50 Years of FFT Algorithms and Applications

Kumar, Gaurav; Sahoo, Subhendu Kumar; Meher, Pramod Kumar

doi:10.1007/s00034-019-01136-8

Cited by 47 publications

(24 citation statements)

References 77 publications

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“…We extracted the amplitudes of the fast Fourier transform (FFT) [30] from every face-towards segment, which is a method that has been widely used [31–33]. FFT transformed the sampled function from the time domain to the frequency domain for every dimension.…”

Section: Resultsmentioning

confidence: 99%

Gait can reveal sleep quality with machine learning models

et al. 2019

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Sleep quality is an important health indicator, and the current measurements of sleep rely on questionnaires, polysomnography, etc., which are intrusive, expensive or time consuming. Therefore, a more nonintrusive, inexpensive and convenient method needs to be developed. Use of the Kinect sensor to capture one’s gait pattern can reveal whether his/her sleep quality meets the requirements. Fifty-nine healthy students without disabilities were recruited as participants. The Pittsburgh Sleep Quality Index (PSQI) and Kinect sensors were used to acquire the sleep quality scores and gait data. After data preprocessing, gait features were extracted for training machine learning models that predicted sleep quality scores based on the data. The t-test indicated that the following joints had stronger weightings in the prediction: the Head, Spine Shoulder, Wrist Left, Hand Right, Thumb Left, Thumb Right, Hand Tip Left, Hip Left, and Foot Left. For sleep quality prediction, the best result was achieved by Gaussian processes, with a correlation of 0.78 (p < 0.001). For the subscales, the best result was 0.51 for daytime dysfunction (p < 0.001) by linear regression. Gait can reveal sleep quality quite well. This method is a good supplement to the existing methods in identifying sleep quality more ecologically and less intrusively.

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Section: Resultsmentioning

confidence: 99%

Gait can reveal sleep quality with machine learning models

et al. 2019

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“…In this study, a bandpass filter is proposed to eliminate baseline drift. The implementation of the bandpass filter is based on fast Fourier transform (FFT) [ 35 , 36 , 37 ], and the calculation process is illustrated in Figure 5 A. The originally captured image is firstly transformed from the spatial domain to the frequency domain via an FFT algorithm.…”

Section: Methodsmentioning

confidence: 99%

A Compact High-Speed Image-Based Method for Measuring the Longitudinal Motion of Living Tissues

Yang

Liao

et al. 2020

Sensors

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Intraoperative imaging of living tissue at the cell level by endomicroscopy might help surgeons optimize surgical procedures and provide individualized treatments. However, the resolution of the microscopic image is limited by the motion of living tissue caused by heartbeat and respiration. An active motion compensation (AMC) strategy has been recognized as an effective way to reduce, or even eliminate, the influence of tissue movement for intravital fluorescence microscopy (IVM). To realize the AMC system, a high-speed sensor for measuring the motion of tissues is needed. At present, state-of-the-art commercialized displacement sensors are not suitable to apply in minimally invasive imaging instruments to measure the motion of living tissues because of the size problem, range of measurement or the update rate. In this study, a compact high-speed image-based method for measuring the longitudinal motion of living tissues is proposed. The complexity of the proposed method is the same as that of the traditional wide-field fluorescent microscopy (WFFM) system, which makes it easy to be miniaturized and integrated into a minimally invasive imaging instrument. Experimental results reveal that the maximum indication error, range of measurement and the sensitivity of the laboratory-built experimental prototype is 150 μm, 6 mm and −211.46 mm−1 respectively. Experimental results indicate that the proposed optical method is expected to be used in minimally invasive imaging instruments to build an AMC system.

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“…It is seen that a FFT of size N can be computed through two FFTs of size N/2 and the computation of X(k) requires 2(N/2) 2 + N/2 = N 2 /2 + N/2 complex multiplications and 2[N/2 (N/2 -1)] complex additions. These computing operations are described in the book Proakis et al [1]- [15].…”

Section: Table I Number Of Operations For N/2 Points Fft Internationmentioning

confidence: 99%

“…The computing operations are described when a 8-point FFT is splitted into even and odd parts, i.e., decimated by 2 for the value of N ≥ 3, but all values deducted in the different books are approximately same. (15); When X(k)even and X(k)odd are further splitted, i.e., decimated by two again, then the equation 1is written,…”

Section: Table I Number Of Operations For N/2 Points Fft Internationmentioning

confidence: 99%

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Comparison of Discrete Fourier Transform and Fast Fourier Transform with Reduced Number of Multiplication and Addition Operations

2020

International Journal of Applied Mathematics and Informatics

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Fast Fourier Transform is an advanced algorithm for computing Discrete Fourier Transform efficiently. Although the results available from the operation of Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) are same, but exploiting the periodicity and symmetry property of phase factor Fast Fourier Transform computes the Discrete Fourier Transform using reduced number of multiplication and addition operations. The basic structure used in the operations of Fast Fourier Transform is the Butterfly structure. For the implementation of Fast Fourier Transform the two methods are used such as decimation in time (DIT) and decimation in frequency (DIF). Both the methods give same result but for decimation in time of Fast Fourier Transform bit reversed inputs are applied and for decimation in frequency of Fast Fourier Transform normal order inputs are applied, and the result is reversed again. In this paper, operations for DFT and FFT have been discussed and shown with examples. It is found that generalized formula for FFT have been described same in the books, but the expressions in the intermediate computations for the first decimation and second decimation are different in the various books of Digital Signal Processing. The expressions in the intermediate computation of FFT described in different books are broadly compared in this paper

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50 Years of FFT Algorithms and Applications

Cited by 47 publications

References 77 publications

Gait can reveal sleep quality with machine learning models

Gait can reveal sleep quality with machine learning models

A Compact High-Speed Image-Based Method for Measuring the Longitudinal Motion of Living Tissues

Comparison of Discrete Fourier Transform and Fast Fourier Transform with Reduced Number of Multiplication and Addition Operations

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