Occupancy maps are used in automotive driving applications to understand the scene around the vehicle using data from sensors like LiDAR and/or radar on vehicles. In state-of-the-art work, pattern-coupled sparse Bayesian learning (PCSBL) was used to estimate the occupancy map by leveraging spatial dependencies across grids in the map for both single modalities and the fusion of multiple modalities. The PCSBL method, however, has high computational complexity, making real-time implementation challenging for large-scale grid maps. To address this limitation, we propose several methods to improve the computational efficiency of PCSBL while maintaining mapping accuracy. First, we utilize a precomputed lookup table to accelerate selection matrix construction. Second, we implement adaptive resolution reduction based on sensor measurements. Third, we develop two novel methods that exploit the narrow angular interactions between measurements and the map regions to enhance computational efficiency. The first method partitions measurements into spatially disjoint submaps that enable parallel processing. The second method exploits the angular structure to impose a block structure on the selection matrix, reducing computational overhead. Experiments on the nuScenes and RADIATE public datasets show that the presented methods reduce computational costs compared to the benchmark PCSBL and fusionbased PCSBL methods while preserving detection accuracy. ... Read more

The growing prevalence of Artificial Intelligence (AI) applications has led to the development of specialized hardware accelerators optimized for performance and energy efficiency. One such accelerator is the Ryzen Neural Processing Unit (NPU), integrated into AMD’s Ryzen AI processors. While primarily designed for AI workloads, this thesis investigates the potential of repurposing the Ryzen NPU for Digital Signal Processing (DSP) applications, with a focus on radio astronomy. Using the All-Sky Imaging Algorithm from the LOFAR telescope system as a case study, the research evaluates whether the NPU can meet the real-time data processing demands imposed by LOFAR's 10 Hz data generation rate.

Four implementations of the algorithm were developed: three using the MLIR-AIE toolchain and one using the TINA framework. These implementations explored various parallelization and pipelining strategies to optimize performance while ensuring correctness and minimal power consumption. Experimental evaluations revealed up to a 77.4× speedup over a CPU baseline and a 2.84× speedup over a GPU implementation. Notably, three of the four implementations met the 10 Hz real-time requirement. All implementations yielded accurate results, with only minor variations due to differences in data types.

Although power consumption data for the NPU implementations was unavailable, the performance gains underscore the Ryzen NPU's potential for non-AI workloads. This thesis provides a proof of concept for DSP acceleration on the Ryzen NPU, contributes a new layer to the TINA toolchain, and offers insights for future application development. ... Read more

This thesis presents the design and implementation of a motion control system intended for a real-time vision-based tracking application. The goal was to track a coloured, free-falling water droplet using lowcost hardware. For initial system verification, a coloured splash ball was used as a proxy target, chosen for its higher visibility and consistent shape. The system integrated a Raspberry Pi 5 with a Raspberry Pi HQ Camera and a Pimoroni PIM183 pan–tilt unit for vertical target tracking. A PD controller adjusted the tilt angle based on positional data to track and centre the target. To compensate for approximately 100 ms of actuation latency, along with additional delays introduced by processing and computation, the PD controller used predicted target positions. These were provided by an Extended Kalman Filter, which was configured to forecast motion 160 ms ahead. Experimental results showed that the splash ball remained in view for approximately 40–50% of its fall duration. Accurate centring was not achieved, as delays in actuator response limited the system’s ability to keep pace with the high velocity of the target. Furthermore, water droplet tracking proved to be infeasible, as the detection system could not detect such small targets. These findings indicate that, due to hardware-induced delays, the system was unable to achieve stable tracking of high-velocity targets. ... Read more

This report entails the design process and development of a rotational ring system that must
serve as an user interface for an existing system, the ADEPTH. The goal of the rotational ring is to allow a surgeon to make selections in the user interface system. After careful consideration of the provided list of requirements, it was decided to use changes in magnetic fields, sensed by a Hall sensor. This Hall sensor detects whether an external ring was rotated to the left or to the right. The inside of the ring contains six samarium-cobalt magnets, chosen for their extreme resistance to demagnetisation at high temperatures. This was a consideration, because the magnets have to undergo repeated cycles of sterilisation as hot as 134◦ C. After iterated prototype testing, a final working prototype has been developed, which can communicate wirelessly with the user interface system and send ’left’ & ’right’ commands. This final prototype is watertight and low power, which satisfies two of the most desired requirements. ... Read more

This report entails the design process and development of an RFID (Radio Frequency Identification) system that must serve as a user interface for a surgical tool developed by SLAM Orthopedic. The goal of the user interface is to allow a surgeon to make selections as input for the surgical tool. The RFID interface is specifically designed to fit into the device, which leads to several design constraints like power consumption and size. The RFID system uses a coil antenna which was tuned for a specific frequency with the help of a Vector Network Analyser and Smith Charts. A prototype for the system was made but not finalised, however, results of the tuning process and research on RFID technology showed that an RFID system could be a promising interface for this surgical tooling. ... Read more

In an era marked by the demand for unprecedented levels of precision in engineering applications, the profound impact of friction forces on motion control systems cannot be underestimated. This thesis extensively investigates the frictional behavior of the Proton Motion Stage, an advanced high-precision motion control system developed by Prodrive Technologies. This research conducts both experimental investigations and computational simulations, offering valuable insights into its friction behavior across diverse conditions and scenarios.
The research begins with an analysis of existing models used to describe friction behavior in precision engineering systems. A critical evaluation of empirical models highlighting strengths and limitations is presented, and the LuGre friction model is selected. Subsequently, a simulation work is conducted to identify the viscous coefficients, the stiffness coefficient, the Coulomb friction, the Stribeck friction, and the Stribeck velocity in the LuGre model. The simulation setup is described, including the incorporation of the LuGre friction model and the identification of system parameters. The accuracy of the identification value to the true value is above 99\%. A comparison of the sensitivity of the objective function to the change of parameters is also conducted to enable a comprehensive exploration of friction dynamics. Finally, the research delves into static and dynamic parameter experiments, where cable slab forces' position-dependent impacts and velocity-friction maps that capture the intricate Stribeck effect are presented, and closed-loop and open-loop setups to dissect friction behavior during rapid motion changes are employed. Residual analysis of histogram and 90\% confidence autocorrelation and cross-correlation is also presented to study the quality of identification and shows that the LuGre model does not fully capture the friction phenomena on the Proton Motion Stage. Future research should involve the modification of the LuGre model and data-driven approaches such as machine learning. Overall, this thesis fills the gap in state-of-the-art works by combining theory and practice to enhance the understanding of friction in precision engineering systems. ... Read more

The goal of this thesis is to develop a ROS package that facilitates the control and navigation of a Duckiebot robot. With the rise of robot swarms the need for autonomous charging system for robots is increasing. An implementation for decentralised autonomous behaviour for a Duckiebot for a wireless charging system in a Duckietown environment is discussed. The devised system is divided among three different modules and is implemented in ROS:
• An image recognition module;
• A navigation module;
• A motion control module;
The image recognition module uses linear image processing techniques and YOLO object detection in order to detect objects in images from the robots front facing camera. It detects traffic lights and road markings in order to tell the robot where to go.

The navigation module uses odometry to keep track of the robots current position. The odometry is reset in order to maintain accuracy. When the battery of the robot reaches a certain point the robot will decide to
charge. It will then initiate path finding using Lee’s algorithm in order to find a path to a charging park.

Finally the motion control processes all the information in order to drive the wheels of the robot.
The system is thought to be able to navigate to a charging station, charge and then leave the charging station using the designed ROS package. ... Read more

In this Bachelor graduation project, a 16x16 Single Photon Avalanche Diode (SPAD) array is designed in 40nm TSMC CMOS for diamond single Nitrogen Vacancy center array readout. It includes an active quenching and recharge circuit (AQC), a hold-off circuit for controllable dead-time and IO electronics for off-chip communication. The chip is part of a proposed high sensitivity magnetometer based on single NV center readout with a focus on detecting cancer in biological samples. From the Quantum Integration Technology (QIT) lab, pre-designed SPADs were received to be implemented into the design together with SPAD quenching, recharge and input-output controller electronics. A SPAD model is adapted from literature for simulations of the electric behaviour of the electronics. We present a design and implementation of the Active Quenching Circuit (AQC), a design and implementation of the recharge and hold-off circuits, Input-Output (IO) interface design and implementation and the final top-level implementation ready for the next tape out. Post-layout simulations show negligible speed slowdown and distortion. The AQC has a 12ns quenching time and a 1ns recharge time, leading to a theoretical maximum count rate of 76Mc/s. The hold-off circuit has a tunable dead-time for afterpulsing reduction and 16, 16 bit parallel-in-serial-out (PISO) modules allow per-row readout of the array. The electronics are co-located with the SPADs and pixel pitch is 24m. The final chip design meets the single NV fluorescence count rate requirement of above 3 Mc/s, the 1.1x1.1 ZZ2 area requirement, the 32-pin IO requirement, the 16x16 SPAD pixel requirement and, steps have been taken to ensure acceptable crosstalk levels in the array. Finally, the SPAD array chip is designed to run on a 1GHz clock. It should interface with an FPGA that configures the hold-off circuit and reads out the SPAD status bits. ... Read more

The evolution of aerial vehicle technology necessitates robust trajectory prediction models. These models are crucial for maintaining safe airspace and enabling autonomous operations. Automatic dependent surveillance–broadcast (ADS-B) is a surveillance system that enables aircraft to receive data from navigation satellites and periodically broadcasts it, enabling it to be tracked. Moreover, using ADS-B data for more general aerial vehicles has become a popular trend because it can provide real-time high-resolution aircraft state information and share this information with other vehicles in real-time for the aviation safety ecosystem.

In this project, we delve into ADS-B-based trajectory prediction for both aircraft and drone motion trajectories with the overarching goal of improving prediction accuracy. We initially implement several model-based Kalman filters—including interactive multiple models (IMM)—to assess the accuracy of aircraft trajectory predictions across different model structures. The results reveal that the IMM filter outperforms the single model predictions in terms of root mean square error (RMSE).

Furthermore, we implement the Gaussian process (GP) with a sliding window scheme to predict online drone trajectories. Recognizing the high computational complexity of the GP, we also introduce a low-rank approximation method, structured kernel interpolation (SKI) GP, aiming to conserve computational resources. Finally, we compare the prediction performances of the IMM filter, classical GP, and SKI GP on real drone trajectories. The results highlight that the classical GP method enhanced prediction accuracy, achieving an RMSE of less than 1.7m, which is 50% lower compared to the model-based IMM filter. Additionally, the SKI GP realizes a 25% reduction in computation time compared to the classical GP, despite a slight compromise in prediction accuracy. ... Read more

For the heart to pump blood throughout the body, electrical impulses that trigger the cellular contraction must be generated and spread through the myocardial tissue. These signals propagate faster along the longitudinal cardiac fiber direction than the transverse direction, conferring the heart with anisotropic conduction properties. Therefore, the arrangement of the fibers within the tissue governs the impulse propagation. Given the variability of the fiber direction across the heart and between patients, incorporating it into electrophysiological models would enhance our understanding of the mechanisms and progression of different heart conditions, such as atrial fibrillation (AF). The study of this common cardiac arrhythmia relies on analyzing electrical recordings of the heart, known as electrograms (EGMs), which, if integrated with the patient’s fiber architecture into cardiac models, can enable effective personalized treatment. Over the years, researchers have proposed different approaches to estimate the fiber direction from EGMs. However, these methods have been evaluated in different, usually simplistic, cardiac tissue models, making their comparison, and therefore selection of the most accurate approach for clinical and research applications, challenging.

The current study aims to identify the best fiber direction estimation method under consistent and realistic conditions. To achieve this goal, synthetic EGMs and local activation time (LAT) maps were generated from 2D and 3D monodomain models that mimicked the muscle bundle, atrial bilayer, and ventricular transmural fiber rotation structures. A comparison analysis of existing fiber direction estimation methods, first as described by their authors and then standardized to have the same spatial resolution, showed the superior performance of the techniques based on fitting an ellipse to local conduction velocity or conduction slowness vectors from a whole LAT map. The estimation accuracy of these methods can be further improved by increasing the number of vectors to which the ellipse is fitted. Nonetheless, given the influence of underlying layers in the epicardial recordings, the estimation error increases in the tissue models where fibers in the epicardial and endocardial layers run perpendicularly. The effect on the estimate of such architecture, characteristic of the inferior side of the right atria and the ventricles, can be accounted for by combining epicardial electrical recordings obtained after pacing either in the endocardium or the epicardium. Although a preliminary assessment of the estimation methods was carried out with human EGMs, future studies should focus on validating the methods in a controlled experimental framework and refining them for more localized fiber direction estimation. All in all, the automation of the techniques and their integration into electrophysiological models brings us a step closer to creating valuable clinical tools for diagnosing and treating electropathologies.
... Read more

Emotion Recognition is one of the vastly studied areas of affective computing. Attempts have been made to design emotion recognition systems for everyday settings. The ubiquitous nature of Intelligent voice assistants (IVAs) in households, make them a great anchor for the introduction of emotion recognition technology to consumers. The existing systems lack such pipelines and rely on dictionary-based architectures in their design. Further, these systems lack conversational properties and are merely an extension of information retrieval engines.

In this setting, we propose to introduce and develop emotion recognition pipelines that are suited to the interactions, common with these IVAs. To augment the existing emotion recognition pipelines which rely on audio information, we look at physiological information derived from wearables. Our proposed model uses multimodal embeddings with a Siamese Network to achieve the task of emotion recognition from a few samples. Physiological signals of blood volume pulse (BVP) and electrodermal activity (EDA) are used as additional input embeddings to two audio embeddings arising from the speech samples. We employ the state-of-the-art training schedules for Siamese Networks, which use a very limited amount of training on support datasets via sample pair comparisons. The performance of the model is evaluated using weighted binary accuracy and f1 scores.

The proposed model is applied on two datasets that denote two unique experimental settings - the K-EmoCon dataset and RECOLA dataset. We demonstrate an improvement in the state-of-the-art accuracy with the K-EmoCon dataset with accuracies of 63.97% and 66.91% on arousal and valence dimensions respectively. Further, on the RECOLA dataset, the model performs moderately well with 53.81% and 53.87% respectively for arousal and valence dimensions. In addition to this, we present a study of the effects of variation of available support set for training from the dataset. We make some salient observations for these experiments across individual participants and also identify how the label distributions affect the performance of the model. Further, we investigate the impact of real-world noise samples from the DEMAND dataset on the two datasets. We observe that the proposed model is robust and performs sustainingly well even in the presence of imputed noise.
... Read more

In this thesis, we propose a new class of pairwise frequency, multi-domain time synchronization and ranging algorithms for anchorless mobile networks of asynchronous nodes. We apply these techniques and study network and mission level aspects of time synchronization to Orbiting Low Frequency Array for Radio astronomy (OLFAR), a proposed distributed radio interferometer. In the first step, the Frequency Pairwise Least Squares (FPLS) that estimates clock skew and relative velocity in a pairwise setup using only frequency measurements is formulated. In the second step, we extend this method to a motion model with constant acceleration. Since frequency domain methods do not estimate clock offset and pairwise range, relying purely on frequency domain estimates is not feasible for various applications. To harness the potential of frequency domain synchronization and ranging, the Combined Pairwise Least Squares (CPLS) has been proposed. The combined method reduces the number of minimum required messages from 4 to 3 compared to current methods and decreases the computational complexity. Using a generic simulation with nodes in pairwise non-linear motion, we show that frequency domain methods can outperform time domain methods in clock skew and relative velocity estimation and that the proposed multi-domain method delivers better clock offset and pairwise range estimation in low to medium SNR conditions. In the second part of our work, we apply the proposed methods to OLFAR –— a space-borne large aperture radio interferometric array platform. We address network level and mission level aspects, proposing network path planning for pairwise synchronization algorithms and determining the required resynchronization period. ... Read more

This project aims to develop a compact and affordable mobile prototype of a Quantum Random Number Generator (QRNG) utilizing the inherently random quantum effect of photons. The system is built exclusively with off-the-shelf components to make it accessible to new user groups who find existing QRNGs too expensive and complex. ... Read more

GNSS receivers can suffer severely from radio frequency interference (RFI). RFI can introduce errors in the position and time calculations or if the interference is very severe, can lead to a total loss of GNSS reception. This vulnerability of GNSS can have large implications on critical infrastructure such as power plants, telephony, aviation or search and rescue operations. RFI is a real threat to GNSS as many interfering incidents are reported every day. A common type of RFI is chirp interference, which is a sweep over a wide range of frequencies that overlap with the frequencies used by GNSS. This is often emitted by cheap Personal Privacy Devices that can be bought online. The question in this thesis was how well such interference can be modelled and if modelling could help mitigation against it. This thesis consists of two main parts. In the first part a novel estimator is proposed that assumes a mathematical model of a chirp and estimates its parameters from recordings of chirps. The estimator has shown to work well in simulations for chirps with an SNR of −9 dB or more. On real recordings the estimates were accurate for 66.7 % of the signals. In the second part the estimator was used to derive a filter. The filter is based on the subtraction of a replica of the chirp interference from the received signal. It uses the proposed estimator to create the replica. In simulations, the filter is able to improve correlation strength by up to 7 dB. On real recordings the performance was worse as for only 46 % of the recordings the GNSS correlation was increased. Both the estimator and filter have many ways in which they could be improved. The estimator can be improved to allow for more complex chirps, which would in turn improve the filter. Both can also be made more computationally efficient. Furthermore, in order to get a better understanding of Personal Privacy Devices, one such device has been tested. It was found that the signal from the device was very unstable and changed much over time, it was also highly dependent on ambient temperature. ... Read more

Ultrawideband technology can be used to measure the distance between two device equipped with ultrawideband transceivers. Multiple ultrawideband devices known as anchors can localize a device that supports ultrawideband communication after each anchor measures the distance between itself and the device. The anchor and the tag can measure the distance between themselves by measuring the time of flight of the ultrawideband messages exchanged between them. If the location of the anchors are known, the location of the device can be computed. However, errors in range measurements can cause errors in localization of the device. There are many sources that can cause errors in the measured range between the anchor and the tag. For example, when the tag transmits a signal, and the path between the anchor and the tag is blocked, the signal may be attenuated to such an extent that it may go undetected at the anchor, causing the anchor to measure the time of arrival of a delayed reflection. In this thesis, we aim to find a solution to improve the ranging accuracy when an anchor is equipped with two antennas. We target approaches that can be implemented on an embedded processor with limited resources. In order to improve the ranging accuracy, we first investigate various machine learning based classifiers that can identify non-line of sight and line of sight signals. Next, for each of the classified signal, we train and test various machine learning based regression models that will predict the true distance from the distance measured by the anchor. We conclude the thesis, by assessing the robustness of the derived classification and regression models by evaluating the range improvements in measurements taken in different scenarios. ... Read more

Functional ultrasound (fUS) is a neuroimaging modality that offers high spatial and temporal resolution while also providing portability. In this thesis, neuroimaging data acquired with fUS at Center for Ultrasound and Brain imaging at Erasmus MC (CUBE) is processed. Due to the fact that fUS data is inherently multidimensional, we propose using tensor decompositions, tensors here referring to generalizations of matrices, for processing of fUS data.

We define two main research questions regarding fUS data analysis. First, for compressing the large-scale raw beamformed fUS data, we apply sequentially truncated multilinear singular value decomposition. This compression method is compared against ensemble averaging used in the conventional pipeline, and shown to provide a higher compression rate while preserving more temporal resolution for specific ranks. Furthermore, it is observed to denoise the data, resulting in a more precise extraction of the active region of Superior Colliculus using correlation maps.

Secondly, in order to investigate the advantage of multi-slice processing that incorporates 3-D informa- tion, blind-source separation methods are applied to single slice and two-slice fUS recordings. After applying independent component analysis (ICA) to the matricized data as a benchmark method, block term decompo- sition (BTD) is used as a way of processing the data as it is, in its natural 3-D structure without vectorization. Through a simulation study, it is shown that the method is able to separate two images even when using a rank that is lower than the true rank, as well as in noisy conditions. Subsequently, BTD is applied to real 4-D fUS data formed by concatenation of slices in a new dimension. However, this method is seen to perform worse than single slice ICA in terms of extracting the active regions. In order to amplify common information between slices, a new 3-D data structure is then formed by summing the fUS data of two slices. For extraction of this common information, a BTD is then applied to the aggregate 3-D data. The findings of this decomposition reveal that both taking a longer portion of single slice data and incorporating the second slice helps to achieve better results. ... Read more

Modern railway signalling systems are based on a wireless communication link between train and trackside entities. Secure communication between these entities is established using cryptographic symmetric keys loaded beforehand. Train and trackside entities across Europe are maintained by different Key Management Centres (KMC), making the distribution of the symmetric keys challenging. The involved parties would benefit from using a single European key distribution system. Nevertheless, a recent study concluded that a centralised approach of such a single system is not feasible.

This work presents, to the best of our knowledge, the first decentralised key management system to be used by railway KMC across Europe. Existing procedures mandate that key distribution activities concerning key generation, distribution and deletion must be logged. To meet this requirement, the proposed decentralised system is based on a private and permissioned blockchain. The network is maintained by the KMC making use of the system and access to the system is granted by Registration Centres.

During the design of a single system to replace several one-to-one solutions between KMC, it came into light that train and/or trackside equipment owners might not accept revealing certain types of relationships, as these could, for example, reveal commercial strategies. To overcome this, the proposed decentralised system introduces privacy-preserving and verifiable combinations of train and trackside entities. The protocol is based around the decisional Diffie–Hellman assumption witness indistinguishable proofs.

The proposed design enables European railway KMC to use a single decentralised and scalable system to exchange cryptographic material in a secure and privacy-preserving way. Scalability is shown by building a proof-of-concept based a Byzantine Fault Tolerance consensus protocol. Performance analysis shows that the proposed system is scalable when a proof of concept is implemented with settings close to the expected railway landscape in 2030. ... Read more

Natural or man-made disasters can have a drastic impact on social, economic and environmental aspects of an affected population. Specifically, earthquakes are one of the most potent natural hazards, which cause a disproportionate amount of fatalities, primarily due to a) unexpected building collapses, b) restricted or limited access to basic amenities and c) potential hazards following earthquakes such as landslides, tsunamis etc. It is crucial to have an overview of the infrastructural damage caused following a disaster for search and rescue services to assess the extent of the damage. For the purpose of this research, Sentinel 1 imagery is used to map the building damage in an urban area after a disaster. A combination of parameters such as persistent scatterers, pixel amplitude and phase is used with a timeseries of full-resolution and spatially averaged radar images. Points that are stable in amplitude over a long timeseries, also known as Persistent Scatterers, are extracted from a stack of full-resolution images. The amplitudes of persistent scatterers, along with amplitude and coherence of pixels derived from a stack of spatially-averaged images, are statistically analysed to check the trends of the parameters pre- and post the disaster. A change detection algorithm is applied to this stack in order to localise the areas of building damage. The results are superimposed on Google Earth for easy interpretation using a graded damage scale. The analysis shows that exploiting the persistent scatterer amplitudes in the manner used in this research provides a novel way of locating building damage. This technique can be used effectively in urban areas. Using a combination of pixel amplitudes and coherence along with the persistent scatterers helps correctly find new and unique points of damage for each parameter used. The results were validated using reference Grading and crowd-sourced maps. The results illustrate that the proposed approach can be used for detecting and producing informative maps on infrastructural damage detection in urban areas. ... Read more

In this thesis, the implementation of a passive, chipless, frequency coded Radio-Frequency Identification (RFID) tag for bedload transport studies is proposed. The proposed tag will be deployed in the semi-arid Río Colorado river, Bolivia with the aim to develop quantitative sediment transport models that relate transport to grain size. The designed tag is an open-loop resonator with a fragment-loading structure, that has an op- timised configuration based on a Multiobjective Evolutionary Algorithm based on Decomposition combined with Enhanced Genetic Operators (MOEA/D-GO). The designed RFID tag can ideally reach a size of 4 by 4 millimetres with a maximum calculated reading range of 1.3 meters, and operates in the ultra wide band from 3 to 7 gigahertz. Numerous simulations on the tags were run to verify their properties. The tags proved to have a good directivity, quality factor and radio cross section on its resonant frequency. The tags could reach resonance frequencies as low as 2.9 gigahertz and quality factors as high as 130. The proof of concept on a Printed Circuit Board with an FR-4 substrate results in a tag of 6.4 by 3.4 millimetres. Unfortunately, these properties could not yet be verified by measuremen ... Read more

A well-established method for finding the optimal control policy for a given dynamical system is to solve the problem iteratively going from its terminal state "backwards" in time, known as Dynamic Programming Algorithm. For a generic problem with discrete state/action space, the algorithm has computational complexity of O(NM) for N states and M actions. In this thesis, we propose a novel numerical algorithm that approaches this problem in the conjugate domain, using the so-called Legendre-Fenchel Transform. In essence, the proposed approach is analogous to, and was inspired by Fast Fourier Transform, and how it can be beneficial to do computations/analysis in the frequency domain. In particular, this approach allows us to exploit the structure of the problem (e.g., in LQ control) to drastically reduce the computational complexity to O(N+M). Of course, this computational gain comes with a cost of introducing error. ... Read more