Complexity of pruning strategies for the frequency domain LMS algorithm

Large adaptive filters are frequently used in diverse applications such as channel equalization, interference suppression, beamforming, etc. The least mean squared (LMS) algorithm and its variants form one of the basic building blocks of adaptive systems. The frequency domain implementations of the LMS algorithm are preferred in practice since the computational burden of LMS can be reduced significantly by using the vast family of fast fourier transform (FFT) algorithms. Despite the advantage of frequency domain LMS over regular-LMS, the increasing computational complexity of the FFT-based LMS algorithms (with filter length) makes them unattractive for applications with a large number of filter taps. In this paper, FFT pruning is used to reduce the computational cost of frequency domain LMS by exploiting the structure of the LMS algorithm. We study various pruning strategies with our objective being reduction in computational burden and conclude that transform decomposition is the most appropriate pruning strategy. Using this pruning technique, worst-case computational savings of 10% and 5% can be achieved for applications that use filter lengths on the order of a few hundreds and a few thousands, respectively. In delay-sensitive applications, substantially more savings can be effected by pruning

An analysis of real-Fourier domain based adaptive algorithms implemented with the Hartley transform using cosine-sine symmetries

The least mean squared (LMS) algorithm and its variants have been the most often used algorithms in adaptive signal processing. However the LMS algorithm suffers from a high computational complexity, especially with large filter lengths. The Fourier transform-based block normalized LMS (FBNLMS) reduces the computation count by using the discrete Fourier transform (DFT) and exploiting the fast algorithms for implementing the DFT. Even though the savings achieved with the FBNLMS over the direct-LMS implementation are significant, the computational requirements of FBNLMS are still very high, rendering many real-time applications, like audio and video estimation, infeasible. The Hartley transform-based BNLMS (HBNLMS) is found to have a computational complexity much less than, and a memory requirement almost of the same order as, that of the FBNLMS. This paper is based on the cosine and sine symmetric implementation of the discrete Hartley transform (DHT), which is the key in reducing the computational complexity of the FBNLMS by 33% asymptotically (with respect to multiplications). The parallel implementation of the discrete cosine transform (DCT) in turn can lead to more efficient implementations of the HBNLMS

Signal denoising techniques for partial discharge measurements

One of the major challenges of on-site partial discharge (PD) measurements is the recovery of PD signals from a noisy environment. The different sources of noise include thermal or resistor noise added by the measuring circuit, and high-frequency sinusoidal signals that electromagnetically couple from radio broadcasts and/or carrier wave communications. Sophisticated methods are required to detect PD signals correctly. Fortunately, advances in analog-to-digital conversion (ADC) technology, and recent developments in digital signal processing (DSP) enable easy extraction of PD signals. This paper deals with the denoising of PD signals caused by corona discharges. Several techniques are investigated and employed on simulated as well as real PD data

System modeling and identification in indicator dilution method for assessment of ejection fraction and pulmonary blood volume

Clinically relevant cardiovascular parameters, such as pulmonary blood volume (PBV) and ejection fraction (EF), can be assessed through indicator dilution techniques. Among these techniques, which are typically invasive due to the need for central catheterization, contrast ultrasonography provides a new emerging minimally invasive option. PBV and EF are then measured by a dilution system identification algorithm after detection of multiple dilution curves by an ultrasound scanner. In this paper, dilution systems are represented by parametric models. Since the measured indicator dilution curves (IDCs) are corrupted by measurement artifacts and outliers, the use of conventional least square error (LSE) estimator for estimating system parameters is not optimal. Different estimators are therefore proposed for estimating the system parameters. Comparison of these estimators with the LSE estimator in assessing EF and PBV is performed on simulated, in vitro and patient data. The results show that the proposed total least absolute deviation estimator (TLAD) outperforms other estimators. The measured IDCs are highly corrupted by noise, which affect the estimation of EF and PBV. Therefore, a two stage denoising method capable of removing outliers is also proposed for removing noise in IDCs