Multiplier-less discrete sinusoidal and lapped transforms using sum-of-powers-of-two (SOPOT) coefficients

This paper proposes a new family of multiplier-less discrete cosine and sine transforms called the SOPOT DCTs and DSTs. The fast algorithm of Wang [10] is used to parameterize all the DCTs and DSTs in terms of certain (2×2) matrices, which are then converted to SOPOT representation using a method previously proposed by the authors [7]. The forward and inverse transforms can be implemented with the same set of SOPOT coefficients. A random search algorithm is also proposed to search for these SOPOT coefficients. Experimental results show that the (2×2) basic matrix can be implemented, on the average, in 6 to 12 additions. The proposed algorithms therefore require only O(N log2N) additions, which is very attractive for VLSI implementation. Using these SOPOT DCTs/DSTs, a family of SOPOT Lapped Transforms (LT) is also developed. They have similar coding gains but much lower complexity than their real-valued counterparts.published_or_final_versio

An efficient multiplierless approximation of the fast Fourier transform using sum-of-powers-of-two (SOPOT) coefficients

This letter proposes a new multiplierless approximation of the discrete Fourier transform (DFT) called the multiplierless fast Fourier transform-like (ML-FFT) transformation. It makes use of a novel factorization to parameterize the twiddle factors in the conventional radix-2 n or split-radix FFT algorithms as certain rotation-like matrices and approximates the associated parameters using the sum-of-powers-of-two (SOPOT) or canonical signed digits (CSD) representations. The ML-FFT converges to the DFT when the number of SOPOT terms used increases and has an arithmetic complexity of O(N log 2 N) additions, where N = 2 m is the transform length. Design results show that the ML-FFT offers flexible tradeoff between arithmetic complexity and numerical accuracy in approximating the DFT.published_or_final_versio

Multiplierless perfect reconstruction modulated filter banks with sum-of-powers-of-two coefficients

This paper proposes an efficient class of perfect reconstruction (PR) modulated filter banks (MFB) using sum-of-powers-of-two (SOPOT) coefficients. This is based on a modified factorization of the DCT-IV matrix and the lossless latrice structure of the prototype filter, which allows the coefficients to be represented in SOPOT form without affecting the PR condition. A genetic algorithm (GA) is then used to search for these SOPOT coefficients. Design examples show that SOPOT MFB with a good frequency characteristic can be designed with very low implementation complexity. The usefulness of the approach is demonstrated with a 16-channel design example.published_or_final_versio

Error analysis and complexity optimization for the multiplier-less FFT-like transformation (ML-FFT)

This paper studies the effect of the signal round-off errors on the accuracies of the multiplier-less Fast Fourier Transform-like transformation (ML-FFT). The idea of the ML-FFT is to parameterize the twiddle factors in the conventional FFT algorithm as certain rotation-like matrices and approximate the associated parameters inside these matrices by the sum-of-power-of-two (SOPOT) or canonical signed digits (CSD) representations. The error due to the SOPOT approximation is called the coefficient round-off error. Apart from this error, signal round-off error also occurs because of insufficient wordlengths. Using a recursive noise model of these errors, the minimum hardware to realize the ML-FFT subject to the prescribed output bit accuracy can be obtained using a random search algorithm. A design example is given to demonstrate the effectiveness of the proposed approach.published_or_final_versio

Lapped orthogonal transform with integer coefficients

In this paper, a new 8-channel integer-valued lapped transform, called the Integer Lapped Orthogonal Transform (ILOT), is proposed. The new transform can be implemented using simple integer arithmetic and has very low implementation complexity. Using 5-bits to represent its transform kernel, it was found that good coding gain and stop band attenuation, similar to the LOT, could be achieved. The multiplier-less fast ILOT requires only 106 additions and 42 shifts and can be implemented in 32-bit integer arithmetic [13].published_or_final_versio

Unified Theory for Biorthogonal Modulated Filter Banks

Modulated filter banks (MFBs) are practical signal decomposition tools for M -channel multirate systems. They combine high subfilter selectivity with efficient realization based on polyphase filters and block transforms. Consequently, the O(M 2 ) burden of computations in a general filter bank (FB) is reduced to O(M log2 M ) - the latter being a complexity order comparable with the FFT-like transforms.Often hiding from the plain sight, these versatile digital signal processing tools have important role in various professional and everyday life applications of information and communications technology, including audiovisual communications and media storage (e.g., audio codecs for low-energy music playback in portable devices, as well as communication waveform processing and channelization). The algorithmic efficiency implies low cost, small size, and extended battery life, bringing the devices close to our skins.The main objective of this thesis is to formulate a generalized and unified approach to the MFBs, which includes, in addition to the deep theoretical background behind these banks, both their design by using appropriate optimization techniques and efficient algorithmic realizations. The FBs discussed in this thesis are discrete-time time-frequency decomposition/reconstruction, or equivalently, analysis-synthesis systems, where the subfilters are generated through modulation from either a single or two prototype filters. The perfect reconstruction (PR) property is a particularly important characteristics of the MFBs and this is the core theme of this thesis. In the presented biorthogonal arbitrary-delay exponentially modulated filter bank (EMFB), the PR property can be maintained also for complex-valued signals.The EMFB concept is quite flexible, since it may respond to the various requirements given to a subband processing system: low-delay PR prototype design, subfilters having symmetric impulse responses, efficient algorithms, and the definition covers odd and even-stacked cosine-modulated FBs as special cases. Oversampling schemes for the subsignals prove out to be advantageous in subband processing problems requiring phase information about the localized frequency components. In addition, the MFBs have strong connections with the lapped transform (LT) theory, especially with the class of LTs grounded in parametric window functions.<br/

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen