Conventional Digital Signal Processing Research Articles

Neural network-based arterial diameter estimation from ultrasound data

Cardiovascular diseases are the leading cause of mortality and early assessment of carotid artery abnormalities with ultrasound is key for effective prevention. Obtaining the carotid diameter waveform is essential for hemodynamic parameter extraction. However, since it is not a trivial task to automate, compact computational models are needed to operate reliably in view of physiological variability. Modern machine learning (ML) techniques hold promise for fully automated carotid diameter extraction from ultrasonic data without requiring annotation by trained clinicians. Using a conventional digital signal processing (DSP) based approach as reference, our goal is to (a) build data-driven ML models to identify and track the carotid diameter, and (b) keep the computational complexity minimal for deployment in embedded systems. A ML pipeline is developed to estimate the carotid artery diameter from Hilbert-transformed ultrasound signals acquired at 500Hz sampling frequency. The proposed ML pipeline consists of 3 processing stages: two neural-network (NN) models and a smoothing filter. The first NN, a compact 3-layer convolutional NN (CNN), is a region-of-interest (ROI) detector confining the tracking to a reduced portion of the ultrasound signal. The second NN, an 8-layer (5 convolutional, 3 fully-connected) CNN, tracks the arterial diameter. It is followed by a smoothing filter for removing any superimposed artifacts. Data was acquired from 6 subjects (4 male, 2 female, 37 ± 7 years, baseline mean arterial pressure 86.3 ± 7.6 mmHg) at rest and with diameter variation induced by paced breathing and a hand grip intervention. The label reference is extracted from a fine-tuned DSP-based approach. After training, diameter waveforms are extracted and compared to the DSP reference. The predicted diameter waveform from the proposed NN-based pipeline has near perfect temporal alignment with the reference signal and does not suffer from drift. Specifically, we obtain a Pearson correlation coefficient of r = 0.87 between prediction and reference waveforms. The mean absolute deviation of the arterial diameter prediction was quantified as 0.077 mm, corresponding to a 1% error given an average carotid artery diameter of 7.5 mm in the study population. This work proposed and evaluated an ML neural network-based pipeline to track the carotid artery diameter from an ultrasound stream of A-mode frames. By contrast to current clinical practice, the proposed solution does not rely on specialist intervention (e.g. imaging markers) to track the arterial diameter. In contrast to conventional DSP-based counterpart solutions, the ML-based approach does not require handcrafted heuristics and manual fine-tuning to produce reliable estimates. Being trainable from small cohort data and reasonably fast, it is useful for quick deployment and easy to adjust accounting for demographic variability. Finally, its reliance on A-mode ultrasound frames renders the solution promising for miniaturization and deployment in on-line clinical and ambulatory monitoring.

Realization of global audio telepresence via a learning-based model-matching approach with an acoustic array system

A Global Audio Telepresence (GOAT) system requires a microphone array to capture the spatial audio signals in the far end and a loudspeaker array to reconstruct the sound field in the near end. This seamlessly immerses near-end users in remote audio scenes with full ambience. In this paper, we use a learning-based GOAT system (L-GOAT) based on the model-matching principle, where a deep neural network (DNN) acts as non-linear filters for the GOAT system. The network training attempts to minimize the matching error between the signals reproduced by the DNN and the desired signals filtered by the far-end acoustic transfer functions (ATFs). Extensive simulations were carried out for multi-source scenarios in two different rooms with different reverberation times. To implement the L-GOAT system, a five-microphone linear array was adopted in the far-end room, while a six-loudspeaker array was utilized in the near-end room. The objective evaluation matrices, including the Perceptual Evaluation of Speech Quality (PESQ), Short-Time Objective Intelligibility (STOI), and the matching errors, were conducted to validate the efficacy of the GOAT systems. The proposed learning-based approach has demonstrated superior performance compared to a conventional digital signal processing (DSP)-based method.

Online digital compensation of pump dithering induced phase and amplitude distortions in transmission links with cascaded fibre-optical parametric amplifiers

We present an advanced online digital signal processing (DSP) method for correcting the phase and amplitude distortions caused by the phase modulation of the pump source and its interaction with the dispersive fibre channel in transmission systems using cascaded fibre-optical parametric amplifiers. The proposed algorithm is numerically demonstrated to achieve significant (up to 3.7 dB for a four-tone pump-phase modulation scheme) Q2-factor performance improvement over conventional DSP in 16 quadrature-amplitude modulation signal transmission.

Low-complexity and low-latency equalization technique - probabilistic noise cancellation.

Both inside data centers (DCs) and in short optical links between data centers (DC campuses), intensity-modulation and direct-detection (IMDD) systems using four-level pulse amplitude modulation (PAM4) will dominate this decade due to low transceiver price and power consumption. The next DC transceiver generation based on 100 Gbaud PAM4 will require advanced digital signal processing (DSP) algorithms and more powerful forward error correction (FEC) codes. Because of bandwidth limitations, the conventional DC DSP based on a few-tap linear feed-forward equalizer (FFE) is likely to be upgraded to more complex but still low-complexity Volterra equalizers followed by a noise whitening filter and either a maximum likelihood sequence estimation (MLSE) or a maximum a posteriori probability (MAP) algorithm. However, stringent power consumption and latency requirements may limit the use of complex algorithms such as decision feedback equalizer (DFE) or MLSE/MAP in DC networks (DCN). In this paper, we introduce a low-complexity, low-latency algorithm based on a feedforward structure, yielding a performance between DFE and MLSE. We call the novel equalization algorithm probabilistic noise cancellation (PNC), since it weights noise patterns based on their probabilities in the presence of bandwidth limitations. The probabilistic weighting is efficiently exploited in correcting correlated errors caused by noise coloring in the FFE.

A system-on-chip microwave photonic processor solves dynamic RF interference in real time with picosecond latency

Radio-frequency interference is a growing concern as wireless technology advances, with potentially life-threatening consequences like interference between radar altimeters and 5 G cellular networks. Mobile transceivers mix signals with varying ratios over time, posing challenges for conventional digital signal processing (DSP) due to its high latency. These challenges will worsen as future wireless technologies adopt higher carrier frequencies and data rates. However, conventional DSPs, already on the brink of their clock frequency limit, are expected to offer only marginal speed advancements. This paper introduces a photonic processor to address dynamic interference through blind source separation (BSS). Our system-on-chip processor employs a fully integrated photonic signal pathway in the analogue domain, enabling rapid demixing of received mixtures and recovering the signal-of-interest in under 15 picoseconds. This reduction in latency surpasses electronic counterparts by more than three orders of magnitude. To complement the photonic processor, electronic peripherals based on field-programmable gate array (FPGA) assess the effectiveness of demixing and continuously update demixing weights at a rate of up to 305 Hz. This compact setup features precise dithering weight control, impedance-controlled circuit board and optical fibre packaging, suitable for handheld and mobile scenarios. We experimentally demonstrate the processor’s ability to suppress transmission errors and maintain signal-to-noise ratios in two scenarios, radar altimeters and mobile communications. This work pioneers the real-time adaptability of integrated silicon photonics, enabling online learning and weight adjustments, and showcasing practical operational applications for photonic processing.

100Gb/s coherent optical secure communication over 1000 km based on analog-digital hybrid chaos.

In recent years, the transmission capacity of chaotic secure communications has been greatly expanded by combining coherent detection and multi-dimensional multiplexing. However, demonstrations over 1000 km fiber are yet to be further explored. In this paper, we propose a coherent optical secure transmission system based on analog-digital hybrid chaos. By introducing an analog-digital converter (ADC) and a bit extraction into the feedback loop of entropy source, the broadband analog chaos is converted into a binary digital signal. This binary digital signal is then mapped to a 65536-level pulse amplitude modulation (PAM) signal and injected into the semiconductor laser (SL) to regenerate the analog chaos, forming a closed loop. The binary digital signal from the chaos source and the encrypted signal are transmitted via wavelength division multiplexing (WDM). By using conventional digital signal processing (DSP) algorithms and neural networks for post-compensation, long-haul high-quality chaotic synchronization and high-performance secure communication are achieved. In addition, the probability density distribution of the analog chaotic signal is effectively improved by adopting the additional higher-order mapping operation in the digital part of the chaos source. The proof-of-concept experimental results show that our proposed scheme can support the secure transmission of 100 Gb/s quadrature phase shift keying (QPSK) signals over 1000 km of standard single-mode fiber (SSMF). The decrypted bit error rate (BER) reaches 9.88 × 10-4, which is well below the 7% forward error correction (FEC) threshold (BER = 3.8 × 10-3). This research provides a potential solution for high-capacity long-haul chaotic optical communications and fills the gap in secure communications based on analog-digital hybrid chaos.

Hardware-Based Architecture for DNN Wireless Communication Models.

Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MIMO OFDM) is a key technology for wireless communication systems. However, because of the problem of a high peak-to-average power ratio (PAPR), OFDM symbols can be distorted at the MIMO OFDM transmitter. It degrades the signal detection and channel estimation performance at the MIMO OFDM receiver. In this paper, three deep neural network (DNN) models are proposed to solve the problem of non-linear distortions introduced by the power amplifier (PA) of the transmitters and replace the conventional digital signal processing (DSP) modules at the receivers in 2 × 2 MIMO OFDM and 4 × 4 MIMO OFDM systems. Proposed model type I uses the DNN model to de-map the signals at the receiver. Proposed model type II uses the DNN model to learn and filter out the channel noises at the receiver. Proposed model type III uses the DNN model to de-map and detect the signals at the receiver. All three model types attempt to solve the non-linear problem. The robust bit error rate (BER) performances of the proposed receivers are achieved through the software and hardware implementation results. In addition, we have also implemented appropriate hardware architectures for the proposed DNN models using special techniques, such as quantization and pipeline to check the feasibility in practice, which recent studies have not done. Our hardware architectures are successfully designed and implemented on the Virtex 7 vc709 FPGA board.

High-security constellation shaped self-homodyne coherent system with 4-D joint encryption.

In recent years, the self-homodyne coherent (SHC) system and the constellation shaping (CS) technique have drawn considerable attention due to their abilities to further improve the transmission capacity for various scenarios. From the security point of view, the CS technique and the SHC infrastructure also provide new dimensions for encryption. We propose a high-security and reliable SHC system based on the CS technique and the digital chaos. With a four-dimensional hyperchaotic system, chaotic sequences are generated and used for the exclusive or operation, chaotic constant composition distribution matching, phase disturbance, and optical-layer time-delay disturbance. Moreover, 64-ary circular quadrature amplitude modulation (64CQAM) format is adopted for transmission due to its advantages of sensitivity to phase noise, immunity to conventional digital signal processing, and ability of time-mismatch masking, which is verified by simulation in a SHC system. Last, we conduct an experimental verification in a 20GBaud probabilistically shaped 64CQAM SHC system. Consequently, with a large-linewidth laser source, optical-layer security can be protected by time mismatches of tens of picoseconds. And the digital-layer security is protected by an enormous key space of 10127. The proposed scheme can provide reliable real-time encryption for the optical fiber transmission, serving as a potential candidate for the future high-capacity inter/intra-datacenter security interconnect.

Big Data Analytics Using Graph Signal Processing

The networks are fundamental to our modern world and they appear throughout science and society. Access to a massive amount of data presents a unique opportunity to the researcher’s community. As networks grow in size the complexity increases and our ability to analyze them using the current state of the art is at severe risk of failing to keep pace. Therefore, this paper initiates a discussion on graph signal processing for large-scale data analysis. We first provide a comprehensive overview of core ideas in Graph signal processing (GSP) and their connection to conventional digital signal processing (DSP). We then summarize recent developments in developing basic GSP tools, including methods for graph filtering or graph learning, graph signal, graph Fourier transform (GFT), spectrum, graph frequency, etc. Graph filtering is a basic task that allows for isolating the contribution of individual frequencies and therefore enables the removal of noise. We then consider a graph filter as a model that helps to extend the application of GSP methods to large datasets. To show the suitability and the effeteness, we first created a noisy graph signal and then applied it to the filter. After several rounds of simulation results. We see that the filtered signal appears to be smoother and is closer to the original noise-free distance-based signal. By using this example application, we thoroughly demonstrated that graph filtration is efficient for big data analytics.

Demonstration of 200 Gbps PAM-4 transmission in a limited-bandwidth system using a two-tap THP with nonlinearity compensator

In this paper, we have proposed a digital signal processing (DSP) method for a 200 Gbps pulse-amplitude modulation level-4 (PAM-4) transmission in a bandwidth-limited system. To mitigate inter-symbol interferences (ISI) in the system and reduce the propagation of errors in the receiver, the Tomlinson-Harashima precoding (THP) technique was applied to the transmitter. For simplicity, the number of THP taps was limited to two (i.e., one coefficient to be optimized); the residual ISI resulting from the short tap was compensated for with a decision feedback equalizer (DFE). The performance of the proposed DSP was analyzed via experiments and simulations. Compared to conventional DSP techniques (such as DFE and the maximum likelihood sequence estimation (MLSE) without THP), the proposed DSP performs better within the limited-bandwidth region. As a result, the soft-decision forward error correction (SD-FEC) threshold (of 2 × 10−2) was satisfied even when the bandwidth fell to below 35% of the baud rate. To enhance this performance, post-filter and MLSE were additionally applied, after which its performance was investigated. In addition, the nonlinear characteristics of the components were alleviated by applying a pre-distortion technique to the THP using look-up tables; this further enhanced performance, lowering the SD-FEC threshold’s bandwidth to 32% of the baud rate.

Independent dual-single sideband lower-IF RF receiver based on a single photodetector.

The two sidebands of the independent dual-single-sideband (dual-SSB) signal can carry different information, which achieves higher spectral efficiency and system capacity. However, the receiver divides the signal into two channels, so a pair of optical bandpass filters (OBPFs) and photodetectors (PDs) are generally required to select and detect an independent dual-SSB signal. To reduce the complexity and cost of the receiver, we propose an independent dual-SSB lower intermediate frequency (IF) radio frequency (RF) signal detection scheme based on a single PD combined with conventional digital signal processing (DSP). A theoretical analysis is presented and validated by a simulation. The left sideband (LSB) and the right sideband (RSB) are quadrature phase-shift keying (QPSK) modulated. After 50-km standard single-mode fiber (SSMF) transmission, a 10-Gbps 16QAM signal is synthesized from 2 × 5-Gbps dual-SSB QPSK and the independent dual-SSB is extracted by DSP. The bit error rate (BER) of the dual-SSB (LSB and RSB) is below the hard-decision forward-error-correction (HD-FEC) threshold of 3.8 × 10-3.

Design of fully interpretable neural networks for digital coherent demodulation.

In this paper, we propose a digital coherent demodulation architecture using fully interpretable deep neural networks (NNs). We show that all the conventional coherent digital signal processing (DSP) is deeply unfolded into a well-structured NN so that the established training algorithms in machine learning can be applied. In contrast to adding or replacing certain algorithms of existing DSP in coherent receivers, we replace all the coherent demodulation algorithms with a fully interpretable NN (FINN), making the whole NN interpretable. The FINN is modular and flexible to add or drop modules, including chromatic dispersion compensation (CDC), the digital back-propagation (DBP) algorithm for fiber nonlinearity compensation, carrier recovery and residual impairments. The resulted FINN can be quickly initialized by straightforwardly referring to the conventional DSP, and can also enjoy further performance enhancement in the nonlinear fiber transmissions by NN. We conduct a 132-Gb/s polarization multiplexed (PM)-16QAM transmission experiment over 600-km standard single mode fiber. The experimental results show that without fiber nonlinearity compensation, FINN-CDC obtains less than 0.06-dB SNR gain than chromatic dispersion compensation (CDC). However, with fiber nonlinearity compensation, 2-steps per span FINN-DBP (FINN-2sps-DBP) and FINN-1sps-DBP bring about 0.59-dB and 0.53-dB SNR improvement compared with the conventional 2sps-DBP and 1sps-DBP, respectively.

Independent dual-single-sideband QPSK signal detection based on a single photodetector.

The two sidebands of the independent dual-single-sideband (dual-SSB) signal can carry different information to achieve higher spectral efficiency. However, the two sidebands of the independent dual-SSB vector signal are received independently. Generally, the receiver divides the signal into two channels. For each channel, we use an optical bandpass filter (OBPF) to select the left sideband (LSB) or right sideband (RSB), respectively. Then a photodetector (PD) is used for photoelectric conversion, followed by subsequent digital signal processing (DSP). To reduce the complexity and cost of the receiver, we propose a new independent dual-SSB vector signal detection scheme based on a single PD combined with conventional DSP. An electric bandpass filter (EBPF) filters out high-frequency components after photoelectric conversion, and then the signal is quadrature demodulated and processed by the DSP algorithm. The LSB and RSB are quadrature phase-shift keying (QPSK) modulated with an initial phase difference of π/4. Simulation results show that the proposed scheme performs better bit error rate (BER). For back-to-back (BTB) transmission, the BER of 2-Gbaud independent dual-SSB vector signal (1-Gbuad RSB and 1-Gbaud LSB) can reach the hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10-3 when the input optical power into PD is -20 dBm. For 1-km and 2-km weak turbulence free-space optical (FSO) channel transmission, the BER of 2-Gbaud independent dual-SSB vector signal can reach the HD-FEC threshold when the input optical power into PD is -18.8 and -17 dBm, respectively. For 1-km weak turbulence FSO channel transmission, the BER of 4-, 8-, and 16-Gbuad independent dual-SSB vector signal can reach the HD-FEC threshold when the input optical power into PD is -17.8, -16, and -15 dBm, respectively.

Demonstration of 10-channel mode- and polarization-division multiplexed free-space optical transmission with successive interference cancellation DSP.

We experimentally demonstrate 10-channel mode-division multiplexed free-space optical transmission with five spatial modes, each carrying 19.6925-Gbaud dual-polarization quadrature phase shift keying signals. Strong inter-mode cross talk is observed in our commercially available photonic lantern based system when using a complete orthogonal mode set as independent channels. A successive interference cancellation based multiple-input multiple-output digital signal processing (DSP) algorithm is first applied to mitigate the inter-mode cross talk in mode-division multiplexed systems. The DSP also supports unequal transmit and receive channel numbers to further improve the cross talk resiliency. Compared to the conventional minimum mean square error DSP, the required optical signal-to-noise ratio of the successive interference cancellation DSP is decreased by approximately 5 dB at the hard-decision forward error correction limit. As a result, this system demonstrates a record-high independent channel number of 10 and spectral efficiency of 13.7 b/s/Hz in mode-division multiplexed free-space optical systems.

Likelihood-Based Selection Radius Directed Equalizer With Time-Multiplexed Pilot Symbols for Probabilistically Shaped QAM

Probabilistically shaped (PS) quadrature amplitude modulation (QAM) recently established itself as the solution to adopt for state-of-the-art coherent transponders. This in turn has drawn attention to the rework of conventional digital signal processing (DSP) algorithms, which are not optimal for QAM-PS. In this context, we propose a novel pilot-aided equalization technique based on the ubiquitous radius directed equalizer (RDE). Our solution employs both payload and time-multiplexed pilot symbols for the adaptive filters update. The payload symbols are treated on the basis of the likelihood of their correct blind assignment. We show that this approach is at the same time able to reduce the global pilot overhead (POH) required by the DSP chain and to provide greatly improved performance in the tracking ability of the equalizer in the event of fast state of polarization rotations. We describe a simulation environment in which we model accurately static and dynamic polarization-related impairments. We test our algorithm over different shaped modulation formats and in the presence of transceiver impairments and demonstrate its superior performance with respect to standard feed-forward implementations in all the scenarios considered.

Cost-effective and robust DSP scheme for a short-reach coherent system in the presence of transmitter IQ skew and chromatic dispersion.

A cost-effective and robust digital signal processing (DSP) scheme is proposed and demonstrated experimentally in a coherent 61 GBaud PDM 16QAM system. In our scheme, multi-stage DSP blocks are used to deal with channel effects, transceiver in-phase and quadrature (IQ) skew, and phase noise. A 4×4 real-valued multiple-input multiple-output (RV-MIMO) with N1 taps is for polarization recovery and receiver IQ skew calibration. After frequency offset compensation, two 2×2 RV-MIMO with N2 taps are used to compensate for chromatic dispersion (CD), inter-symbol interference, transmitter IQ skew, and phase noise. Finally, the residual phase noise is eliminated by the maximum likelihood (ML) estimator. The experimental results indicate that the proposed scheme provides better received optical power sensitivity and CD tolerance than the existing simplified DSP schemes. In addition, the proposed scheme can tolerate transmitter IQ skew up to 7 ps in a 10 km case, which outperforms both simplified and conventional DSP schemes. Meanwhile, the proposed scheme can keep the same transceiver IQ skew and CD tolerance and has reduced complexity by 25% after 10 km links, compared to 4×4 RV-MIMO followed by a transmitter skew compensator. To the best of our knowledge, the proposed scheme is the most cost-effective solution for a high baud rate datacenter interconnects where transmitter IQ skew and CD have to be dealt with.

Palliation of Four-Wave Mixing in Optical Fibers Using Improved DSP Receiver

A long haul optical communication system (LHOCS) is one of the key resources to fulfill the higher capacity requirements in future communication networks. To launch LHOCS, the system mainly faces high order nonlinear effects. The four-wave mixing (FWM) is one of the major nonlinear effects, which limits the transmission distance. Therefore, in this paper, an advanced duo-binary (DB) modulation scheme-based system is evaluated by employing an improved digital signal processing (IDSP) approach at the receiver side to suppress the FWM effect. In addition, an analytical analysis is also performed for the proposed system. To observe the difference between the IDSP and conventional digital signal processing (DSP), the various performance metrics such as bit error rate (BER), Q-factor, and optical signal-to-noise ratio (OSNR) parameters are evaluated. Variable channel spacing along with polarization mode dispersion (PMD) are analyzed at several ranges of input powers and fiber lengths. The analytical and simulation-based calculations exhibit the effectiveness of the proposed model and hence, FWM effect are compensated to achieve 500 km optical fiber propagation range with a BER below 10−6.

A comprehensive computational model of animal biosonar signal processing.

Computational models of animal biosonar seek to identify critical aspects of echo processing responsible for the superior, real-time performance of echolocating bats and dolphins in target tracking and clutter rejection. The Spectrogram Correlation and Transformation (SCAT) model replicates aspects of biosonar imaging in both species by processing wideband biosonar sounds and echoes with auditory mechanisms identified from experiments with bats. The model acquires broadband biosonar broadcasts and echoes, represents them as time-frequency spectrograms using parallel bandpass filters, translates the filtered signals into ten parallel amplitude threshold levels, and then operates on the resulting time-of-occurrence values at each frequency to estimate overall echo range delay. It uses the structure of the echo spectrum by depicting it as a series of local frequency nulls arranged regularly along the frequency axis of the spectrograms after dechirping them relative to the broadcast. Computations take place entirely on the timing of threshold-crossing events for each echo relative to threshold-events for the broadcast. Threshold-crossing times take into account amplitude-latency trading, a physiological feature absent from conventional digital signal processing. Amplitude-latency trading transposes the profile of amplitudes across frequencies into a profile of time-registrations across frequencies. Target shape is extracted from the spacing of the object’s individual acoustic reflecting points, or glints, using the mutual interference pattern of peaks and nulls in the echo spectrum. These are merged with the overall range-delay estimate to produce a delay-based reconstruction of the object’s distance as well as its glints. Clutter echoes indiscriminately activate multiple parts in the null-detecting system, which then produces the equivalent glint-delay spacings in images, thus blurring the overall echo-delay estimates by adding spurious glint delays to the image. Blurring acts as an anticorrelation process that rejects clutter intrusion into perceptions.

Smartphone-Based Real-Time Digital Signal Processing, Third Edition

Real-time or applied digital signal processing courses are offered as follow-ups to conventional or theory-oriented digital signal processing courses in many engineering programs for the purpose of teaching students the technical know-how for putting signal processing algorithms or theory into practical use. These courses normally involve access to a teaching laboratory that is equipped with hardware boards, in particular DSP boards, together with their supporting software. A number of textbooks have been written discussing how to achieve real-time implementation on these hardware boards. This book discusses how to use smartphones as hardware boards for real-time implementation of signal processing algorithms, thus providing an alternative to the hardware boards that are used in signal processing laboratory courses. The fact that mobile devices, in particular smartphones, have become powerful processing platforms led to the development of this book to enable students to use their own smartphones to run signal processing algorithms in real-time considering that these days nearly all students possess smartphones. Changing the hardware platforms that are currently used in applied or real-time signal processing courses to smartphones creates a truly flexible laboratory experience or environment for students. In addition, it relieves the cost burden associated with using dedicated signal processing boards noting that the software development tools for smartphones are free of charge and are well-maintained by smartphone manufacturers. This book is written in such a way that it can be used as a textbook for real-time or applied digital signal processing courses offered at many universities. Ten lab experiments that are commonly encountered in such courses are covered in the book. It is written primarily for those who are already familiar with signal processing concepts and are interested in their real-time and practical aspects. Similar to existing real-time courses, knowledge of C programming is assumed. This book can also be used as a self-study guide for those who wish to become familiar with signal processing app development on either Android or iOS smartphones/tablets. A zipped file of the codes discussed in the book can be acquired from this third-party website: http://sites.fastspring.com/bookcodes/product/SignalProcessingBookcodesThirdEdition

Continuous scattering angle control of transmission terahertz wave by convolution manipulation of all-dielectric encoding metasurfaces

The digitally encoded metasurface provides flexible manipulation of the scattering properties of electromagnetic wave beams, and it can connect metasurface particles to digital codes to achieve unusual physical phenomena. At first, the research of coding metasurface mainly focused on the structural elements of metal materials. However, the ohmic loss of metal materials seriously affects the scattering efficiency of coding metasurface. To overcome ohmic loss, we propose to construct coded metasurface using all-dielectric element structure. Here, a complete $$2{\uppi }$$ transmitted phase with high efficiency can be controlled by cylindrical unit structures in terahertz frequency. Different coding sequences can control different transmission and scattering angles. However, these commonly coded metasurfaces cannot achieve continuous control of the scattering angle. In this study, Fourier convolution principle in digital signal processing is introduced through the four-bit operation of adding and subtracting two coding sequences to construct a new code sequence metasurface. The required coding pattern to flexible and continuous control scattering angle can be realized by the modulus of two encoding sequences. The Fourier convolution calculations of two gradient one-dimension encoding sequences and chessboard encoding sequences are implemented to realize the flexible control of single transmission beam and multiple beams. This fully digital perspective on the encoding metasurface can combine conventional digital signal processing with the encoding metasurface to achieve powerful manipulation of electromagnetic wave.