scholarly journals WAVELET TRANSFORM AND LIP MODEL

2011 ◽  
Vol 21 (2) ◽  
pp. 121 ◽  
Author(s):  
Guy Courbebaisse ◽  
Frederic Trunde ◽  
Michel Jourlin
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
The Other ◽  
Mathematical Framework ◽  
Fast Computation ◽  
Microscope Images ◽  
Computation Algorithm ◽  
Logarithmic Image Processing ◽  
The Fourier Transform

The Fourier transform is well suited to the study of stationary functions. Yet, it is superseded by the Wavelet transform for the powerful characterizations of function features such as singularities. On the other hand, the LIP (Logarithmic Image Processing) model is a mathematical framework developed by Jourlin and Pinoli, dedicated to the representation and processing of gray tones images called hereafter logarithmic images. This mathematically well defined model, comprising a Fourier Transform "of its own", provides an effective tool for the representation of images obtained by transmitted light, such as microscope images. This paper presents a Wavelet transform within the LIP framework, with preservation of the classical Wavelet Transform properties. We show that the fast computation algorithm due to Mallat can be easily used. An application is given for the detection of crests.

The infrared spectrum of CS

1984 ◽  
Vol 62 (12) ◽  
pp. 1414-1419 ◽  
Author(s):  
R. J. Winkel Jr. ◽  
Sumner P. Davis ◽  
Rubén Pecyner ◽  
James W. Brault
Keyword(s):  
Fourier Transform ◽  
Infrared Emission ◽  
Solar Observatory ◽  
Band Head ◽  
The Other ◽  
Fourier Transform Spectrometer ◽  
National Solar Observatory ◽  
Carbon Monosulfide ◽  
Vibration Rotation ◽  
The Fourier Transform

The infrared emission spectrum of carbon monosulfide was observed as a sequence of vibration–rotation bands in the X1Σ+ state, with strong heads of the Δν = 2 sequence degraded to the red. Eight bands of 12C32S were identified, and bands corresponding to the isotope 12C34S were also observed. The most prominent band head, that of the (2–0) band, is at 2585 cm−1, with the other heads spaced approximately 26 cm−1 to smaller wavenumbers. Our data, taken with the Fourier transform spectrometer at the National Solar Observatory (Kitt Peak) include the first reported laboratory observations of the band heads and as many as 200 lines in each band. These observations allowed the calculation of vibrational and rotational constants to higher order than previously reported.

The Study of Tire Pattern Noise by Using Wavelet Transform

2011 ◽  
Vol 105-107 ◽  
pp. 267-270 ◽  
Author(s):  
Sung Wook Hwang ◽  
Jin Hyuk Han ◽  
Ki Duck Sung ◽  
Sang Kwon Lee
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
The Other ◽  
Road Noise ◽  
Signal Process ◽  
The Road ◽  
Pattern Noise ◽  
On The Road ◽  
Non Stationary Signal ◽  
The Relationship

Tire noise is classified by pattern noise and road noise in a vehicle. Especially pattern noise has impulsive characteristics since it is generated by impacting of tire’s block on the road. Therefore, a special signal process is needed other than traditional Fourier Transform, because the characteristic of signal is varying with time. On the other hand, the pattern noise is a kind of non-stationary signal and is related to the impulsive train of pitch sequence of a block. In this paper, Wavelet Transform is applied to verify the impulse signal caused by impact of block and groove and to verify the relationship between the pattern noise and the train of pitch sequence.

The Research and Application of Auto-Focus Based on Hi3515

2012 ◽  
Vol 192 ◽  
pp. 440-444
Author(s):  
Yan Long Liu ◽  
Jian Jun Guo ◽  
Fu Mei Zhao
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
High Speed ◽  
The Other ◽  
Hill Climbing ◽  
Discrete Wavelet ◽  
Key Technology ◽  
Integer Dct ◽  
Auto Focus ◽  
Peak Value

Auto-focus is a key technology for visual presenter, this paper mainly presents how to achieve the function of auto-focus on Hi3515. The 4x4 integer DCT (Discrete Cosine Transform) shown as Eq. (2) was used to indicate whether the system was on accurate focus or not. Because the 4x4 integer DCT not only has the characteristics of single peak value, non-deflection, reliability, high-speed, but also has lower complex computation than the other frequency methods such as FFT(Fast Fourier Transform), DWT (Discrete Wavelet Transform). This paper employed the method of monotonic and blind hill climbing to achieve auto-focus. The result of auto-focus is shown as Fig. 6.

scholarly journals Extracting Features of Transient Electric Fields With Fourier And Wavelet Transform–A Case Study Of Lightning Positive Return Stroke

2021 ◽  
Vol 14 (14) ◽  
pp. 44-50
Author(s):  
Shriram Sharma
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Spectral Density ◽  
Frequency Spectrum ◽  
Electric Fields ◽  
Frequency Range ◽  
Return Stroke ◽  
The Fourier Transform ◽  
Positive Return ◽  
Domain Information

Frequency domain information were extracted from the time domain electric fields pertinent to the lightning positive return strokes applying Fourier transform and Wavelet transform. The electric field radiated by positive ground flashes striking the sea were recorded at 10 ns resolution at a coastal station to minimize the propagation effects. The frequency spectrum of the electric field of positive return strokes were computed applying the Fourier transform technique in the range of 10 kHz to 20 MHz owing to the fact that this range of frequency is of very much interest to the researchers and design engineers. The amplitude of the energy spectral density decreases nearly as ƒ-1 from 10 kHz to about 0.1 MHz and drops nearly as ƒ-2 up to 8 MHz.  Applying the wavelet transform technique, the same positive return strokes are found to radiate in the frequency range of 5.5 to 81 kHz with the average spread distribution of 13.6 kHz to about 30 kHz. From frequency spectrum obtained from the Fourier transform it is difficult to identify as which phase of the return stroke radiates in the higher frequency range and that in the lower frequency range, whereas, one can easily identify from the frequency spectrum obtained with the wavelet transform that ramp portion of the positive return stroke radiates in the larger spectral range as compared to that of initial peak of the return stroke.  Also, from the spectral density map obtained from wavelet transform one can easily observe the contribution of each phase in a range of frequency, which is not possible from the Fourier transform technique. Clearly, the wavelet transform is much more powerful tool to extract the frequency domain information of a non-stationary signal as compared to that of Fourier transform.

The role of amplitude and phase of the Fourier transform in the digital image processing

1991 ◽  
Vol 59 (8) ◽  
pp. 744-748 ◽  
Author(s):  
I. Juvells ◽  
S. Vallmitjana ◽  
A. Carnicer ◽  
J. Campos
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Digital Image Processing ◽  
Digital Image ◽  
The Fourier Transform

Parameters Estimation and Waveform Reconstruction of Chirp Signal Based on FRFT

2014 ◽  
Vol 989-994 ◽  
pp. 3993-3996 ◽  
Author(s):  
Yan Jun Wu ◽  
Gang Fu ◽  
Fei Liu
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Signal Reconstruction ◽  
Parameters Estimation ◽  
The Other ◽  
Fourier Domain ◽  
Chirp Signal ◽  
The Fourier Transform ◽  
Definition Of ◽  
Noisy Background

The fractional Fourier transform (FRFT) is a generalization of the Fourier transform. The article first introduces the definition of FRFT transformation; then analyzed FRFT Chirp signal based on this humble proposed restoration Chirp signal in a noisy background in two ways: one is based on parameter estimation, and the other is based on the scores Fourier domain filtering to achieve signal reconstruction; Finally, simulation verify the feasibility of the above analysis.

scholarly journals Invariants of optimal integration of rapidly oscillatory functions

2021 ◽  
pp. 121-125
Author(s):  
Valeriy Zadiraka ◽  
Liliya Luts ◽  
Inna Shvidchenko
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Computer Technology ◽  
Quadrature Formulas ◽  
Common Elements ◽  
Optimal Integration ◽  
Different Types ◽  
Bessel Transform ◽  
The Fourier Transform ◽  
Computational Resources

The paper presents some common elements (invariants) of optimal integration of rapidly oscillatory functions for the different types of oscillations, in particular, for calculating the Fourier transform from finite functions, wavelet transform, and Bessel transform. Their brief description is given. The application of the invariants allows to increase the potential of quadrature formulas due to the fullest use of apriori information. Invariants form the basis of computer technology of integration of rapidly oscillatory functions with a given accuracy with limited computational resources.

scholarly journals Implementation of FFT Architecture using Various Adders

2019 ◽  
Vol 8 (10) ◽  
pp. 3750-3755
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Orthogonal Frequency Division Multiplex ◽  
Cell Phones ◽  
Frequency Division ◽  
Ripple Carry Adder ◽  
Significant Area ◽  
Area Optimization ◽  
The Fourier Transform

In 1965 a technique called Fast Fourier Transform (FFT) was invented to find the Fourier Transform. This paper compares three architectures, the basic architecture/ non-reduced architecture of FFT, decomposed FFT architecture without retiming and decomposed FFT architecture with retiming. In each case, the adder used will be Ripple Carry Adder (RCA) and Carry Save Adder (CSA). A fast Fourier transform (FFT) calculates the discrete Fourier transform (DFT) or the inverse (IDFT) of a sequence. Fourier analysis transforms a signal from time to frequency domain or vice versa. One of the most burgeoning use of FFT is in Orthogonal Frequency Division Multiplex (OFDM) used by most cell phones, followed by the use in image processing. The synthesis has been carried out on Xilinx ISE Design Suite 14.7. There is a decrease in delay of 0.824% in Ripple Carry Adder and 6.869% in Carry Save Adder, further the reduced architecture for both the RCA and CSA architectures shows significant area optimization (approximately 20%) from the non-reduced counterparts of the FFT implementation.

The Possibility of Improving Scanning Microscope Images by After-Treatment

1968 ◽  
Vol 26 ◽  
pp. 358-358
Author(s):  
M. G. R. Thomson ◽  
A. V. Crewe
Keyword(s):  
Fourier Transform ◽  
Electron Beam ◽  
Fourier Transformation ◽  
Finite Size ◽  
Scanning Microscope ◽  
Constant Intensity ◽  
Low Contrast ◽  
Microscope Images ◽  
The Fourier Transform ◽  
Scanning Electron

The scanning electron microscope is particularly suited to the after-treatment of the image because the information is obtained in serial form, and may be processed using electronic analogue or digital computers. The techniques employed at present include logarithmic amplification, differentiation, and the subtraction of a constant intensity; all of these being intended to render low contrast detail more visible, and so making staining of the specimen less necessary.One further technique is the removal from the final picture of some of the effects of the finite size of the scanning electron beam. Essentially this involves construction of the Fourier transform of the picture, division by the Fourier transform of the scanning spot, and Fourier transformation of this result. It is possible to perform these operations in the case either of a scanning or conventional microscope by digitising the picture, doing the calculations numerically, and reconstructing the improved picture.

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