Wave-based analog computing is a new computing paradigm heralded as a potentially superior alternative to existing digital computers. Currently, there are optical and low-frequency acoustic analog Fourier transformers. However, the former suffers from phase retrieval issues, and the latter is too physically bulky for integration into CMOS-compatible chips. This paper presents a solution to these problems: the Ultrasonic Fourier Transform Analog Computing System (UFT-ACS), a metalens-based analog computer that utilizes ultrasonic waves to perform Fourier transform calculations. Through wave propagation simulations on MATLAB, the UFT-ACS has been shown to calculate the Fourier transform of various input functions with a high degree of accuracy. Moreover, the optimal selection of parameters through sufficient zero padding and appropriate truncation and bandlimiting to minimize errors is also discussed.

The Wilberforce pendulum is a coupled spring-mass system, where a mass with adjustable moment of inertia is suspended from a helical spring. Energy is converted between the translational and torsional modes, and this energy conversion is most clearly observed at resonance, which occurs when the damped natural frequencies of the two oscillation modes are equal. A theoretical model—with energy losses due to viscous damping accounted for—was formulated using the Lagrangian formalism to predict the pendulum mass’ trajectory. Theoretical predictions were compared with experimental data, showing good agreement. Fourier analysis of both theoretical predictions and experimental data further corroborate the validity of our quantitative model. The dependence of oscillation features like beat frequency and maximum conversion amplitude on relevant parameters such as the initial vertical displacement, initial angular displacement and moment of inertia was also investigated and experimentally verified.

The Fourier transform is a powerful tool that has manifold applications in various disciplines. With the rise of new applications, such as real-time image processing, there is a need for more efficient Fourier transformation methods. This has led to a number of advancements in the field of wave-based analog computing, with the development of the ultrasonic Fourier transform most recently. This paper presents an alternative design to existing ultrasonic Fourier transform analog computing systems, with its relative compactness being the main advantage. In this study, its capabilities and limitations are extensively examined.

No abstract

An electric current flowing through a bimetallic coil heats it up, and due to thermal expansion, the coil either unwinds or winds depending on the direction of net heat transfer and the specific heat capacities of the metals used. This means that by relating a certain measure of its mechanical displacement with current, the bimetallic coil can be used as an ammeter. Thus, a mathematical model relating the current to the time taken by the bimetallic coil to unwind a fixed displacement was developed and verified through experiments, which show a good agreement between theoretical and experimental values.