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.

A High Efficient Baseband GNSS Signal Narrow Band Anti-Jamming Approach in Frequency Domain

2014 ◽  
Vol 926-930 ◽  
pp. 1857-1860
Author(s):  
Zhou Zheng ◽  
Meng Yuan Li ◽  
Wei Jiang Wang
Keyword(s):  
Signal Processing ◽  
Frequency Domain ◽  
Narrow Band ◽  
Low Frequency ◽  
Frequency Resolution ◽  
Interference Rejection ◽  
High Efficient ◽  
Digital Down Conversion ◽  
Down Conversion ◽  
Low Rate

In order to reduce the burden of the calculation and the low frequency resolution of the tradition GNSS signal intermediate narrow band anti-jamming method, it introduces a high efficient approach of narrow band interference rejection based on baseband GNSS signal processing. After digital down conversion to baseband and down sampling to a low rate, the interference is removed in frequency domain. According to the theoretical analysis and simulation, it claims that the method can reduce the calculation and increase the detection resolution in frequency domain which will realize a high efficient interference rejection.

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.

scholarly journals Characterization of Frequency Domains of Bandlimited Frame Multiresolution Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1050
Author(s):  
Zhihua Zhang
Keyword(s):  
Frequency Domain ◽  
Multiresolution Analysis ◽  
Background Noise ◽  
Sparse Reconstruction ◽  
Time Frequency ◽  
Processing Data ◽  
Narrowband Signal ◽  
Frequency Domains ◽  
Frame Multiresolution Analysis

Framelets have been widely used in narrowband signal processing, data analysis, and sampling theory, due to their resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information. The well-known approach to construct framelets with useful properties is through frame multiresolution analysis (FMRA). In this article, we characterize the frequency domain of bandlimited FMRAs: there exists a bandlimited FMRA with the support of frequency domain G if and only if G satisfies G⊂2G, ⋃m2mG≅Rd, and G\G2⋂G2+2πν≅∅(ν∈Zd).

Four Band Cardinal Orthogonal Scaling Functions and Wavelets in Higher Dimensions

2013 ◽  
Vol 275-277 ◽  
pp. 2523-2526
Author(s):  
Xin Cheng Zhang
Keyword(s):  
Image Processing ◽  
Signal Processing ◽  
Symmetry Property ◽  
Scaling Function ◽  
Digital Communications ◽  
Higher Dimensions ◽  
Sampling Theorem ◽  
Scaling Functions ◽  
Highpass Filter

Sampling theorem plays an important role in the engineering such as signal processing, image processing, digital communications, and so on. In this paper, the symmetry property of cardinal orthogonal scaling function is discussed. Then, a 4-band cardinal orthogonal scaling function from the relation between the highpass filter coefficients and wavelet is provided. Thus, sampling theorem in the wavelet subspace is obtained.

On scaling functions of non-uniform multiresolution analysis in L2(ℝ)

2019 ◽  
Vol 18 (02) ◽  
pp. 1950055
Author(s):  
Hari Krishan Malhotra ◽  
Lalit Kumar Vashisht
Keyword(s):  
Frequency Domain ◽  
Multiresolution Analysis ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Scaling Functions ◽  
Necessary And Sufficient

The main purpose of this paper is to provide a characterization of scaling functions for non-uniform multiresolution analysis (NUMRA, in short). Some necessary and sufficient conditions for scaling functions of wavelet NUMRA in the frequency domain are also obtained.

The M-Band Symmetric Orthogonal Scaling Function in Higher Dimensions

2013 ◽  
Vol 482 ◽  
pp. 322-325
Author(s):  
Fang Jun Zhang
Keyword(s):  
Image Processing ◽  
Signal Processing ◽  
Scaling Function ◽  
Higher Dimensions ◽  
One Dimension ◽  
Wavelet Theory

Wavelet theory has a key role in signal processing and image processing. In this paper, the characterization of the M-band symmetric orthogonal scaling function is obtained in higher dimensions. Then, a symmetric cardinal orthogonal scaling function is classified. The existing some results in one dimension are generalized to the case of higher dimensions.

Sampling Theorems of Wavelet Subspaces with M Band in Higher Dimensions

2013 ◽  
Vol 709 ◽  
pp. 563-566
Author(s):  
Jin Zhou Li ◽  
Xin Cheng Zhang
Keyword(s):  
Image Processing ◽  
Signal Processing ◽  
Symmetry Property ◽  
Scaling Function ◽  
Higher Dimensions ◽  
Sampling Theorem ◽  
Scaling Functions ◽  
Sampling Theorems ◽  
Highpass Filter ◽  
Wavelet Subspaces

Sampling theorem has a key role in signal processing and image processing. In this paper, the scaling functions with cardinal property are discussed in the dimensions and their symmetry property is classified. Therefore, sampling theorems of wavelet subspaces are obtained. Then, the cardinal orthogonal scaling function with cardinal property is characterized in the dimensions and an equation between the highpass filter coefficients and wavelet samples are got. The existing results are generalized to the case of M band.

The Technology of Line-Spectrum Enhancement Based on Image Processing

2012 ◽  
Vol 429 ◽  
pp. 308-312
Author(s):  
Dai Zhu Zhu ◽  
Wen Hua Huang
Keyword(s):  
Image Processing ◽  
Signal Processing ◽  
Data Analysis ◽  
Frequency Domain ◽  
Signal To Noise Ratio ◽  
Trial Data ◽  
Line Spectrum ◽  
Signal To Noise ◽  
Time Frequency ◽  
Low Snr

Time-frequency spectrogram analysis is a basic method in passive radar and sonar. It′s necessary to enhance the line-spectrum to improve the performance in low SNR(Signal to Noise Ratio) and strong interference presented that wider detecting range and long reacting time can be obtained. The traditional line-spectrum enhancing technology based on signal′s coherence can′t work well in very low SNR, and the performance will drop sharply when the line-spectrums are close in frequencies or the number of line-spectrums increases. A new method which combines image processing with signal processing is brought out to overcome these defects. It can work well when the SNR in frequency domain is close to 0dB,which is much lower than ALE and other traditional technology. The results derived from simulation and trial data analysis show that it′s stable and can be applied in the field with line-spectrums.

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