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.

The human ankle is a complex joint, most commonly represented as talocrural and subtalar axes. It is difficult to locate and take in vivo measurements of the ankle joint. There are no instruments for patients lying on a bed or the floor; that can be used in outdoor or remote sites. We have developed a "Turmell-meter" to address these issues. We started with the study of ankle anatomy and anthropometry, then we used the product of exponentials’ formula to visualize the movements. Furthermore, we built a prototype using human proportions and statistics. For pose estimation, we used a trilateration method by applying tetrahedral geometry. Additionally, we computed the axis direction by fitting 3D circles, plotting the manifold and chart as an ankle joint model. We presented the results of simulations, a prototype comprising 45 parts, specifically designed draw-wire sensors, and electronics. Finally, we tested the device by capturing positions and fitting them into the bi-axial ankle model as a Riemannian manifold. The Turmell-meter is intended to be a hardware platform for human ankle joint axis estimation, it is adjustable and has an easy setup. The proposed model has the properties of a chart in a geometric manifold, we provided the details