrical charges within the thundercloud. These sub-processes can last for tens to hundreds of milliseconds, many orders of magnitude longer than the return stroke. Each sub-process causes radiation with specific time-domain characteristics, having maxima at different frequencies. Thus, if the radiation is measured at a single narrow frequency band, it is difficult to identify the sub-processes, and some sub-processes can be missed altogether. However, narrowband detectors are simple to design and miniaturize. In particular, near the High Frequency band (High Frequency, 3 MHz to 30 MHz), ordinary shortwave radios can, in principle, be used as detectors. This dissertation utilizes a prototype detector which is essentially a handheld AM radio receiver. Measurements were made in Scandinavia, and several independent data sources were used to identify lightning sub-processes, as well as the distance to each individual flash. It is shown that multiple sub-processes radiate strongly near the HF band. The return stroke usually radiates intensely, but it cannot be reliably identified from the time-domain signal alone. This means that a narrowband measurement is best used to characterize the energy of the radiation integrated over the whole flash, without attempting to identify individual processes. The dissertation analyzes the conditions under which this integrated energy can be used to estimate the distance to the flash. It is shown that flash-by-flash variations are large, but the integrated energy is very sensitive to changes in the distance, dropping as approximately the inverse cube root of the distance. Flashes can, in principle, be detected at distances of more than 100 km, but since the ground conductivity can vary, ranging accuracy drops dramatically at distances larger than 20 km. These limitations mean that individual flashes cannot be ranged accurately using a single narrowband detector, and the useful range is limited to 30 kilometers at the most. Nevertheless, simple statistical corrections are developed, which enable an accurate estimate of the distance to the closest edge of an active storm cell, as well as the approach speed. The results of the dissertation could therefore have practical applications in real-time short-range lightning detection and warning systems.

A silicon micromachined photonic band gap cell, characteristics and an application

A novel PBG cell based on micromachining of Silicon using wet anisotropic etching has been considered. Since this is based on etching of the Silicon substrate, it is amenable to fabrication with standard Silicon processes and integration with millimeter wave circuits. We characterize this kind of PBG cell by full wave simulations using a time domain code. For the purpose of characterization, the scenario of a 50 ohm microstrip line placed on a Silicon substrate which is anisotropically etched to create patterns with sloping walls is considered. This is shown to produce the well known PBG response of stop bands in certain frequency bands. We look at the variation in the transmission coefficient (S-21) response as the number of periods, length based average fill factor and depth of micromachining are varied. One application of a low pass filter has been proposed and simulated results are given.

A new approach for simple and rapid shape measurement of objects with surface discontinuities

A new approach for unwrapping phase maps, obtained during the measurement of 3-D surfaces using sinusoidal structured light projection technique, is proposed. "Takeda's method" is used to obtain the wrapped phase map. Proposed method of unwrapping makes use of an additional image of the object captured under the illumination of a specifically designed color-coded pattern. The new approach demonstrates, for the first time, a method of producing reliable unwrapping of objects even with surface discontinuities from a single-phase map. It is shown to be significantly faster and reliable than temporal phase unwrapping procedure that uses a complete exponential sequence. For example, if a measurement with the accuracy obtained by interrogating the object with S fringes in the projected pattern is carried out with both the methods, new method requires only 2 frames as compared to (log(2)S +1) frames required by the later method.

The Line Spectral Frequency Model of a Finite-Length Sequence

The line spectral frequency (LSF) of a causal finite length sequence is a frequency at which the spectrum of the sequence annihilates or the magnitude spectrum has a spectral null. A causal finite-length sequencewith (L + 1) samples having exactly L-LSFs, is referred as an Annihilating (AH) sequence. Using some spectral properties of finite-length sequences, and some model parameters, we develop spectral decomposition structures, which are used to translate any finite-length sequence to an equivalent set of AH-sequences defined by LSFs and some complex constants. This alternate representation format of any finite-length sequence is referred as its LSF-Model. For a finite-length sequence, one can obtain multiple LSF-Models by varying the model parameters. The LSF-Model, in time domain can be used to synthesize any arbitrary causal finite-length sequence in terms of its characteristic AH-sequences. In the frequency domain, the LSF-Model can be used to obtain the spectral samples of the sequence as a linear combination of spectra of its characteristic AH-sequences. We also summarize the utility of the LSF-Model in practical discrete signal processing systems.