scholarly journals A New Fast Approximate Hilbert Transform with Different Applications

1970 ◽  
Vol 2 (2) ◽  
Author(s):  
Abdulnasir Hossen
Keyword(s):  
Signal Processing ◽  
Hilbert Transform ◽  
Narrow Band ◽  
Analytic Signal ◽  
Time Signal ◽  
Subband Decomposition ◽  
Single Sideband ◽  
Full Band ◽  
The Hilbert Transform ◽  
Band Signal

A new and fast approximate Hilbert transform based on subband decomposition is presented. This new algorithm is called the subband (SB)-Hilbert transform.  The reduction in complexity is obtained for narrow-band signal applications by considering only the band of most energy.  Different properties of the SB-Hilbert transform are discussed with simulation examples.  The new algorithm is compared with the full band Hilbert transform in terms of complexity and accuracy. The aliasing errors taking place in the algorithm are found by applying the Hilbert transform to the inverse FFT (time signal) of the aliasing errors of the SB-FFT of the input signal.  Different examples are given to find the analytic signal using SB-Hilbert transform with a varying number of subbands.  Applications of the new algorithm are given in single-sideband amplitude modulation and in demodulating frequency-modulated signals in communication systems.Key Words:  Fast Algorithms, Hilbert Transform, Analytic Signal Processing.

The properties of generalized offset linear canonical Hilbert transform and its applications

2017 ◽  
Vol 15 (04) ◽  
pp. 1750031 ◽  
Author(s):  
Shuiqing Xu ◽  
Li Feng ◽  
Yi Chai ◽  
Youqiang Hu ◽  
Lei Huang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Hilbert Transform ◽  
Analytic Signal ◽  
Linear Canonical Transform ◽  
Single Sideband ◽  
Generalized Hilbert Transform ◽  
Offset Linear Canonical Transform ◽  
The Fourier Transform ◽  
The Hilbert Transform

The Hilbert transform is tightly associated with the Fourier transform. As the offset linear canonical transform (OLCT) has been shown to be useful and powerful in signal processing and optics, the concept of generalized Hilbert transform associated with the OLCT has been proposed in the literature. However, some basic results for the generalized Hilbert transform still remain unknown. Therefore, in this paper, theories and properties of the generalized Hilbert transform have been considered. First, we introduce some basic properties of the generalized Hilbert transform. Then, an important theorem for the generalized analytic signal is presented. Subsequently, the generalized Bedrosian theorem for the generalized Hilbert transform is formulated. In addition, a generalized secure single-sideband (SSB) modulation system is also presented. Finally, the simulations are carried out to verify the validity and correctness of the proposed results.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

scholarly journals Combination of HP and LP filters for narrow band antialiasing filter

2021 ◽  
Vol 72 (4) ◽  
pp. 283-286
Author(s):  
Bohumil Brtník
Keyword(s):  
Signal Processing ◽  
Discrete Time ◽  
Operational Amplifier ◽  
Narrow Band ◽  
Time Signal ◽  
Spice Simulation ◽  
Output Resistance ◽  
High Frequencies ◽  
Filter Structure ◽  
Reconstruction Filter

Abstract The discrete time signal processing requires an anti-aliasing filter at the input and a reconstruction filter at output. Some filters of biquads structure are characterized by a decreasing of the attenuation at high frequencies, caused by the final value of the output resistance of the operational amplifier. In this paper we discuss a design of combined BP filter without mentioned decrease. The proposed filter structure was verified by SPICE simulation.

Toward a three‐dimensional automatic interpretation of potential field data via generalized Hilbert transforms: Fundamental relations

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 780-786 ◽  
Author(s):  
Misac N. Nabighian
Keyword(s):  
Hilbert Transform ◽  
Potential Field ◽  
Field Data ◽  
Three Dimensional ◽  
Analytic Signal ◽  
Three Dimensions ◽  
Hilbert Transforms ◽  
Potential Field Data ◽  
Automatic Interpretation ◽  
The Hilbert Transform

The paper extends to three dimensions (3-D) the two‐dimensional (2-D) Hilbert transform relations between potential field components. For the 3-D case, it is shown that the Hilbert transform is composed of two parts, with one part acting on the X component and one part on the Y component. As for the previously developed 2-D case, it is shown that in 3-D the vertical and horizontal derivatives are the Hilbert transforms of each other. The 2-D Cauchy‐Riemann relations between a potential function and its Hilbert transform are generalized for the 3-D case. Finally, the previously developed concept of analytic signal in 2-D can be extended to 3-D as a first step toward the development of an automatic interpretation technique for potential field data.

Frequency domain of weakly translation invariant frame MRAs

2021 ◽  
Author(s):  
Zhihua Zhang
Keyword(s):  
Signal Processing ◽  
Data Analysis ◽  
Frequency Domain ◽  
Scaling Function ◽  
Narrow Band ◽  
Scaling Functions ◽  
Translation Invariant ◽  
Frequency Domains ◽  
Band Signal

Frequency domain of bandlimited frame multiresolution analyses (MRAs) plays a key role when derived framelets are applied into narrow-band signal processing and data analysis. In this study, we give a characterization of frequency domain of weakly translation invariant frame scaling functions [Formula: see text] with frequency domain [Formula: see text]. Based on it, we further study convex and ball-shaped frequency domains. If frequency domain of bandlimited frame scaling function [Formula: see text] is convex and completely symmetric about the origin, then it must be weakly invariant and [Formula: see text]. If [Formula: see text] has a ball-shaped frequency domain, the ball radius must be bounded by [Formula: see text]. These frequency domain characters are owned uniquely by frame scaling functions and not by orthogonal scaling functions.

scholarly journals Phase and the Hilbert transform

2014 ◽  
Vol 33 (10) ◽  
pp. 1164-1166 ◽  
Author(s):  
Steve Purves
Keyword(s):  
Signal Processing ◽  
Data Processing ◽  
Hilbert Transform ◽  
Seismic Data ◽  
Seismic Attributes ◽  
Seismic Data Processing ◽  
Data Set ◽  
The Hilbert Transform

The concept of phase permeates seismic data processing and signal processing in general, but it can be awkward to understand, and manipulating it directly can lead to surprising results. It doesn't help that the word phase is used to mean a variety of things, depending on whether we refer to the propagating wavelet, the observed wavelet, poststack seismic attributes, or an entire seismic data set. Several publications have discussed the concepts and ambiguities (e.g., Roden and Sepúlveda, 1999 ; Liner, 2002 ; Simm and White, 2002 ).

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