Logarithmic Modules Research Articles

A tunable high-performance architecture for enhancement of stream video captured under non-uniform lighting conditions

A novel architecture for performing hue-saturation-value (HSV) domain enhancement of digital color images captured under non-uniform lighting conditions is proposed in this paper for video streaming applications. The approach promotes log-domain computation to eliminate all multiplications, divisions and exponentiations utilizing the compact high-speed logarithmic estimation modules. An optimized quadrant symmetric architecture is incorporated into the design of homomorphic filter for the enhancement of intensity value. Efficient modules are also presented for conversion between RGB and HSV color spaces with tunable H and S components in HSV for more flexible color rendering. The design is able to bring out details hidden in shadow regions of the image and preserve the bright parts with adjustable vividness and color shift for improvement of visual quality while maintaining its consistency. It is capable of producing 187.86 million outputs per second (MOPs) on Xilinx’s Virtex II XC2V2000-4ff896 field programmable gate array (FPGA) at a clock frequency of 187.86 MHz. It can process over 179.1 (1024 × 1024) frames per second, which is very suitable for high definition videos, and consumes approximately 70.7% and 76.8% less hardware resource with 127% and 280% performance boost when compared to the designs with machine learning algorithm in [M.Z. Zhang, M.J. Seow, V.K. Asari, A high performance architecture for color image enhancement using a machine learning approach, International Journal of Computational Intelligence Research – Special Issue on Advances in Neural Networks 2(1) (2006) 40–47], and with separated dynamic and contrast enhancements in [H.T. Ngo, M.Z. Zhang, L. Tao, V.K. Asari, Design of a high performance architecture for real-time enhancement of video stream captured in extremely low lighting environment, International Journal of Embedded Systems: Special Issue on Media and Stream Processing, in press], respectively. This approach also provide 83.4 times performance gain with more consistent fidelity in the results compared to some DSP based implementations (256 × 256 frame size) [G.D. Hines, Z. Rahman, D.J. Jobson, G.A. Woodell, DSP implementation of the retinex image enhancement algorithm, visual information processing XIII, in: Proceedings of the SPIE, vol. 5438, 2004, pp. 13–24; G.D. Hines, Z. Rahman, D.J. Jobson, G.A. Woodell, Single-scale retinex using digital signal processors, in: Proceedings of the Global Signal Processing Conference, September 2004, pp. 1–6] under the reflectance-illuminance category of image enhancement models.

On the triplet vertex algebra [formula omitted

We study the triplet vertex operator algebra W ( p ) of central charge 1 − 6 ( p − 1 ) 2 p , p ⩾ 2 . We show that W ( p ) is C 2 -cofinite but irrational since it admits indecomposable and logarithmic modules. Furthermore, we prove that W ( p ) is of finite-representation type and we provide an explicit construction and classification of all irreducible W ( p ) -modules and describe block decomposition of the category of ordinary W ( p ) -modules. All this is done through an extensive use of Zhu's associative algebra together with explicit methods based on vertex operators and the theory of automorphic forms. Moreover, we obtain an upper bound for dim ( A ( W ( p ) ) ) . Finally, for p prime, we completely describe the structure of A ( W ( p ) ) . The methods of this paper are easily extendable to other W -algebras and superalgebras.

An efficient multiplier-less architecture for 2-D convolution with quadrant symmetric kernels

Design of a high-performance digital architecture for computing 2-D convolution utilizing the quadrant symmetry of the kernels is proposed in this paper. Pixels in the four quadrants of the kernel region with respect to an image pixel are considered simultaneously for computing the partial results of the convolution sum. The new architecture performs computations in the logarithmic domain by utilizing novel multiplier-less log 2 and inverse-log 2 modules. An effective data-handling strategy is developed in conjunction with the logarithmic modules to eliminate the necessity of multipliers in the architecture. The systolic architecture employs parallel and pipelined processing and is able to produce one output every clock cycle. The new design resulted in approximately 40% reduction in hardware resource when compared to the approach of multiplier-based quadrant symmetric architecture. The proposed architecture design is capable of performing convolution operations for 63.3, 1024×1024 frames or 66.4 million outputs per second with 22×22 kernel in a Xilinx's Virtex 2v2000ff896-4 FPGA at maximum clock frequency of 66.4 MHz. The error analysis performed in two image-processing applications of edge detection and noise filtering shows that the hardware implementation with proposed design provides accurate results similar to the software implementation.

Multiplier-less VLSI architecture for real-time computation of multi-dimensional convolution

A VLSI efficient multiplier-less architecture for real-time computation of multi-dimensional convolution is presented in this paper. The new architecture performs computations in the logarithmic domain by utilizing novel multiplier-less log 2 and inverse-log 2 modules which are capable of converting the fraction numbers currently not available in the literature. An effective data handling strategy is developed in conjunction with the logarithmic modules to eliminate the necessity of multipliers in the architecture. The proposed approach reduces hardware resources significantly compared to other approaches maintaining a high degree of accuracy. The architecture is developed as a combined systolic-pipelined design that produces an output in every clock cycle after an initial latency of 93.19 uSec. The architecture is capable of operating with a clock frequency of 99 MHz based on Xilinx’s Virtex II 2v2000ff896-4 FPGA and the throughput of the system is observed as 99 MOPS (million outputs per second). Error analysis performed with the FPGA-based system in the image processing examples of edge detection and noise filtering shows that the proposed architecture produces outputs similar to that obtained by software simulation using Matlab.

Modulation cepstrum discriminating between speech and environmental noise

We introduce modulation cepstrum, a novel representation of an acoustic signal used to distinguish speech signal and environmental noises. The modulation cepstrum was computed by taking the inverse Fourier transform of the logarithmic modulation spectrum, a spectral representation of the temporal dynamics of a sub-band. We calculated the center of gravity of accumulated the modulation cepstrum for eight seconds of an acoustic signal as an index. The experimental result showed that this index enabled us to discriminate between speech and noise signals.

The structure of echolocation sounds used by the big brown bat Eptesicus fuscus: Some consequences for echo processing

Analysis of the sonar emissions produced by five big brown bats (Eptesicus fuscus) during detection and range-discrimination tests show that each bat has a distinctive, “personal” emission. This may help bats distinguish their own emissions from those of others and thereby prevent jamming. Emissions usually contain three harmonics and are strongly frequency swept. Modeling of the sweep shape showed it to be more nearly linear in log time than hyperbolic (linear period modulation), which is optimal for Doppler tolerance. However, logarithmic time and linear period modulation are similar in their Doppler properties, and so bats may suffer little penalty for using a slightly nonoptimal sweep shape. We suggest that bats use logarithmic time modulation rather than linear period modulation in order to simplify signal processing during approach to prey, as this type of modulation stabilizes the filtering of echoes resulting from the bat’s automatic gain control. Likewise, the use of several harmonics in the emission may simplify signal processing of Doppler-shifted echoes by reducing the number of matched filters needed for reception.

Monoparametric models of flow cytometric karyotypes with spreadsheet software

Theoretical flow karyotypes from both plant and mammalian species have been simply modelled using computer spreadsheet software. The models are based upon published values of relative DNA content or relative lengths of each of the chromosomes. From such data, the histograms of chromosome distribution have been simulated for both linear and logarithmic modules of a flow cytometer, and as a function of the coefficient of variation. Simulated and experimental histograms are compard for Nicotiana plumbaginifolia. This readily accessible exercise facilitates the planning and execution of flow cytometric analysis and sorting of chromosomes.

Variable-Length Packetization of μ-Law PCM Speech*

A variable-length packetization process is proposed for logarithmic Pulse Code Modulation (log-PCM)-encoded speech signals. Blocks of W log-PCM words are reduced in size by discarding words on the basis that the receiver can recover the speech with a signal-to-noise ratio (s/n) that is, in general, above a specified value. Specifically, blocks of two hundred fifty-six, 8-bit, μ-law PCM words are left unchanged or reduced to either 214, 205, 192, 171, or 128 words. These blocks are then formulated into packets. The discarded samples at the dispatching terminal are replaced at the receiver by means of adaptive interpolation. We found that by specifying the s/n of the decoded speech in each variable-length packet to be above 27 dB, the reduction in the transmitted speech data was 25 percent, while the recovered speech signal had negligible perceptual degradation.

Comment on the ultraviolet behavior of guage-dependent Green's functions in QCD

The ultraviolet behavior of gauge-dependent covariant Green's functions in QCD is shown to have a discontinuous behavior in both the number of flavors (${n}_{f}$) and the gauge parameter ($\ensuremath{\alpha}$). In particular, we show that for ${n}_{f}<10$ and $\ensuremath{\alpha}\ensuremath{\ne}0$ the behavior is, up to a normalization constant, that of pure free field theory without the usual logarithmic power modulation normally associated with asymptotic freedom.

Multifunction Generation with Logarithmic Pulse Width/Pulse Height Modulation

A new method for the generation of the multifunction operation W = sign(X).Z(X/Y) <R xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</R> is treated in this paper. The method is based on logarithmic function generation by means of logarithmic pulse width modulation, which is pulse width modulation with an exponential carrier signal (Ye <R xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-α</R> X <R xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</R> ). Demodulation is done by feeding the pulse width modulated signal into an integrator which has a logarithmic pulse width modulator in its feedback path. This feedback pulse width modulator has an exponential carrier signal of the form Ze <R xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-α</R> W <R xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</R> . Moreover, this logarithmic pulse width modulator in the feedback path also performs the antilog operation. Hence, multifunction operation is accomplished based on the log-antilog principle. The exponent m is equal to the ratio of the inverse of the time constants of the exponential carrier signals for the input and feedback modulators (m = α <L xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</L> /α <L xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</L> ).Hence, the exponent m can easily be adjusted. Experiments on the analog computer showed that an accuracy of 0.2% of a 1 V full scale was easily obtainable. The frequency response and the signal-to-noise ratio of the system was determined through simulation on a digital computer.

Dynamic strength of metals and logarithmic plasticity module

1. The greater the difference between the limiting propagation rates of plastic Ve and elastic Vu deformation (at degrees of deformation exceeding or equalling 0.01–0.03), the greater the tendency of metals to brittle rupture. 2. The logarithm of the ratio between the limiting propagation rates of elastic and plastic deformation is a linear function of the degree of plastic deformation: $$\log \frac{{V_u }}{{V_{\varepsilon _{pl} } }} = K_V^T \varepsilon _{pl} .$$ 3. The slope KVT (logarithmic plasticity module) depends on the nature of the material and on temperature. 4. The module KVT can be a natural logarithm or a logarithm for the base 10, is a novel characteristic of the material, determines the lag between plastic and elastic deformation at a given temperature, and consequently, determines the stability against brittle rupture. Its value is the higher, the greater the tendency of the material to brittle rupture, and tends to infinity in brittle materials. 5. When the module KVT is known, the limiting strength and plasticity of the material under dynamic loading can be determined.

A Symmetric Triangle-Square Waveform Generator Using a Single Constant Current Source

A symmetric and accurate triangular waveform generating circuit is described. A simple approach in maintaining the symmetry and linearity of triangular waveform is made by using a single constant current generator to alternately charge and discharge a capacitor in a linear manner. This features perfect symmetry of the waveform over a wide frequency range while maintaining amplitude constancy. The circuit also provides square waveforms of equal on and off periods with rise and fall times of the order of a few nanoseconds. Continuous variation of frequency of the waveform generated is possible by changing a single parameter and it is feasible to have linear, exponential, or logarithmic modulation of frequency. It can be used as a triangle-square waveform generator and as a triangle-to-sine converter with the addition of a few components.

Pulse compression by means of linear-period modulation

In applications where large time-bandwidth products and high target speeds combine, linear FM pulse-compression systems used in radar or sonar suffer considerable losses in performance. This paper deals with the problem of wide-band signal optimizintion for the purpose of minimizing signal degradation resulting from Doppler distortion effects. The equation for the instantaneous frequency of a Doppler-transformed signal is derived. The optimum frequency-modulation law is then shown to be the linear period modulation (it can be with equal rights called hyperbolic frequency modulation or logarithmic phase modulation). It is interesting to note that some kinds of bats use this type of signal in their "sonar." Exact and approximate expressions for the spectrum of a linear-period-modulated rectangular pulse are given, and the shape of the compressed output pulse is considered. Signal degradation due to Doppler distortion is shown to be negligible in the case of linear-period-modulation pulses. The influence of pulse envelope on the compressed signal waveform is discussed, and envelope-optimization examples are presented. A possibility for active generation of the optimum signal is mentioned. Significant properties of linear FM and linear-period-modulation pulse compression systems are compared.

A Large Time-Bandwidth Product Pulse-Compression Technique

A pulse-compression radar system which utilizes a linear FM waveform has a theoretical upper limit to the magnitude of its compression ratio or time-bandwidth product. This limit is a function of the observed target's relative radial velocity, and the effect on the return signal is characterized by both a pulse stretching and amplitude reduction if the limit is exceeded. The use of a logarithmic phase-modulation signal waveform and a corresponding ``matched'' receiver possesses the desirable characteristics of the linear FM and in addition has no upper limit to the magnitude of the compression ratio. A single receive pulse-compression filter is matched for all target velocities. A linear FM signal can be thought of as a very good approximation to a logarithmic phase-modulation signal for compression ratios less than the maximum limit. A general method of implementing a variety of systems employing pulse-compression ratios up to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> and utilizing logarithmic phase modulation is presented.

The Gradation of Television Pictures

The requirements of adequate gradation and contrast range in television pictures are discussed in relation to what the human eye can perceive. Thus it is shown that reproduction of the average brightness of the transmitted scene on the receiver screen is unnecessary, besides being possible only at the expense of reduced signal-to-noise ratio and contrast range. Because of the presence of synchronizing pulses, a fraction (15 per cent for the American standard) of the transmitted direct-current component reaches the screen even through pure alternating-current couplings. A comparison is made between the usual assumption of a linear modulation characteristic of the transmitter and linear light-signal characteristic of the receiver and a suggested alternative in which a logarithmic modulation characteristic of the transmitter is combined with an exponential light-signal characteristic of the receiver. The advantages of the latter are higher transmitter economy, measured in signal-to-noise ratio; free choice of contrast in the receiver, the control affecting high lights and shadows evenly; less critical background-light control because it has no effect on contrasts; independence of the contrast ranges of receiver and transmitter; and simpler design of cathode-ray-tube guns.