Digital compensation is a widely used methodology to compensate for circuit nonidealities and design robust analog and mixed-signal systems. In this work, we use nonlinear cascaded polynomial adaptive filters to compensate for nonlinear nonidealities in bipolar junction transistor (BJT) and metal oxide semiconductor field effect (MOS) based amplifiers which find applications as a front end block in mixed-signal systems. Several architectures are proposed and simulation results on 16-bit data obtained from cadence simulations indicate that the proposed methods result in signal to noise and distortion ratio (SNDR) improvement of up to $67. 22dB$ and spurious free dynamic range (SFDR) improvement of up to $70. 87dB$, respectively for BJTs, and SNDR and SFDR improvement of upto $42. 64dB$ and $46. 72dB$ respectively for MOS circuits.

The bio-inspired Levy Flight Firefly Algorithm (LFFA) can be effectively applied to IIR adaptive filters designed with conventional second order structures, coupled form structures, and lattice-ladder structures. Adaptive Fault Tolerant (AFT) digital filters take advantage of non-canonical architectures that use the inherent adaptive procedure as an automatic fault recovery mechanism. Since the LFFA is based on particle swarm optimization (PSO), the swarm provides many additional adaptive parameters. This paper presents some advanced experimental results to further confirm that the LFFA contains inherent adaptive fault tolerant capabilities which are very important when the LFFA is used in adaptive digital filtering applications.

It is well-known that the Lévy Flight Firefly Algorithm (LFFA) can be effectively applied to IIR adaptive filters designed with conventional second order structures, coupled form structures, and adaptive lattice-ladder structures. Adaptive Fault Tolerant (AFT) digital filters take advantage of non-canonical architectures that use the inherent adaptive process as an automatic fault recovery mechanism. Since the LFFA is based on particle swarm optimization, the swarm provides many additional adaptive parameters. This paper presents results to confirm that the LFFA provides inherent adaptive fault tolerant capabilities which is very important when the LFFA algorithm is applied in adaptive digital filtering applications.

It is well-known that the Lévy Flight Firefly Algorithm (LFFA) can be effectively applied to IIR adaptive filters designed with conventional second order structures, coupled form structures, and adaptive lattice-ladder structures. Adaptive Fault Tolerant (AFT) digital filters take advantage of non-canonical architectures that use the inherent adaptive process as an automatic fault recovery mechanism. Since the LFFA is based on particle swarm optimization, the swarm provides many additional adaptive parameters. This paper presents advanced results to confirm that the LFFA provides inherent adaptive fault tolerant capabilities which are very important when the LFFA is applied in adaptive digital filtering applications.

Deep in memory architecture (DIMA) has been proposed as a means to improve energy efficiency and latency over conventional digital architectures. DIMA reads multiple bits per bit-line (BL) in each cycle, and performs mixed-signal processing at the periphery of the bit cell array (BCA). While DIMA provides considerable performance benefits, the multi-row read is a non-linear operation. This work studies the impact of non-linearity and variations on stochastic gradient descent (SGD). The analysis is carried out in the context of LMS adaptive filters. The steady state MSE of the filter remains unaffected while convergence rate depends parameters associated with DIMA read operation. The insights are useful in context of learning systems employing gradient descent techniques.

Recently published results demonstrated that bio-inspired Lévy Flight Firefly Algorithms (LFFAs) can be effectively applied to IIR adaptive filter structures, non-linear adaptive structures, adaptive filters using second order coupled form sections, and adaptive lattice-ladder structures which have been well known for many decades. This paper shows how the LFFA can be used in 2D McClellan Unconstrained Transform adaptive filters so the transform domain parameters can be adjusted to accurately approximate the frequency domain contours when no a priori contour information is available. It appears that this is the first time that the LFFA has been used in 2D adaptive filtering.

Recently published results demonstrated that the Lévy Flight Firefly Algorithm (LFFA) can be effectively applied to IIR adaptive filter structures designed with parallel or cascade second order sections. Recently published results also demonstrated that the LFFA can be effectively used for IIR adaptive filters designed with second order coupled form sections. This paper now proposes that bio-inspired optimization algorithms can be applied to FIR and IIR adaptive lattice-ladder structures, which have been well known throughout the literature for many past decades. Experimental results are presented to demonstrate that the LFFA performs effectively on several different types of adaptive lattice-ladder structures.

During many past decades it has been known that when using finite word-length binary arithmetic in IIR digital filters, coupled form second order sections implement conjugate-pair poles that have relatively uniform pole locations located inside the unit circle in the z-plane. However, coupled form 2nd order sections could never be used in IIR adaptive filter designs using steepest descent adaptive algorithms due to the multi-modal error surfaces created by coupled form structures. Results presented in this paper demonstrate that the LFFA can be effectively applied to IIR adaptive filter structures designed with parallel or cascade second order coupled form sections.

Finite word-length binary arithmetic used in IIR digital filter coupled form second order sections implements conjugate-pair poles that have uniform pole locations located throughout the z-plane unit circle. When an LFFA IIR adaptive filter is implemented with direct form second order sections, due to high pole sensitivities the effects of arithmetic quantization error vary a great amount as the adaptive algorithm moves poles to different locations in the z-plane. Research results presented in this paper verify that for IIR adaptive filters implemented with coupled form second order sections, arithmetic quantization error effects are not very sensitive to the adaptive filter pole locations.

The mathematical theory of Residue Number System (RNS) arithmetic existed in the mathematical literature for thousands of years, having first been published by Sun Tzu in 100 A.D. In the mid 1900's RNS number theory began to evolve into many engineering applications as the evolution of digital computers began. In recent times RNS arithmetic has again emerged extensively in cryptography, cyber security, machine learning, fault tolerant signal processing, biomedical signal processing, etc. This paper reviews the history of how over many decades RNS arithmetic has emerged into rapidly developing digital signal processing applications to provide efficient DSP solutions.

Reliable execution of optimization algorithms is an essential requirement in both digital signal processing (DSP) and machine learning applications. DSP systems designed using nanoscale process technologies are susceptible to transient errors. In addition, power saving techniques like voltage over-scaling can also cause reliability issues in circuits. These errors often manifest themselves as large magnitude errors at the application level and can considerably slow down the convergence speed of the chosen algorithm. In this work we explore the behavior of Conjugate Gradient (CG) algorithm under stochastic computational errors. The expanding subspace property and modular redundancy is exploited to develop a robust conjugate gradient based method with applications in adaptive filtering and machine learning.

Relentless pursuit of Moore's law, while providing immense speed, power, and cost benefits in digital circuits, has thrown open many challenges in analog circuit design, especially analog-to-digital converter (ADC) design. Present day ADC's must be able to achieve an extremely high level of performance in terms of both resolution and bandwidth. High-resolution and high-bandwidth input modulated parallel ΔΣ-ADCs have been proposed earlier [1]. However, the large size of a conventional ΔΣ-ADC severely constrains the amount of parallelism. Voltage Controlled Oscillator (VCO) based 1 st -order noise-shaped ADCs being mostly digital in nature can exploit the scaling trend and can therefore be realized in a small area. Thus, using VCO based 1 st -order noise-shaping, a large amount of parallelism can be achieved to enable the design of high-resolution, high-bandwidth ADCs. This work provides an intuitive explanation of input modulated parallel ADCs and proposes a 32-channel VCO based ADC operating at a sampling rate, Fs, of 200 MHz and achieving an SNR of 65-dB, with the VCOs in each channel oscillating at a meagre frequency, F vco = F s /2 = 100 MHz.

Recently the Modified Fermat Number Transform (MFNT) was extended to the Modified Discrete Fourier Transform (MDFT) to enable overlap-add FFT block processing to be implemented without zero padding. The MDFT was then extended into two dimensions and published results described how the 2-D extension manages two-dimensional wrap around effects. This paper investigates how the modularity of these transforms can be used to achieve fault tolerant designs that strive to achieve minimal hardware redundancy. Fault tolerant designs are presented for both the MNT and the MDFT and the resulting efficiencies of the two designs are analyzed and compared.

Previously published results showed that when an FFT-based transform domain Fault Tolerant Adaptive Filter (FTAF) operates on real-valued signals, parameter redundancy inherent in the complex arithmetic provides fault tolerant capabilities. It was shown experimentally that the Modified Discrete Fourier Transform (MFFT) generates frequency domain samples that are not strictly real-valued or constrained to have conjugate symmetry in the transform domain. This paper provides a more detailed analysis of the fault tolerant capabilities of MFFT-FTAF architectures and further demonstrates how the MFFT-FTAF architecture is able to overcome certain fault conditions that cannot be properly handled in a conventional FFT-based FTAF architecture.

Fault Tolerant Adaptive Filters (FTAFs) rely on inherent learning capabilities of the adaptive process to compensate for transient (soft) or permanent (hard) errors in hardware implementations. This paper investigates fault tolerant transform domain adaptive noise canceling filters to cancel noise from corrupted speech signals. Two transform domain adaptive FIR architectures are compared, one based on the conventional FFT and one on the Modified Discrete Fourier Transform (MDFT), both without zero padding. Results support the fact that the MDFT- based FTAF architecture is able to overcome certain fault conditions that cannot be properly handled with a conventional FFT-based FTAF architecture.

Recently the Quadratic Modified Fermat Number Transform (QMFNT) was extended to an analogous Modified Discrete Fourier Transform (MDFT) that enables overlap-add FFT block processing to be implemented without zero padding, resulting in reduced computational complexity and lower power requirements for nanoscale VLSI implementations. The MDFT was then extended into two dimensions and an experimental example was presented to illustrate how the 2-D extension manages two-dimensional wrap around effects. This paper presents an analysis of the how the modulation parameters should be chosen under various circumstances and how the computational complexity of the 2D-MDFT compares with more traditional 2D-FFT block processing.

System architectures for fault tolerant computing and signal processing can be based on either modular hardware redundancy or arithmetic error detection and correction coding. Traditional triple modular redundancy (TMR) is very general but often leads to hardware intensive high-power implementations. In contrast, fault tolerant designs that rely on arithmetic coding reduce hardware requirements but result in higher computational requirements that must be implemented in a separate decoding unit. This paper proposes a hybrid combination of redundant hardware modules and arithmetic (algorithmic) error detection to produce efficient and reliable designs for transform domain adaptive filters.

Recently the Quadratic Modified Fermat Number Transform (QMFNT) based on Left-angle and Right-angle Circular Convolution (LCC and RCC) was extended to define a new Modified Discrete Fourier Transform (MDFT) that relies on a similar combination of RCC and LCC. It was shown that the MDFT enables overlap-add FFT block processing to be implemented without zero padding, resulting in reduced computational complexity and potentially reduced power requirements for nanoscale VLSI implementations. This paper extends the MDFT into two dimensions and analyzes how the 2-D extension manages two-dimensional wrap-around effects while implementing 2-D overlap-add block processing without zero padding.

Previously it was shown that when an FFT-based transform domain Fault Tolerant Adaptive Filter (FTAF) operates on real-valued signals parameter redundancy inherent in the complex arithmetic provides fault tolerant capabilities for adaptive filters implemented in highly scaled nano-technologies that are prone to both soft errors and hardware faults. This work replaces the conventional DFT with the Modified Discrete Fourier Transform (MDFT) to provide frequency domain samples that are not constrained to be strictly real-valued. It is shown that the MDFT-FTAF architecture resulting from the MDFT provides considerable fault tolerant capabilities by means of the parameter redundancy in the complex arithmetic.

Recently the Modified Fermat Number Transform (MFNT) was extended to a Quadratic MFNT (QMFNT) by combining Right Circular Convolution (RCC) and Left Circular Convolution (LCC) to produce a quadratic representation of the convolution output. This paper investigates nesting of two distinct quadratic number representations, the first associated with quadratic coding of complex input sequences, and the second associated with QMFNT block processing. Quadratic coding of complex sequences combined with QMFNT block processing eliminates cross-products in the complex multiplication. Finally, a generalized form of the QMFNT (GMFNT) is introduced and then extended into two dimensions.