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The authors present a novel 16/32/64/128-point single-path delay feedback pipeline fast Fourier transform (FFT) architecture targeting the multi-rate and multi-regional orthogonal frequency division multiplexing (MR-OFDM) physical layer of IEEE 802.15.4-g. The proposed FFT architecture employs a mixed-radix algorithm to significantly reduce the number of complex multipliers. It utilises a configurable complex constant multiplier structure instead of a fixed constant multiplier to efficiently conduct $W_{32}$W32, $W_{64}$W64, and $W_{128}$W128 twiddle factor multiplication. A hardware-sharing mechanism has also been formulated to reduce the memory space requirements of the proposed 16/32/64/128-point FFT computation scheme. The proposed design is implemented in Xilinx Virtex-5 and Altera's field-programmable gate array devices. For the computation of 128-point FFT, the proposed mixed-radix FFT architecture significantly reduces the hardware cost in comparison with existing FFT architecture. The proposed FFT architecture is also implemented by adopting the 90 nm complementary metal-oxide-semiconductor technology with a supply voltage of 1 V. Post-synthesis results reveal that the design is efficient in terms of gate count and power consumption, compared to earlier reported designs. The proposed variable-length FFT architecture gate count is 22.3K and consumes 3.832 mW, while the word-length is 12-bits and can be efficiently useful for the IEEE 802.15.4-g standard.

The discrete Fourier transform (DFT) is the most commonly used signal processing method in modern digital sensor design for signal study and analysis. It is often implemented in hardware, such as a field programmable gate array (FPGA), using the fast Fourier transform (FFT) algorithm. The frequency resolution (i.e., frequency bin size) is determined by the number of time samples used in the DFT, when the digital sensor’s bandwidth is fixed. One can vary the sensitivity of a radio frequency receiver by changing the number of time samples used in the DFT. As the number of samples increases, the frequency bin width decreases, and the digital receiver sensitivity increases. In some applications, it is useful to compute an ensemble of FFT lengths; e.g., 2P−j for j=0, 1, 2, …, J, where j is defined as the spectrum level with frequency resolution  2j·Δf. Here Δf is the frequency resolution at j=0. However, calculating all of these spectra one by one using the conventional FFT method would be prohibitively time-consuming, even on a modern FPGA. This is especially true for large values of P; e.g., P≥20. The goal of this communication is to introduce a new method that can produce multi-resolution spectrum lines corresponding to sample lengths  2P−j for all J+1 levels, concurrently, while one long 2P-length FFT is being calculated. That is, the lower resolution spectra are generated naturally as by-products during the computation of the 2P-length FFT, so there is no need to perform additional calculations in order to obtain them.

The rolling element bearing is one of the most critical components in a machine. Vibration signals resulting from these bearings imply important bearing defect information related to the machinery faults. Any defect in a bearing may cause a certain vibration with specific frequencies and amplitudes depending on the nature of the defect. Therefore, the vibration analysis plays a key role for fault detection, diagnosis, and prognosis to reach the reliability of the machines. Although fast Fourier transform for time–frequency analysis is still widely used in industry, it cannot extract enough frequencies without enough samples. If the real frequency does not match fast Fourier transform frequency grid exactly, the spectrum is spreading mostly among neighboring frequency bins. To resolve this drawback, the recent proposed enhanced fast Fourier transform algorithm was reported to improve this situation. This article reviews and compares both fast Fourier transform and enhanced fast Fourier transform for vibration signal analysis in both simulation and practical work. The comparative results verify that the enhanced fast Fourier transform can provide a better solution than traditional fast Fourier transform.

Sparse fast Fourier transform is a new spectrum analysis method based on signal sparse characteristics in recent years. Sparse fast Fourier transform can quickly and accurately process large data by identifying and discarding frequency signals that have no effect on the analysis results. In order to explore the practicality of Sparse fast Fourier transform in aero-engine vibration data analysis, this paper combines the actual flight test vibration data, and studies the sparse fast Fourier transform method and the traditional fast Fourier transform method in terms of spectral characteristics, running time, algorithm stability. By comparison, it can be found that the sparse fast Fourier transform algorithm can greatly improve the efficiency of vibration data analysis while ensuring accuracy.

The ‘Malay’ rebab is a vertical, strung chordophone played similarly to a cello. The rebab strings sit on a bridge. The bridge is placed on a buffalo intestine on the front face. The buffalo intestine surface is pressed by the bridge in such a way that the string tension is not in a fully stable position. A ball of beeswax attached near the bridge mutes the sound reverberations. This investigation was undertaken by analyzing the rebab sound utilizing Fast Fourier Transform (FFT) for spectrum analysis via a PicoScope. The highest note is Bb (Bb3 = 0.231 kHz), played on the 1st string. The intermediate note is F (F3 = 0.172 kHz) played on the 2nd string. The lowest note is C (C3 = 0.135 kHz), played on the 3rd string. For string 1, the fundamental pitches (f0) were 0.222 kHz, 0.237 kHz and 0.224 kHz for rebab A, B, and C, respectively. For string 2, the f0 were 0.174 kHz, 0.177 kHz and 0.168 kHz for rebab A, B and C respectively. For string 3, the f0 were 0.125 kHz, 0.149 kHz and 0.126 kHz for rebab A, B and C respectively. All the strings show non-harmonicity.

In this paper, we established some new operations and formulas of set theory for complex fuzzy sets (CFSs). We introduced the basic results of CFSs with their examples using union, intersection, complement, dot product, complex fuzzy probalistic sum, complex fuzzy bold sum, complex fuzzy bold sum over associative law of union, etc. Moreover, we introduced an algorithm to identify a reference signal out of large number of signal having bigger N Samples received by a digital receiver. Thus, a new model is introduced for measuring the values of the signals in a faster way using CFSs.

The computational characteristics of the fast Fourier transform associated with real-time information signals using traditional techniques is deemed the maximal hardware void with peak power consumption, which is an essential task for any researchers while illustrating the designs of architectures in very large-scale integration circuits. The proposed scheme associated with the pipeline reduces the time of processing at the cost of several registers, and to ensure the efficient contribution for reducing the power, the modification over the complex and critical multiplier has been introduced with minimal internal real-time multipliers, which in turn is reconstructed by canonical signed digit multipliers with the adaptation over the technique of resource sharing. The verification of the results of experimentation has been made. It is inferred that the proposed incorporated design is highly efficient regarding area, speed, and power compared to state-of-the-art techniques.

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv’s distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

It is known that the vibration impulses occurred from a bearing defect are non-periodic but cyclostationary due to the slippage of rollers. The vibration status is often perceived to be synonymous with quality and thus used for predictive maintenance before breakdown. As a result, the analysis of vibration has been used as a key condition tool for fault detection, diagnosis, and prognosis. Any defect in a bearing causes some vibration that consists of certain frequencies depending on the nature and location of the defect. Although many techniques for time–frequency analysis are reported to measure vibration signals, they were found less efficient in practical applications. For this reason, this article develops an on-line bearing vibration detection and analysis using enhanced fast Fourier transform algorithm. The relation between major vibration frequency and dispersed leakage caused from fast Fourier transform can be induced, and it is then used to establish a mathematical model to find major frequencies of vibration signal. Also, the dispersed energy can be collected to retrieve its original gravitational acceleration. The proposed model is developed using a simple arithmetic operation based on fast Fourier transform so that it is feasible for more efficient calculation in impulse signal analysis. Both measurement calibration and practical results verify that the proposed scheme can achieve accurate, rapid, and reliable outcomes.

To improve the dynamic balancing accuracy of the micro‐motor rotor, an unbalanced vibration feature extraction based on an all‐phase fast Fourier transform (APFFT) method is proposed. The amplitude and phase of the signal are extracted by spectrum analysis after windowing the unbalanced signal. The mathematical model is derived to simulate the weak signal of rotor unbalance. The simulation results show that this method is accurate in extracting the weak signal of the rotor under different noise levels. The micro‐motor rotor unbalanced test system is developed for experimental validations. The accuracy and stability of the vibration amplitude and phase extracted by the APFFT are better than the accuracy and stability from the hardware filtering method. The rotor unbalance is reduced by more than 80%. Furthermore, secondary balance of the rotor after the first balance is carried out. The proposed method can still extract the residual unbalance of the rotor. The results demonstrated that the proposed method can achieve a reduction rate of 90% and the accuracy is within 5 mg, verifying the effectiveness of the proposed method for high‐precision rotor dynamic balance.