Logarithmic Axis Research Articles

Cascaded warped-FIR and FIR filter structure for loudspeaker equalization with low computational cost requirements

This paper proposes an improved filter structure and methodology for the equalization of loudspeakers and other audio systems. It employs a cascaded structure of a finite impulse response (FIR) filter and a warped-FIR filter in order to obtain the best performance of both types of filters. In the task of loudspeaker equalization, FIR filters achieve excellent resolution and equalization at high frequencies, but at low frequencies the resolution obtained is too poor when evaluated in a logarithmic frequency axis, that could only be improved using high order filters. To solve this lack of resolution at low frequencies, warped-FIR filters have been employed, but at the expense of decreasing the resolution of the filter at high frequencies and increasing the complexity of the filter structure and its computational cost. The proposed combination of both types of filters, combined with the correct selection of their orders, and the @l value for the warped-FIR filter, allows the FIR filter to maintain its good resolution at high frequencies and achieve enough resolution at low frequencies with the warped-FIR filter. In this way, lower order filters with lower computational cost could be obtained than when using FIR or warped-FIR only. This approximation attains a more uniform resolution of the filter when evaluated in octaves, behaving much more like human hearing, than the linear frequency resolution obtained when employing only FIR filters.

Detection of the Left Bundle Branch Block in Continuous Wavelet Transform of ECG Signal

The shapes of wavelet transform of QRS complex in ECG signal for healthy patient and for patient with Left Bundle Branch Block (LBBB) are presented. The Continuous Wavelet Transform (CWT) is used with Morlet wavelet to analyze signals in Time-Frequency domain. In order to present results, CWT diagram is drawn using linear axis for translation in time and logarithmic axis for scale. By comparison of CWT diagrams for healthy and for patient with LBBB it is easy to clearly identify the differences in time-frequency coefficients of ECG signals mentioned. Peaks of the CWT coefficients are in higher frequencies for healthy patients and in lower frequencies for patients with LBBB. By using ECG signal waveform and CWT of the same signal, simultaneously, it would be easier, for cardiologist, to confirm LBBB diagnosis, because the peaks can be read in frequency axis. Ill. 4, bibl. 10 (in English; summaries in English, Russian and Lithuanian).

An F0 contour control model using an F0 contour codebook

AbstractIn this paper the authors propose a fundamental frequency (F0) control model using a representative vector and then propose a method to train the control rules for the model parameters using a speech database. The representative vector is a vector which represents the typical F0 contour for accent phrases, and a set of representative vectors is referred to as a representative vector codebook. The authors generated F0 contour for sentences by performing linear expansion or contraction by mora in line with the length of the phoneme duration and the parallel shift (offset) on the logarithmic frequency axis and then concatenating them for representative vectors selected for each accent phrase. Training the control rules corresponds to extracting from the speech database the representative vector codebook, the representative vector selection rules, and the offset prediction rules. Based on the criterion that the error between the F0 contour for the speech database and the contour generated by the model (the approximation error) be minimized, the control rules were trained. The results of training experiments for the control rules using a speech database consisting of four female speakers showed that an F0 contour close to the original speaker can be generated even for sentences not included in the training data. © 2006 Wiley Periodicals, Inc. Syst Comp Jpn, 38(1): 62–72, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10386

Improved spectrum estimation from digitized time series on a logarithmic frequency axis

We present a practical technique for spectrum and spectral density estimation from long time series by Fourier transforms. We apply Welch’s popular technique of “averaging over modified periodograms” which uses Fourier transforms of fixed length with time-domain windows and overlap. Our technique retains the basic properties of this method, but computes the optimal frequency resolution individually for each Fourier frequency on a logarithmic frequency axis, thus yielding results that are more useful than those of the standard techniques.

Comparison of numerical methods for identification of viscoelastic line spectra from static test data

Viscoelastic line spectra are identified from creep or relaxation data of static experiments with different numerical methods, which may or may not depend on additional informations, to be provided by the user, about the unknown parameters. If the least square method is applied, a non-linear optimization problem with non-negative constraints on the parameters has to be solved. Its solution can be achieved directly by using a gradient-based optimization algorithm like the projected Newton method of Bertsekas. However, appropriate starting values for the unknown parameters must be chosen. The problem can be alleviated by dividing the identification task into three successive steps, based on the Tschebyscheff approximation and the quadratic optimization method by Wolfe. Alternatively, the identification task can be reduced to a quadratic optimization problem, if the user provides additional informations about the distribution of the respondance times of the spectra. The windowing-method of Emri and Tschoegl is based on this assumption. If the line spectrum is assumed to have equally distributed spectrum lines on the logarithmic axis, the identification problem can also be solved by standard regularization techniques, like the truncated singular value decomposition or the Tikhonov regularization. The choice of qualified respondance times as additional information requires some experience with the identification task at hand. Its results may be improved after several reruns of the algorithms. Various applications of the methods to test and experimental data are given and a comparison of their performance is discussed. Copyright © 2005 John Wiley & Sons, Ltd.

Logarithmic temporal axis manipulation and its application for measuring perceptually salient acoustic features of loudspeakers based on multiple observations

A new procedure for measuring impulse responses of loudspeakers in a real world situations were proposed, specifically aiming at extracting perceptually saliant features of the acoustic systems. The procedure consists of two stages. The first stage is an impulse response measurement using specially designed test signals (TSP or M-sequence). Post-processing using a logarithmic transformation of the temporal axis and filtering enables selective elimination of a time-frequency representation of the response that does not consists of components stimulated by the input signal. The second stage is to extract perceptual ‘‘variance’’ based on multi-location observations. The procedure was optimized to provide the best inverse filter in terms of the signal duration of the compensated response. Simulations were conducted to test general behavior of the proposed method. Preliminary tests using a robot controlled measuring stage demonstrated feasibility and effectiveness of the proposed method. [Work partly supported by the grant in aids in scientific research (B) 14380165 and Wakayama University.]

Logarithmic temporal axis manipulation and its application for measuring auditory contributions in F0 control using a transformed auditory feedback procedure

A new parameter extraction procedure based on logarithmic transformation of the temporal axis was applied to investigate auditory effects on voice F0 control to overcome artifacts due to natural fluctuations and nonlinearities in speech production mechanisms. The proposed method may add complementary information to recent findings reported by using frequency shift feedback method [Burnett and Larson, J. Acoust. Soc. Am. 112 (2002)], in terms of dynamic aspects of F0 control. In a series of experiments, dependencies of system parameters in F0 control on subjects, F0 and style (musical expressions and speaking) were tested using six participants. They were three male and three female students specialized in musical education. They were asked to sustain a Japanese vowel /a/ for about 10 s repeatedly up to 2 min in total while hearing F0 modulated feedback speech, that was modulated using an M-sequence. The results replicated qualitatively the previous finding [Kawahara and Williams, Vocal Fold Physiology, (1995)] and provided more accurate estimates. Relations with designing an artificial singer also will be discussed. [Work partly supported by the grant in aids in scientific research (B) 14380165 and Wakayama University.]

The synergy between speech production and perception

Speech intelligibility is known to be relatively unaffected by certain deformations of the acoustic spectrum. These include translations, stretching or contracting dilations, and shearing of the spectrum (represented along the logarithmic frequency axis). It is argued here that such robustness reflects a synergy between vocal production and auditory perception. Thus, on the one hand, it is shown that these spectral distortions are produced by common and unavoidable variations among different speakers pertaining to the length, cross-sectional profile, and losses of their vocal tracts. On the other hand, it is argued that these spectral changes leave the auditory cortical representation of the spectrum largely unchanged except for translations along one of its representational axes. These assertions are supported by analyses of production and perception models. On the production side, a simplified sinusoidal model of the vocal tract is developed which analytically relates a few "articulatory" parameters, such as the extent and location of the vocal tract constriction, to the spectral peaks of the acoustic spectra synthesized from it. The model is evaluated by comparing the identification of synthesized sustained vowels to labeled natural vowels extracted from the TIMIT corpus. On the perception side a "multiscale" model of sound processing is utilized to elucidate the effects of the deformations on the representation of the acoustic spectrum in the primary auditory cortex. Finally, the implications of these results for the perception of generally identifiable classes of sound sources beyond the specific case of speech and the vocal tract are discussed.

Sources of variation in profile analysis. II. Component spacing, dynamic changes, and roving level.

Profile-analysis experiments have typically employed static profiles with constant frequency components spaced at equal intervals along a logarithmic frequency axis. Most periodic, naturally occurring stimuli, however, have components that are harmonically related and vary dynamically in time. One goal of these studies was to determine whether amplitude-increment detection thresholds are different in dynamic, harmonically spaced profiles compared to those for static-log profiles, and why such differences might exist. A second goal was to determine the impact of roving levels (within-trial variation of level). Thresholds for static-log profiles were, on average, 8.7 dB lower than for static-harmonic profiles. A traditional filter-bank model could not account for this result. No consistent effect of dynamic contour (an exponential rising frequency glide) was observed. Thresholds were consistently poorer by 4 to 7 dB when the level was roved, but the differences in thresholds among the different profiles varied little. It is proposed that the higher thresholds observed in static-harmonic profiles may be accounted for by the more intense pitch strength associated with the harmonic profiles.

The synergy between speech production and perception

Speech intelligibility is relatively unaffected by certain spectro-temporal deformations of the signal spectrogram. These include spectral and dynamic translations, stretching or contracting dilations, and shearing of the spectrogram along its temporal or logarithmic frequency axis. We shall argue that this stability results from a synergy between the dynamics and characteristics of the auditory cortex (the receiver) and of the vocal tract (the source). Specifically, on the perception side, neurophysiological evidence suggests that the acoustic spectrogram is represented in the primary auditory cortex along multiple spectro-temporal scales, and that the above deformations correspond to simple translations of the representation of the dynamic acoustic spectrum along these axes. On the production side, these spectro-temporal distortions can be caused by common variations among talkers in speaking rates, slurred articulatory dynamics, vocal tract length, cross-sectional profile, and losses. Using a simplified sinusoid model of the vocal tract, it is possible to relate ‘‘articulatory’’ parameters (e.g., the extent and location of a vocal tract constriction) directly to the formants, and hence to the cortical representation of the spectrum. A similar remarkable synergy exists between the dynamics of perception (e.g., via the perceived spectro-temporal modulation transfer functions) and the speed of articulation and hence the syllabic rates of speech. These results suggest an intimate link between perception and production, a view which offers new insights into the organization of speech phonemes (such as vowels) in terms of different vocal tract configurations.

Chemical class information in ion mobility spectra at low and elevated temperatures

Mobility spectra for organic compounds at temperatures of ∼50°C and 175–250°C were categorized by chemical class using back-propagation neural networks with the successful classification even of chemicals not familiar to the networks. Network performance suggested that chemical class information in spectra at ∼50°C differed from that in spectra at high temperatures, prompting a detailed analysis of regions where chemical class information was located. These regions, or drift times in the mobility spectra, were identified at each temperature using a method of incrementally removing portions of spectra so that the value or structural content of the subtracted region could be seen in comparisons of network performance. At high temperatures (175–250°C), chemical class information was contained in fragment ions located in a narrow region of the spectra with reduced mobilities of 3.06–2.11 cm 2 V −1 s −1 corresponding to the drift times near and encompassing the reactant ions peaks. In contrast, spectra at low temperature (∼50°C) were classified through fragment ions that resided in a broad region of drift time between protonated water clusters and product cluster peaks. This corresponded to reduced mobilities of 1.8–1.2 cm 2 V −1 s −1. These findings suggest that fragmentation in ion mobility spectrometry and other atmospheric pressure chemical ionization based methods, with moisture <1 ppm, may be more common than previously understood. Class specific fragmentation reactions for ions at low temperature have never been described in IMS and became evident only when mobility spectra were formatted with a logarithmic axis for ion intensity.

Lévy dusts, Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension

We study the L\'evy dusts on the line on two accounts: the fluctuations around the average power law that characterizes the mass-radius relation for self-similar fractals, and the statistics of the intervals between strides along the logarithmic axis (their tail distribution is related to the dust's fractal dimension). The L\'evy dusts are suggested as a yardstick of neutral lacunarity, against which non-neutral lacunarity can be measured objectively. A notion of perceived dimension is introduced. We conclude with an application of the Mittag-Leffler statistics to a nonlinear electrical network.

Contrast dependencies of two types of motion aftereffect.

We examined the effects of adaptation and test contrasts on the duration of two types of motion aftereffect (MAE) that presumably reveal different levels of motion processing: MAE with a static test stimulus (static MAE), and that with a counterphasing test stimulus (flicker MAE). MAE duration increased with increasing adaptation contrast. When the test contrast was low, it increased rapidly, and saturated at a low adaptation contrast. When the test contrast was high, however, it gradually increased over a wide range of adaptation contrasts. These complex effects of stimulus contrasts could be well described by a dependency on adaptation contrast normalized by test contrast on a logarithmic axis. Little difference was found between the results for two types of MAE. The interaction between adaptation and test contrasts leads us to reject the idea that the shape of adaptation contrast dependency of MAE duration reflects that of the sensitivity function of motion detecting mechanisms. The results also suggest a functional similarity between the processes underlying static and flicker MAEs with regard to their responses to contrasts.

Analysis of dynamic spectra in ferret primary auditory cortex. I. Characteristics of single-unit responses to moving ripple spectra.

1. Auditory stimuli referred to as moving ripples are used to characterize the responses of both single and multiple units in the ferret primary auditory cortex. Moving ripples are broadband complex sounds with a sinusoidal spectral profile that drift along the logarithmic frequency axis at a constant velocity. 2. Neuronal responses to moving ripples are locked to the phase of the ripple, i.e., they exhibit the same periodicity as that of the moving ripple profile. Neural responses are characterized as a function of ripple velocity (temporal property) and ripple frequency (spectral property). Transfer functions describing the response to these temporal and spectral modulations are constructed. Temporal transfer functions are inverse Fourier transformed to obtain impulse response functions that reflect the cell's temporal characteristics. Ripple transfer functions are inverse Fourier transformed to obtain the response field, a measure analogous to the cell's response area. These operations assume linearity in the cell's response to moving ripples. 3. Transfer functions and other response functions are shown to be fairly independent on the overall level or depth of modulation of the ripple stimuli. Only downward moving ripples were used in this study. 4. The temporal and ripple transfer functions are found to be separable, in that their shapes remain unchanged for different test parameters. Thus ripple transfer functions and response fields remain statistically similar in shape (to within an overall scale factor) regardless of the ripple velocity or whether stationary or moving ripples are used in the measurement. The same stability in shape holds for the temporal transfer functions and the impulse response functions measured with different ripple frequencies. Separability implies that the combined spectrotemporal transfer function of a cell can be written as the product of a purely ripple and a purely temporal transfer functions, and thus that the neuron can be computationally modeled as processing spectral and temporal information in two separate and successive stages. 5. The ripple parameters that characterize cortical cells are distributed somewhat evenly, with the characteristic ripple frequencies ranging from 0.2 to > 2 cycles/octave and the characteristic angular frequency typically ranging from 2 to 20 Hz. 6. Many responses exhibit periodicities in the spectral envelope of the stimulus. These periodicities are of two types. Slow rebounds, not found in the spectral envelope, and with a period of approximately 150 ms, appear with various strengths in approximately 30% of the cells. Fast regular firings with interspike intervals of approximately 10 ms are much less common and appear to correspond to interactions between the component tones that make up a ripple.

Analysis of dynamic spectra in ferret primary auditory cortex. II. Prediction of unit responses to arbitrary dynamic spectra.

1. Responses of single units and multiunit clusters were recorded in the ferret primary auditory cortex (AI) with the use of broadband complex dynamic spectra. Previous work has demonstrated that simpler spectra consisting of single moving ripples (i.e., sinusoidally modulated spectral profiles that travel at a constant velocity along the logarithmic frequency axis) could be used effectively to characterize the response fields and transfer functions of AI cells. 2. A complex dynamic spectral profile can be thought of as being the sum of moving ripple spectra. Such a decomposition can be computed from a two-dimensional spectrotemporal Fourier transform of the dynamic spectral profile with moving ripples as the basis function. 3. Therefore, if AI units were essentially linear, satisfying the superposition principle, then their responses to arbitrary dynamic spectra could be predicted from the responses to single moving ripples, i.e., from the units' response fields and transfer functions (spectral and temporal impulse response functions, respectively). 4. This conjecture was tested and confirmed with data from 293 combinations of moving ripples, involving complex spectra composed of up to 15 moving ripples of different ripple frequencies and velocities. For each case, response predictions based on the unit transfer functions were compared with measured responses. The correlation between predicted and measured responses was found to be consistently high (84% with rho > 0.6). 5. The distribution of response parameters suggests that AI cells may encode the profile of a dynamic spectrum by performing a multiscale spectrotemporal decomposition of the dynamic spectral profile in a largely linear manner.

Body size distribution in aphids: relative surface area of specific plant structures

Abstract.The distribution of the body sizes of British aphids is right‐skewed on a logarithmic axis, as in other taxa. Over the size range 2–5 mm there is a marked decrease in numbers of species with increase in size, which on a log log scale has an exponent of ‐3, The exponent for the right‐hand side of the size distribution of British plants is ‐0.7.The sizes of sixty‐eight species of the genusAphisare weakly correlated with the size of their respective host plants.An aphid's size is strongly correlated with the length of its proboscis, which indicates the depth to which it has to probe plant tissues in order to feed.On average, trees host more species of aphids than either shrubs or herbaceous plants, which appears to be associated with the relative surface area of specific plant structures. The surface area of plants is mainly made of leaves and most species of aphids are leaf feeders. The largest and least numerous species of aphids feed on the branches and trunks of trees, the proportional cover of which is less than that of leaves.Taking into account all the above observations, a functional explanation in terms of the relative surface area of specific plant structures is offered to account for the size diversity curve of aphids.

Representation of the acoustic spectrum in the primary auditory cortex

A fundamental goal in auditory cortical physiology has been to understand how the spectral profile is represented in the firing rate of cortical cells. Recent experimental findings shed light on two basic properties of this representation in AI: (1) Responses to sounds with broadband spectra (such as speech and most environmental sounds) superimpose linearly. Thus if a complex arbitrary spectral profile is viewed as composed of elementary spectral profiles, then AI responses to such a profile can be reconstructed from the sum of the responses to these simpler elementary profiles. This seems to be true both for stationary and dynamic spectra. (2) AI units are rather selective to the spectral and temporal parameters of the acoustic profile. Specifically, when tested with elementary spectral profiles that are sinusoidally shaped against the logarithmic frequency axis (or so called rippled spectra), and that slide against this axis at various velocities, AI units are found to be tuned around different ripple densities, ripple phases, and ripple velocities. The above two findings suggest that AI performs a Fourier-like analysis of the spectral profile into a composite of weighted sinusoidally shaped spectra (ripples). Such an analysis is analogous to that of visual scenes found in the primary visual cortex (VI).

Graphical presentation of trends in rates.

A variety of graphical approaches have been used to visually portray and analyze temporal trends, especially annual rates of change, in disease rates. In reviewing their own work, the authors have found that they could improve on their graphical presentations by choosing an arithmetic or logarithmic scale according to the research question being addressed, by selecting scaling ratios of the axes that allow one to detect specific rates of change, and by using uniform scaling ratios to facilitate comparisons across graphs. Different presentations of the same data can result in different impressions. The authors used rates over a 40-year period to illustrate the concepts involved and to investigate the portrayal of various rates of change. These principles extend to the plotting of odds ratios or relative risks, where the choice of an arithmetic rather than a logarithmic axis also can result in a misleading plot. The authors conclude that a graph should be designed and studied with care, clearly reflect the truth, convey information, and make a point without overemphasizing. For the particular problem addressed here, displaying temporal trends in disease rates, they see advantages in justifiable uniformity. Attention to plotting techniques in the epidemiologic and medical literature should be encouraged.

Spectral shape analysis in the central auditory system

A model of spectral shape analysis in the central auditory system is developed based on neurophysiological mappings in the primary auditory cortex and on results from psychoacoustical experiments in human subjects. The model suggests that the auditory system analyzes an input spectral pattern along three independent dimensions: a logarithmic frequency axis, a local symmetry axis, and a local spectral bandwidth axis. It is shown that this representation is equivalent to performing an affine wavelet transform of the spectral pattern and preserving both the magnitude (a measure of the scale or local bandwidth of the spectrum) and phase (a measure of the local symmetry of the spectrum). Such an analysis is in the spirit of the cepstral analysis commonly used in speech recognition systems, the major difference being that the double Fourier-like transformation that the auditory system employs is carried out in a local fashion. Examples of such a representation for various speech and synthetic signals are discussed, together with its potential significance and applications for speech and audio processing. >

The Influence of Experimental Design and Data Analysis on the Determination of Recovery Kinetics of Radiation Damage between Acute Dose-rate Treatmentsin Vivo

Current interest in determining the rate of recovery of damage between radiation doses in fractionated treatments has resulted in the development of several experimental designs and methods of analysis to address this. One approach is where two or more fractions are given with a varying interval. Isoeffect doses are then determined from the dose-response curves for each interval, and these are plotted on a logarithmic axis against time on a linear scale. An estimate of the rate of dose recovery can then be made if the data show monoexponential or well-defined multiexponential kinetics. However, three problems can be identified in this simple protocol. First, most repair models (e.g. Thames' IR and Curtis' LPL) assume that between two doses loge (cell survival), i.e. underlying effect, not dose itself, recovers exponentially with time. Experimental data support this assumption. Since underlying effect and dose are not linearly related, recovery measured from the change in isoeffect dose can appear substantially slower (depending on dose per fraction) than the true underlying recovery rate of damage. This artifact is avoided by converting dose increments into changes in underlying effect (with the linear-quadratic model) or by measuring underlying effect more directly in 'top-up' experiments. The use of (neutron) top-up experiments is preferred, as it enables recovery between constant X-ray doses per fraction to be studied, and makes no prior assumptions regarding either the shape of the X-ray dose-response curve or how recovery takes place, although the shape of the neutron dose-response curve must be known. Second, plotting log (unrecovered damage) against time can overestimate recovery half-times, because such plots cannot handle negative values and therefore become naturally weighted in favour of the data from the longer time intervals where the difference from complete recovery is smallest. This problem is managed by using nonlinear regression to fit the values of unrecovered damage expressed on a linear scale against interval. Third, experiments using three or more evenly spaced fractions, 'concertina'-style, permit interaction between non-adjacent fractions. If this is not taken account of, then recovery appears to be initially faster and multiexponential, even though the underlying recovery may be actually monoexponential. Thus concertina experiments are poor at resolving the precise shape of recovery-kinetics profiles and are less suited for measuring any dependence of recovery rate on dose per fraction compared with approaches using either just two fractions, or two fractions per day.