The emergence of the semiconductor industry in the early 1960s resulted in a significant stage in the evolution of computing when large computational problems, as typified by the application of the discrete Fourier transform (DFT) to the task of spectrum estimation, could suddenly, with the availability of suitable algorithms, be solved in close to real time fashion. This paper provides a brief and meandering account of the history of the DFT’s various solutions, referred to generically as the fast Fourier transform (FFT), the algorithm being chosen for its mathematical elegance, practical significance and ever‑increasing range of applications. We touch upon a few of the most striking personalities, places and events that were encountered along the way and look, in particular, at the recent British contribution to the journey.

Microgrids of varying size and applications are regarded as a key feature of modernizing the power system. The protection of those systems, however, has become a major challenge and a popular research topic for the reason that it involves greater complexity than traditional distribution systems. This paper addresses the issue through a novel approach which utilizes detailed analysis of current and voltage waveforms through windowed fast Fourier and wavelet transforms. The fault detection scheme involves bagged decision trees which use input features extracted from the signal processing stage and selected by correlation analysis. The technique was tested on a microgrid model developed using PSCAD/EMTDS, which is inspired from an operational microgrid in Goldwind Sc. Tech. Co. Ltd, in Beijing, China. The results showed great level of effectiveness to accurately identify faults from other non-fault disturbances, precisely locate the fault and trigger opening of the right circuit breaker/s under different operation modes, fault resistances and other system disturbances.

The two-stage direct thermal contact (2sDTC) process is a rapid dewatering approach for fluid fine tailings (FFT) that is integrated into an oil sands bitumen extraction plant to reduce tailings pond storage and freshwater usage. In the first stage, combustion gas directly contacts atomized FFT, vaporizing water and yielding dry solids and steam-rich hot gas. The second stage involves pond effluent water directly contacting the steam-rich hot gas, recovering heat and condensing moisture. Case studies confirm the technical feasibility of the integration. Benefits include producing a dry discharge, reducing tailings water discharge and conserving an equivalent to 0.2 barrels of freshwater per barrel of oil produced. Most importantly, these benefits incur no additional energy cost to the plant as the integration eliminates the energy penalty and CO2 emissions associated with FFT dewatering. Further capacity enhancement can be achieved by using centrifuge-concentrated FFT. The study reveals that FFT concentrated to ~50 wt% solids could still maintain its pump-ability and be accommodated by the 2sDTC process, leading to an integration which could dewater more FFT annually and conserve more freshwater ( 0.58 barrels per barrel of oil produced), with the sole energy requirement being the power to drive the centrifuge machinery.

Quantitative evaluation of the musical timbre and its variations is important for the analysis of audio recordings and computer-aided music composition. Using the FFT acoustic descriptors and their representation in an abstract timbral space, variations of a sample of monophonic sounds of chordophones (violin, cello) and aerophones (trumpet, transverse flute, and clarinet) sounds are analyzed. It is concluded that the FFT acoustic descriptors allow us to distinguish the timbral variations of the musical dynamics, including crescendo and vibrato. Furthermore, using the Random Forest algorithm, it is shown that the FFT-Acoustic provides a statistically significant classification to distinguish musical instruments, family of instruments, and dynamics. We observed a better behavior for the FFT-Acoustic descriptors when classifying pitch compared to some timbral features of Librosa.

Orbitrap mass spectrometers have been widely used in environmental component analysis . This paper presents an enhanced data acquisition system for in-situ detection of Orbitrap mass spectrometry, which enables in-suit real-time signal processing and analysis for atmospheric molecules with small mass numbers.During previous space atmospheric explorations, quadrupole mass spectrometry (QMS) was usually utilized for analyzing isotopic compositions and complicated compounds in the mixture. However, the inevitable ion scattering and drift during mass transfer, as well as the QMS attenuator loss, result in a relatively lower signal-to-noise ratio of the produced mass spectrum. In recent years, a novel mass spectrometer, called an Orbitrap mass spectrometer, has been gradually accepted and used because of its non-destructive detection ability, high mass resolution, and accuracy. Nevertheless, Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) is preferred over the Orbitrap mass spectrometry for ground applications, especially for detecting low-mass components (e.g. below 50 atomic mass units) due to the former’s superior resolution. As the mass number decreases, the detection system demands a higher sampling and processing rate. Additionally, in ground-based scenarios, mass spectrometry analysis software on computers is often employed to analyze the signals. Therefore, in order to achieve in-situ detection of the space atmospheric environment using the Orbitrap mass spectrometer, this paper proposes a real-time signal acquisition and processing system for mass spectrometry analysis. The system comprises of signal conditioning circuits, analog-to-digital conversion circuits, programmable logic circuits, and related software. These components perform spectrum analysis and process the signal in real-time on hardware components, allowing for high-speed acquisition and analysis of the signals produced by the Orbitrap mass spectrometer.

In this paper, a new approach is proposed for designing ultra-low-power FFT (Fast Fourier Transform) system suitable for use in energy harvesting powered sensors. Bit-serial architecture is adopted to reduce the power consumption of butterfly operation. Simulation results show that, compared with state-of-the-art bit-serial and conventional parallel processors, the proposed technique is superior in terms of silicon area, power consumption, dynamic energy use due to variable precision arithmetic. A sample design of a 64-point FFT shows that the implementation can save about 40% area and 36% leakage power compared with a conventional parallel counterpart, accordingly achieving significant power benefits at a low sample rate and low voltage domain. The dynamic variation of the arithmetic precision can be achieved through a simple modification of the controller with hardware area overhead of 10% gate count.

Microarray gene expression analysis is a powerful technique used in cancer classification and research to identify and understand gene expression patterns that can differentiate between different cancer types, subtypes, and stages. However, microarray databases are highly redundant, inherently nonlinear, and noisy. Therefore, extracting meaningful information from such a huge database is a challenging one. The paper adopts the Fast Fourier Transform (FFT) and Mixture Model (MM) for dimensionality reduction and utilizes the Dragonfly optimization algorithm as the feature selection technique. The classifiers employed in this research are Nonlinear Regression, Naïve Bayes, Decision Tree, Random Forest and SVM (RBF). The classifiers' performances are analyzed with and without feature selection methods. Finally, Adaptive Moment Estimation (Adam) and Random Adaptive Moment Estimation (RanAdam) hyper-parameter tuning techniques are used as improvisation techniques for classifiers. The SVM (RBF) classifier with the Fast Fourier Transform Dimensionality Reduction method and Dragonfly feature selection achieved the highest accuracy of 98.343% with RanAdam hyperparameter tuning compared to other classifiers.

Accurately predicting electrical signals of three-phase Direct Torque Control (DTC) induction motors is crucial for optimal motor performance and effective condition monitoring. However, multiple DTC motors’ complexity and operating conditions’ variations pose challenges for traditional prediction methods. To overcome these challenges, we propose an innovative approach that combines Fast Fourier Transform (FFT) to transform electrical motor simulation data and a Bi-directional Long Short-Term Memory (Bi-LSTM) network to forecast processed motor data. By transforming the DTC induction motor signals from the time domain to the frequency domain, we enhance the capability of learning models to capture subtle differences and generate various input features. The Bi-LSTM model effectively captures both forward and backward dependencies in time series data, enabling accurate prediction of electrical signals. We evaluate the proposed approach using our simulated dataset and compare the proposed method to a state-of-the-art model, the Gated Recurrent Unit (GRU), demonstrating its effectiveness in improving the accuracy and reliability of induction motor signals forecasting. The finding provides valuable insights for advancing motor control and operation in industrial applications.

Fault detection at the early stage of development is of great importance in the maintenance of electric motors. In this regard, Motor Current Signature Analysis (MCSA) is cited in many articles to detect rotor bar fracture. The popularity of MCSA is due to its non-invasive and non-destructive nature, simplicity, and, compatibility with several signal processing tools. The vast variety of the signal processing tools which are commonly used for detecting the broken rotor bar fault is based on the Fast Fourier Transform (FFT) of the stator current signal and analysis of the produced Fourier spectrum; however, because of the small amplitude at the fault frequency relative to the main frequency amplitude, the former cannot be easily discriminated from the latter. Therefore, the peak at the fault frequency is hidden in the shadow of the main frequency component, hence the fault will not be detectable. As a solution to vanish the base frequency component, a method based on the Algebraic Identity of trinomial expansion is proposed in this paper which enables us to display the difference between the frequency of the fault signature and the base frequency. In this article, the fault of the broken rotor bars of the squirrel cage induction motor is revealed by the proposed method. In addition, a frequency weighting technique is presented to magnify the component at the fault related frequency compared to the lower frequencies. To validate the proposed methods, they are examined on the laboratory data obtained from three different operating conditions including the direct online start, the direct torque control, and the scalar control and the results show the ability of the proposed methods in fault detection of an induction motor.

Despite the increasing role of machine learning in various fields, very few works considered artificial intelligence for frequency estimation (FE). This work presents a comprehensive analysis of deep-learning (DL) approach for frequency estimation of single-tones. It is shown that DL network with two layers having a few nodes can estimate frequency more accurately than well-known classical techniques. The study is comprehensive, filling gaps of existing works, where it analyzes error under different signal-to-noise ratios, numbers of nodes, and numbers of input samples; also, under missing SNR information. It is found that DL-based FE is not significantly affected by SNR bias or number of nodes. DL-based approach can work properly using minimal number of input nodes N at which classical methods fail. It is possible for DL to use as little as two layers with two or three nodes each, with complexity of O{N} versus O{Nlog2 (N)} for DFT-based FE, noting that less N is required for DL. Hence, DL can significantly reduce FE complexity, memory, cost, and power consumption, making DL-based FE attractive for resource-limited systems like some IoT sensor applications. Also, reduced complexity opens the door for hardware-efficient implementation using short word-length (SWL) or time-efficient software-defined radio (SDR) communications.