Quasi-analytic multidimensional signals

2013 ◽  
Vol 61 (4) ◽  
pp. 1017-1024
Author(s):  
S.L. Hahn ◽  
K.M. Snopek
Keyword(s):  
Carrier Frequency ◽  
Analytic Signal ◽  
Specific Form ◽  
Unified Theory ◽  
Frequency Space ◽  
Fourier Frequency ◽  
Multidimensional Signals ◽  
Low Pass ◽  
Base Band ◽  
Analytic Signals

Abstract In a recent paper, the authors have presented the unified theory of n-dimensional (n-D) complex and hypercomplex analytic signals with single-orthant spectra. This paper describes a specific form of these signals called quasi-analytic. A quasi-analytic signal is a product of a n-D low-pass (base-band) real (in general non-separable) signal and a n-D complex or hypercomplex carrier. By a suitable choice of the carrier frequency, the spectrum of a low-pass signal is shifted into a single orthant of the Fourier frequency space with a negligible leakage into other orthants. A measure of this leakage is defined. Properties of quasi-analytic signals are studied. Problems of polar representation of quasi-analytic signals and of its lower rank representation are discussed.

Gm-C low-pass-filter designed for a Zero-IF base-band demodulator

2007 ◽  
Author(s):  
H. Barthelemy ◽  
S. Bourdel ◽  
N. Dehaese ◽  
J. Gaubert ◽  
G. Bas
Keyword(s):  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Base Band

scholarly journals A Novel Receiving and Extraction Method for Echoes of Multistatic Sonar

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Lanyong Zhang ◽  
Yixuan Du ◽  
Bing Li
Keyword(s):  
Carrier Frequency ◽  
Extraction Technology ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Correlation Processing ◽  
Low Pass ◽  
Band Pass ◽  
Simulation Results ◽  
Channelized Receiver ◽  
Low Pass Filters

Multiple carrier frequency detecting signals are transmitted simultaneously by multiple transmitters in multistatic sonar. The echoes mixed with different carrier frequency in the receiver. The different carrier frequency echoes must be separated from one another before features of echoes are extracted in the receiver. Such a problem can be solved by band-pass and low-pass filters. But the amount of operation by this way is too large for real-time realization. Thus this paper presents the technique of channelized receiver based on multiphase filter and the receiving schemes of echo. The proposed receiver has a smaller amount of operation compared to low-pass filter. At last, the feature extraction technology correlation processing and FDWT are introduced. In order to verify the feasibility of this scheme in multistatic sonar, the extracted features of original echo are contrasted with those of processed echo via simulation. Simulation results show that the proposed receiver provides considerable performance.

scholarly journals Sensitivity to Envelope Interaural Time Difference: Models of Diverse LSO Neurons

2020 ◽  
Author(s):  
Andrew Brughera ◽  
Jimena A. Ballestero ◽  
David McAlpine
Keyword(s):  
Carrier Frequency ◽  
Human Performance ◽  
Interaural Time Difference ◽  
Low Frequency ◽  
Performance Model ◽  
Time Difference ◽  
Half Wave ◽  
Low Pass ◽  
Behavioral Sensitivity ◽  
Modulation Rate

AbstractA potential auditory spatial cue, the envelope interaural time difference (ITDENV) is encoded in the lateral superior olive (LSO) of the brainstem. Here, we explore computationally modeled LSO neurons, in reflecting behavioral sensitivity to ITDENV. Transposed tones (half-wave rectified low-frequency tones, frequency-limited, then multiplying a high-frequency carrier) stimulate a bilateral auditory-periphery model driving each model LSO neuron, where electrical membrane impedance low-pass filters the inputs driven by amplitude-modulated sound, limiting the upper modulation rate for ITDENV sensitivity. Just-noticeable differences in ITDENV for model LSO neuronal populations, each distinct to reflect the LSO range in membrane frequency response, collectively reproduce the largest variation in ITDENV sensitivity across human listeners. At each stimulus carrier frequency (4-10 kHz) and modulation rate (32-800 Hz), the top-performing model population generally reflects top-range human performance. Model neurons of each speed are the top performers for a particular range of modulation rate. Off-frequency listening extends model ITDENV sensitivity above 500-Hz modulation, as sensitivity decreases with increasing modulation rate. With increasing carrier frequency, the combination of decreased top membrane speed and decreased number of model neurons capture decreasing human sensitivity to ITDENV.

Prestack seismic data reconstruction and denoising by orientation-dependent tensor decomposition

Geophysics ◽  
2020 ◽  
pp. 1-66
Author(s):  
Quézia Cavalcante ◽  
Milton J. Porsani
Keyword(s):  
Covariance Matrix ◽  
Seismic Data ◽  
Missing Values ◽  
Tensor Decomposition ◽  
Low Rank ◽  
Eigenvalue Decomposition ◽  
Data Reconstruction ◽  
Frequency Space ◽  
Multidimensional Signals ◽  
Seismic Data Reconstruction

Multidimensional seismic data reconstruction and denoising can be achieved by assuming noiseless and complete data as low-rank matrices or tensors in the frequency-space domain. We propose a simple and effective approach to interpolate prestack seismic data that explores the low-rank property of multidimensional signals. The orientation-dependent tensor decomposition represents an alternative to multilinear algebraic schemes. Our method does not need to perform any explicit matricization, only requiring to calculate the so-called covariance matrix for one of the spatial dimensions. The elements of such a matrix are the inner products between the lower-dimensional tensors in a convenient direction. The eigenvalue decomposition of the covariance matrix provides the eigenvectors for the reduced-rank approximation of the data tensor. This approximation is used for recovery and denoising, iteratively replacing the missing values. We present synthetic and field data examples to illustrate the method's effectiveness for denoising and interpolating 4D and 5D seismic data with randomly missing traces.

Amplitude spaces of mono-components from Blaschke products and an intrinsic multiresolution analysis

2020 ◽  
Vol 18 (06) ◽  
pp. 2050051
Author(s):  
Qiuhui Chen ◽  
Luoqing Li ◽  
Weibin Wu
Keyword(s):  
Multiresolution Analysis ◽  
Phase Modulation ◽  
Real Variable ◽  
Finite Energy ◽  
Analytic Signal ◽  
Blaschke Products ◽  
Frequency Components ◽  
The Hilbert Transform ◽  
Complex Valued ◽  
Analytic Signals

A mono-component is a real-variable and complex-valued analytic signal with nonnegative frequency components. The amplitude of an analytic signal is determined by its phase in a canonical amplitude-phase modulation. This paper investigates the amplitude spaces of analytic signals in terms of the Blaschke products with zeros in [Formula: see text]. It is proved that these amplitude spaces are invariant under the Hilbert transform and form a multiresolution analysis in the Hilbert space of signals with finite energy.

An analysis of 3-D analytic signal

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 531-536 ◽  
Author(s):  
N. L. Mohan ◽  
L. Anand Babu
Keyword(s):  
Magnetic Field ◽  
Andhra Pradesh ◽  
Field Data ◽  
Analytic Signal ◽  
Vertical Magnetic Field ◽  
Gridded Data ◽  
Magnetic Field Data ◽  
Derivatives Of ◽  
Analytic Signals ◽  
Godavari Basin

The mathematical and physical basis of defining the 3-D analytic function and the corresponding analytic signal is critically examined, and it is proved that 3-D analytic signals based on (1) scalar and (2) vector additions of the horizontal derivatives of the total magnetic fields are completely identical. Two sets of simulated gridded data are considered, and 3-D analytic signals are computed using both scalar and vector additions and are found to be identical. The equality of scalar and vector additions of 3-D analytic signals is further demonstrated with the help of gridded‐surface vertical magnetic field data from the Krishna‐Godavari Basin, Andhra Pradesh, India.

Analytic signals of gravity gradient tensor and their application to estimate source location

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. I59-I74 ◽  
Author(s):  
Majid Beiki
Keyword(s):  
Analytic Signal ◽  
Three Dimensions ◽  
Gravity Gradient ◽  
Automatic Identification ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Signal Functions ◽  
First Vertical Derivative ◽  
Tensor Data ◽  
Analytic Signals

The analytic signal concept can be applied to gravity gradient tensor data in three dimensions. Within the gravity gradient tensor, the horizontal and vertical derivatives of gravity vector components are Hilbert transform pairs. Three analytic signal functions then are introduced along [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-directions. The amplitude of the first vertical derivative of the analytic signals in [Formula: see text]- and [Formula: see text]-directions enhances the edges of causative bodies. The directional analytic signals are homogenous and satisfy Euler’s homogeneity equation. The application of directional analytic signals to Euler deconvolution on generic models demonstrates their ability to locate causative bodies. One of the advantages of this method is that it allows the automatic identification of the structural index from solving three Euler equations derived from the gravity gradient tensor for a collection of data points in a window. The other advantage is a reduction of interference effects from neighboring sources by differentiation of the directional analytic signals in [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-directions. Application of the method is demonstrated on gravity gradient tensor data in the Vredefort impact structure, South Africa.

2FSK Signal Generator Based on AT89C51 Microcontroller

2013 ◽  
Vol 722 ◽  
pp. 260-264
Author(s):  
Xue Fei Gao ◽  
Yong Li An
Keyword(s):  
Second Order ◽  
Signal Generator ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Output Side ◽  
Base Band ◽  
Band Signal

In order to simplify the devices used for generating the 2FSK signal, a 2FSK signal generator based on AT89C51 microcontroller is proposed in this paper. A digital base band signal is inputted to the microcontroller through one of I/O ports. Then microcontrollers program is executed, which are designed for generating PWM signals according to the sine waveforms corresponding with 2FSK signals required. Consequently, an appropriate PWM signal is outputted from another I/O port. This PWM signal is sent into a simple second order passive low-pass filter, and the 2FSK signal can be obtained on the output side of the filter. The 2FSK signal generator makes full use of the resources of the microcontroller, and as a result, it is simple, easy to use, economical and reliable.

A NOTE ON ANALYTIC SIGNALS WITH NONLINEAR PHASE

2009 ◽  
Vol 07 (05) ◽  
pp. 711-720 ◽  
Author(s):  
SHOUYIN CHEN
Keyword(s):  
Information Processing ◽  
Instantaneous Frequency ◽  
Basic Concept ◽  
Analytic Signal ◽  
Analytic Representation ◽  
Nonlinear Phase ◽  
Band Limited ◽  
Instantaneous Frequencies ◽  
Analytic Signals

Instantaneous frequency, defined as the derivative of the phase of a complex analytic representation of the signal, is a basic concept and plays an important role in communication and information processing. It is not unusual to expect that the instantaneous frequency of an analytic signal is nonnegative. In this note, we exhibit new families of analytic signals with band-limited amplitudes and positive nonlinear instantaneous frequencies. The structures of analytic signals with band-limited amplitude and rational as well as linear plus periodic instantaneous frequencies have been analyzed.

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