On: “The Use of Linear Filtering in Gravity Problems,” by C. C. Ku, W. M. Telford, and S. H. Lim (GEOPHYSICS, December 1971, p. 1174–1203)

Geophysics ◽  
1972 ◽  
Vol 37 (4) ◽  
pp. 704-705
Author(s):  
William D. Hibler
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Boundary Effects ◽  
Linear Filtering ◽  
Filter Function ◽  
Space Domain ◽  
Frequency Space ◽  
Finite Samples ◽  
Space Filter

In a subsection of their paper entitled “Convolution versus Multiplication,” the authors state that when using finite samples of equally spaced data, multiplication of the filter function in the frequency domain and the equivalent convolution in the space domain will yield different outputs. This is normally true but may be circumvented by using a carefully chosen frequency space‐filter function. Such a technique is normally referred to as the aperiodic fast Fourier transform convolution technique (Stockham, 1966), whereas normally multiplication in frequency space yields a periodic convolution with spurious boundary effects.

THE USE OF LINEAR FILTERING IN GRAVITY PROBLEMS

Geophysics ◽  
1971 ◽  
Vol 36 (6) ◽  
pp. 1174-1203 ◽  
Author(s):  
C. C. Ku ◽  
W. M. Telford ◽  
S. H. Lim
Keyword(s):  
Fourier Transform ◽  
Fourier Analysis ◽  
Frequency Domain ◽  
Gibbs Phenomenon ◽  
Downward Continuation ◽  
Main Lobe ◽  
Linear Filtering ◽  
Space Domain ◽  
Actual Field ◽  
High Pass

The technique of Fourier analysis is reviewed and the equivalence and relative advantages of convolution filtering in the space domain and multiplication filtering in the frequency domain are demonstrated with actual field examples. We discuss the design of ideal filters in terms of the relationships between the main lobe and the side lobes. Cut‐and‐try methods appear to favor the hanning window or the hamming window, since these windows minimize the Gibbs phenomenon associated with the downward continuation or high‐pass filtering operation. New sets of coefficients for convolution filtering, based upon Fourier transform theory and the sampling theory, are derived.

scholarly journals Application of two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for 4k fixed format digital image of satellite data in frequency domain processing

2020 ◽  
Vol 149 ◽  
pp. 02010 ◽  
Author(s):  
Mikhail Noskov ◽  
Valeriy Tutatchikov
Keyword(s):  
Fourier Transform ◽  
Numerical Experiment ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
Satellite Data ◽  
Digital Image ◽  
Digital Images ◽  
Two Dimensional ◽  
Fast Fourier Transform Algorithm

Currently, digital images in the format Full HD (1920 * 1080 pixels) and 4K (4096 * 3072) are widespread. This article will consider the option of processing a similar image in the frequency domain. As an example, take a snapshot of the earth's surface. The discrete Fourier transform will be computed using a two-dimensional analogue of the Cooley-Tukey algorithm and in a standard way by rows and columns. Let us compare the required number of operations and the results of a numerical experiment. Consider the examples of image filtering.

scholarly journals Improved Carrier Frequency-Shifting Algorithm Based on 2-FFT for Phase Wrap Reduction

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zhouqiang Zhang ◽  
Feilei Wang ◽  
Guangshen Xu ◽  
Jiangtao Jia ◽  
Xuejing Liu ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Frequency Shift ◽  
Frequency Domain ◽  
Rational Number ◽  
Carrier Frequency ◽  
Integer Number ◽  
Shift Method ◽  
Frequency Shifting

The number of phase wraps that result from the carrier component can be completely eliminated or reduced by first applying a fast Fourier transform (FFT) to the image and then shifting the spectrum to the origin. However, because the spectrum can only be shifted by an integer number, the phase wraps of the carrier component cannot be completely reduced. In this paper, an improved carrier frequency-shifting algorithm based on 2-FFT for phase wrap reduction is proposed which allows the spectrum to be shifted by a rational number. Firstly, the phase wraps are reduced by the conventional FFT frequency shift method. Secondly, the wrapped phase with residual carrier components is filtered and magnified sequentially; the amplified phase is transformed into the frequency domain using an FFT, and then, the wrapped phase with the residual carrier components can be further reduced by shifting the spectrum by a rational number. Simulations and experiments were conducted to validate the efficiency of the proposed method.

scholarly journals High Performing Sentiment Analysis based on Fast Fourier Transform over Temporal Intuitionistic Fuzzy Value

2021 ◽  
Author(s):  
Basanti Pal Nandi ◽  
Amita Jain ◽  
Devendra Kumar Tayal ◽  
Poonam Ahuja Narang
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Sentiment Analysis ◽  
Frequency Domain ◽  
Fuzzy Set ◽  
Opinion Mining ◽  
New Technology ◽  
Intuitionistic Fuzzy Set ◽  
Sentiment Classification ◽  
Intuitionistic Fuzzy

Abstract Sentiment analysis or opinion mining has an extensive area in the field of research. Today we consider the huge amount of structured and unstructured data available in the web for a particular subject to get an opinion. The surplus data handling termed as big data requires some new technology to deal with. This paper considers the requirement of sentiment analysis of such huge data for fast processing. Based on Fast Fourier Transform on Temporal Intuitionistic fuzzy set generated from text, this algorithm (FFT-TIFS) expedites the sentiment classification. Fourier analysis converts a signal from its time domain to its representation in frequency domain. Such frequency domain algorithm on Temporal Intuitionistic fuzzy set is used in Sentiment analysis for the first time. This algorithm is useful for short twitter text, document level as well as sentence level binary sentiment classification. It is tested on aclImdb, Polarity, MR, Sentiment140 and CR dataset which gives an average of 80% accuracy. The proposed method shows significant improvement in required time complexity where the method achieves 17 times faster processing in comparison to sequential Fuzzy C Means(FCM) method and again it is at least 7 times faster than distributed FCM method present in literature. The method presented in this paper has a novel approach towards fastest processing time and suitability of various sizes of the text sentiment analysis.

scholarly journals Periodic Noise Removal in Strain and Natural Images Using 2-D Fast Fourier Transform

2013 ◽  
pp. 90-94
Author(s):  
Mandeep Kaur ◽  
Dinesh Kumar ◽  
Ekta Walia ◽  
Manjit Sandhu
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Noise Removal ◽  
Natural Images ◽  
Periodic Pattern ◽  
Periodic Noise ◽  
Mean Filter ◽  
The Mean

This paper presents a 2-D FFT removal algorithm for reducing the periodic noise in natural and strain images. For the periodic pattern of the artifacts, we apply the 2-D FFT on the strain and natural images to extract and remove the peaks which are corresponding to periodic noise in the frequency domain. Further the mean filter applied to get more effective results. The performance of the proposed method is tested on both natural and strain images. The results of proposed method is compared with the mean filter based periodic noise removal and found that the proposed method significantly improved for the noise removal.

scholarly journals USING WAVELETS WITH A RECTANGULAR AMPLITUDE-FREQUENCY RESPONSE TO FILTER SIGNALS

2021 ◽  
Author(s):  
Vladimir Semenov ◽  
Aleksandr Shurbin
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Fast Fourier Transform ◽  
Frequency Response ◽  
Frequency Domain ◽  
Digital Filters ◽  
Bandpass Filter ◽  
Amplitude Frequency Response

The wavelet transform is the transmission of a signal through a bandpass filter. The design of wavelets with a rectangular amplitude-frequency response makes it possible to obtain almost ideal digital filters. The wavelet transform is calculated in the frequency domain using the fast Fourier transform.

Establishing the State of Operation on Vibration Behavior of the Industrial Robot

2012 ◽  
Vol 186 ◽  
pp. 247-253 ◽  
Author(s):  
Dan Niculescu ◽  
Marek Vagaš ◽  
Adrian Olaru ◽  
Mikuláš Hajduk ◽  
Adrian Ghionea
Keyword(s):  
Fourier Transform ◽  
Life Cycle ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Preventive Maintenance ◽  
Industrial Robot ◽  
Maintenance Management ◽  
Automatic Diagnosis ◽  
Made In

Diagnosis measurement of vibration and noise, should allow monitoring of equipment defects, through a system of preventive maintenance, predictive. Automatic diagnosis of machinery and equipment was made in order to ensure a higher reliability of these and how to obtain a more extended life cycle without the occurrence of defects. Vibrations are always measured in analog format (time domain) and must be transformed into the frequency domain. Therefore Fast Fourier Transform (FFT) method is used to evaluate vibration Almega AX-V6 robot. The application of preventive and predictive maintenance management supports enterprise, because it proves effective, the information you provide in making decisions.

Synthesis and Simplification of Fractal Profile

2011 ◽  
Vol 279 ◽  
pp. 262-265
Author(s):  
Chao Zhou ◽  
Cheng Hui Gao ◽  
Jie Chen ◽  
Lian Feng Lai
Keyword(s):  
Finite Element ◽  
Fourier Transform ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
High Frequency ◽  
Space Domain ◽  
Finite Element Software ◽  
Redundant Data ◽  
Frequency Components

In order to import a synthesized fractal profile into finite element software, the profile synthesized by discrete Fourier transform was studied. The synthesized profile was filtered in frequency domain in order to filter its high frequency components and to make it smooth, and then the chord deviation algorithm was used to reduce its redundant data in space domain. It was found that: after filtering, the profile is smooth but with lots of redundant data; the chord deviation algorithm can simplify the profile which is redundant in space domain; the time needed in the process of importing a profile into finite element software can be reduced greatly after profile simplification.

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