scholarly journals Continuous window functions for NFFT

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Daniel Potts ◽  
Manfred Tasche
Keyword(s):  
Fourier Transform ◽  
Shape Parameter ◽  
Optimal Choice ◽  
Approximate Algorithm ◽  
Window Function ◽  
Truncation Parameter ◽  
Error Constant ◽  
Window Functions ◽  
Nonequispaced Fast Fourier Transform ◽  
Error Behavior

AbstractIn this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. Here, we consider the continuous Kaiser–Bessel, continuous exp-type, sinh-type, and continuous cosh-type window functions with the same support and same shape parameter. We present novel explicit error estimates for NFFT with such a window function and derive rules for the optimal choice of the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter. For the considered continuous window functions, the error constants have an exponential decay with respect to the truncation parameter.

scholarly journals Uniform error estimates for nonequispaced fast Fourier transforms

2021 ◽  
Vol 19 (2) ◽  
Author(s):  
Daniel Potts ◽  
Manfred Tasche
Keyword(s):  
Error Estimates ◽  
Fourier Transforms ◽  
Approximate Algorithm ◽  
Window Function ◽  
Truncation Parameter ◽  
Compactly Supported ◽  
Window Functions ◽  
Nonequispaced Fast Fourier Transform ◽  
Error Behavior ◽  
Uniform Error Estimates

AbstractIn this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. So far, various window functions have been used and new window functions have recently been proposed. We present novel error estimates for NFFT with compactly supported, continuous window functions and derive rules for convenient choice from the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter.

An analysis of the spectrum of a gravity anomaly over an inclined dike

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1500-1501
Author(s):  
B. N. P. Agarwal ◽  
D. Sita Ramaiah
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
Fourier Spectrum ◽  
Fourier Transforms ◽  
Weighted Average ◽  
Window Function ◽  
Average Spectrum ◽  
Amplitude Spectra ◽  
Distance Data ◽  
The Fourier Transform

Bhimasankaram et al. (1977) used Fourier spectrum analysis for a direct approach to the interpretation of gravity anomaly over a finite inclined dike. They derived several equations from the real and imaginary components and from the amplitude and phase spectra to relate various parameters of the dike. Because the width 2b of the dike (Figure 1) appears only in sin (ωb) term—ω being the angular frequency—they determined its value from the minima/zeroes of the amplitude spectra. The theoretical Fourier spectrum uses gravity field data over an infinite distance (length), whereas field observations are available only for a limited distance. Thus, a set of observational data is viewed as a product of infinite‐distance data with an appropriate window function. Usually, a rectangular window of appropriate distance (width) and of unit magnitude is chosen for this purpose. The Fourier transform of the finite‐distance and discrete data is thus represented by convolution operations between Fourier transforms of the infinite‐distance data, the window function, and the comb function. The combined effect gives a smooth, weighted average spectrum. Thus, the Fourier transform of actual observed data may differ substantially from theoretic data. The differences are apparent for low‐ and high‐frequency ranges. As a result, the minima of the amplitude spectra may change considerably, thereby rendering the estimate of the width of the dike unreliable from the roots of the equation sin (ωb) = 0.

Filtering of the Atmospheric Phase Screen in InSAR Data Using the Nonequispaced Fast Fourier Transform

2021 ◽  
Author(s):  
Riccardo Palama ◽  
Michele Crosetto ◽  
Oriol Monserrat ◽  
Anna Barra ◽  
Maria Cuevas ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Phase Screen ◽  
Nonequispaced Fast Fourier Transform

scholarly journals The Comparison of the Effect of Haimming Window and Blackman Window in the Time-Scaling and Pitch-Shifting Algorithms

2011 ◽  
Vol 1 ◽  
pp. 221-225
Author(s):  
Zhi Wei Lin ◽  
Li Da ◽  
Hao Wang ◽  
Wei Han ◽  
Fan Lin
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Domain Method ◽  
Domain Type ◽  
Domain Method ◽  
Time Scaling ◽  
Window Functions ◽  
Inherent Frequency ◽  
The Time Domain

The real-time pitch shifting process is widely used in various types of music production. The pitch shifting technology can be divided into two major types, the time domain type and the frequency domain type. Compared with the time domain method, the frequency domain method has the advantage of large shifting scale, low total cost of computing and the more flexibility of the algorithm. However, the use of Fourier Transform in frequency domain processing leads to the inevitable inherent frequency leakage effects which decrease the accuracy of the pitch shifting effect. In order to restrain the side effect of Fourier Transform, window functions are used to fall down the spectrum-aliasing. In practical processing, Haimming Window and Blackman Window are frequently used. In this paper, we compare both the effect of the two window functions in the restraint of frequency leakage and the performance and accuracy in subjective based on the traditional phase vocoder[1]. Experiment shows that Haimming Window is generally better than Blackman Window in pitch shifting process.

The Time-Frequency Resolution of Short Time Fourier Transform Based on Multi-Window Functions

2011 ◽  
Vol 214 ◽  
pp. 122-127 ◽  
Author(s):  
Li Hua Wang ◽  
Qi Dong Zhang ◽  
Yong Hong Zhang ◽  
Kai Zhang
Keyword(s):  
Fourier Transform ◽  
Time Resolution ◽  
High Performance ◽  
Frequency Resolution ◽  
Good Time ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Window Functions ◽  
Short Time ◽  
Good Time Resolution

The short-time Fourier transform has the disadvantage that is does not localize time and frequency phenomena very well. Instead the time-frequency information is scattered which depends on the length of the window. It is not possible to have arbitrarily good time resolution simultaneously with good frequency resolution. In this paper, a new method that uses the short-time Fourier transform based on multi-window functions to enhance time-frequency resolution of signals has been proposed. Simulation and experimental results present the high performance of the proposed method.

scholarly journals Selection of window for inter-pulse analysis of simple pulsed radar signal using the short time Fourier transform

2015 ◽  
Vol 4 (4) ◽  
pp. 531 ◽  
Author(s):  
Ashraf Adamu Ahmad ◽  
Abdullahi Daniyan ◽  
David Ocholi Gabriel
Keyword(s):  
Fourier Transform ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Side Lobe ◽  
Radar Signal ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Window Functions ◽  
Pulse Analysis ◽  
Short Time

The electronic intelligence (ELINT) system is used by the military to detect, extract information and classify incoming radar signals. This work utilizes short time Fourier transform (STFT) - time frequency distribution (TFD) for inter-pulse analysis of the radar signal in order to estimate basic radar signal time parameters (pulse width and pulse repetition period). Four well-known windows functions of different and unique characteristics were used for the localization of STFT to determine their various effects on the analysis. The window functions are Hamming, Hanning, Bartlett and Blackman window functions. Monte Carlo simulation is carried out to determine the performance of the signal analysis in presence of additive white Gaussian noise (AWGN). Results show that the lower the transition of main lobe width and higher the peak side lobe, the better the performance of the window function irrespective of time parameter being estimated. This is because 100 percent probability of correct estimation is achieved at signal to noise ratio of about -2dB for Bartlett, 4dB for both Hamming and Hanning, and 9dB for Blackman.

scholarly journals A Minimum Side-Lobe Optimization Window Function and Its Application in Harmonic Detection of an Electricity Gird

Energies ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2619 ◽  
Author(s):  
Zhenhua Li ◽  
Tinghe Hu ◽  
Ahmed Abu-Siada
Keyword(s):  
Detection Method ◽  
Interpolation Method ◽  
Side Lobe ◽  
Detection Algorithm ◽  
Window Function ◽  
Small Range ◽  
Harmonic Detection ◽  
Standard Requirement ◽  
Spectrum Line ◽  
Window Functions

Several window functions are currently applied to improve the performance of the discrete Fourier transform (DFT) harmonic detection method. These window functions exhibit poor accuracy in measuring the harmonic contents of a signal with high-order and weak-amplitude components when the power frequency fluctuates within a small range. In this paper, a minimum side-lobe optimization window function that is aimed at overcoming the abovementioned issue is proposed. Moreover, an improved DFT harmonic detection algorithm based on the six-term minimum side-lobe optimization window and four-spectrum-line interpolation method is proposed. In this context, the minimum side-lobe optimization window is obtained by optimizing the conventional cosine window function according to the optimization rules, and the characteristics of the new proposed window are provided to analyze its performance. Then, the proposed optimization window function is employed to improve the DFT harmonic detection algorithm based on the six-term minimum side-lobe optimization window and four-spectrum-line interpolation method. The proposed technique is used to detect harmonics of an electricity gird in which the six-term minimum side-lobe optimization window is utilized to eliminate the influence of spectrum leakage caused by nonsynchronous sampling of signal processing. The four-spectrum-line interpolation method is employed to eliminate or mitigate the fence effect caused by the inherent measurement error of the DFT method. Simulation experiments in two complex conditions and an experiment test are carried out to validate the improved performance of the proposed window. Results reveal that the six-term minimum side-lode optimization window has the smallest peak side lobe when compared with existing windows, which can effectively reduce the interaction influence of spectrum leakage, improve the measurement accuracy of the DFT harmonic detection method, and meet the standard requirement of harmonic measurement in complex situations.

Statistical Analysis of Strain Images Estimated from Overlapped and Filtered Echo Signals

1997 ◽  
Vol 19 (3) ◽  
pp. 209-220 ◽  
Author(s):  
Mehmet Bilgen ◽  
Michael F. Insana ◽  
Timothy J. Hall ◽  
Pawan Chaturvedi
Keyword(s):  
Time Delay ◽  
Window Function ◽  
Analytical Models ◽  
Image Sharpness ◽  
Sound Beam ◽  
Window Functions ◽  
Experimental Parameters ◽  
Varying Time Delay ◽  
Correlation Window ◽  
Deformation Patterns

The visibility of soft-tissue lesions in strain imaging is currently limited by strain noise from waveform decorrelation. Attempts to balance noise reduction with concerns for contrast and spatial resolution rely on accurate models of time delay covariance for guidance. The most useful analytical models describe the covariance of time-varying time delay estimates in terms of experimental parameters and tissue deformation patterns. Assuming compressed tissue deforms linearly along the axis of the sound beam, we derived a delay covariance expression for echo data with Gaussian spectra that were filtered by a Gaussian window function before correlation. The Gaussian filter reduced the number of assumptions needed to obtain closed-form expressions and minimized the effects of strain within the correlation window. However, strain images are often made using uniformly weighted (sinc filtered) window functions. This paper compares time delay covariances for these two window functions, and describes an equivalent window duration at which delay variances for Gaussian and uniform windows are equal. At the equivalent window length, the analysis can be used to predict strain errors for either window function. Finally, this paper uses the delay covariance data to show how strain noise and image sharpness vary depending on the amount of overlap between correlation windows. For an applied strain less than 5%, an overlap near 50% offers an adequate compromise. These results can guide the selection of experimental parameters for improving the visibility of lesions in strain images.

General Interpolated Fast Fourier Transform: A New Tool for Diagnosing Large Rotating Machinery

2004 ◽  
Vol 127 (4) ◽  
pp. 351-361 ◽  
Author(s):  
D. F. Shi ◽  
L. S. Qu ◽  
N. N. Gindy
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Gas Turbines ◽  
Transient Behavior ◽  
Rotating Machinery ◽  
Vibration Monitoring ◽  
New Approach ◽  
Maintenance Program ◽  
Window Functions ◽  
Run Up

Vibration monitoring and diagnosis of rotating machinery is an important part of a predictive maintenance program to reduce operating and maintenance costs. In order to improve the efficiency and accuracy of diagnosis, the general interpolated fast Fourier transform (GIFFT) is introduced in this paper. In comparison to present interpolated fast Fourier transform, this new approach can deal with any type of window functions and possesses high accuracy and robust performance, especially coping with a small number of sampling points. Then, for the purpose of rotating machinery diagnosis, the harmonic vibration ellipse and orbit is reconstructed based on the GIFFT to extract the features of faults and remove the interference from environmental noise and some irrelevant components. This novel scheme is proving to be very effective and reliable in diagnosing several types of malfunctions in gas turbines and compressors and characterizing of the transient behavior of rotating machinery in the run-up stage.

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