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Register a new userFilter Design for Autoregressive Moving Average Graph Filters
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Added by
Jiani Liu
Publication date
2017
fields
Electronic Engineering
and research's language is
English
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In the field of signal processing on graphs, graph filters play a crucial role in processing the spectrum of graph signals. This paper proposes two different strategies for designing autoregressive moving average (ARMA) graph filters on both directed and undirected graphs. The first approach is inspired by Pronys method, which considers a modified error between the modeled and the desired frequency response. The second technique is based on an iterative approach, which finds the filter coefficients by iteratively minimizing the true error (instead of the modified error) between the modeled and the desired frequency response. The performance of the proposed algorithms is evaluated and compared with finite impulse response (FIR) graph filters, on both synthetic and real data. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy and they are suitable for graph signal interpolation, compression and prediction.
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We present and validate a novel method for noise injection of arbitrary spectra in quantum circuits that can be applied to any system capable of executing arbitrary single qubit rotations, including cloud-based quantum processors. As the consequences of temporally-correlated noise on the performance of quantum algorithms are not well understood, the capability to engineer and inject such noise in quantum systems is paramount. To date, noise injection capabilities have been limited and highly platform specific, requiring low-level access to control hardware. We experimentally validate our universal method by comparing to a direct hardware-based noise-injection scheme, using a combination of quantum noise spectroscopy and classical signal analysis to show that the two approaches agree. These results showcase a highly versatile method for noise injection that can be utilized by theoretical and experimental researchers to verify, evaluate, and improve quantum characterization protocols and quantum algorithms for sensing and computing.
Vocal tract resonance characteristics in acoustic speech signals are classically tracked using frame-by-frame point estimates of formant frequencies followed by candidate selection and smoothing using dynamic programming methods that minimize ad hoc cost functions. The goal of the current work is to provide both point estimates and associated uncertainties of center frequencies and bandwidths in a statistically principled state-space framework. Extended Kalman (K) algorithms take advantage of a linearized mapping to infer formant and antiformant parameters from frame-based estimates of autoregressive moving average (ARMA) cepstral coefficients. Error analysis of KARMA, WaveSurfer, and Praat is accomplished in the all-pole case using a manually marked formant database and synthesized speech waveforms. KARMA formant tracks exhibit lower overall root-mean-square error relative to the two benchmark algorithms, with third formant tracking more challenging. Antiformant tracking performance of KARMA is illustrated using synthesized and spoken nasal phonemes. The simultaneous tracking of uncertainty levels enables practitioners to recognize time-varying confidence in parameters of interest and adjust algorithmic settings accordingly.
In this paper we derive closed-form formulas of feedback capacity and nonfeedback achievable rates, for Additive Gaussian Noise (AGN) channels driven by nonstationary autoregressive moving average (ARMA) noise (with unstable one poles and zeros), based on time-invariant feedback codes and channel input distributions. From the analysis and simulations follows the surprising observations, (i) the use of time-invariant channel input distributions gives rise to multiple regimes of capacity that depend on the parameters of the ARMA noise, which may or may not use feedback, (ii) the more unstable the pole (resp. zero) of the ARMA noise the higher (resp. lower) the feedback capacity, (iii) certain conditions, known as detectability and stabilizability are necessary and sufficient to ensure the feedback capacity formulas and nonfeedback achievable rates {it are independent of the initial state of the ARMA noise}. Another surprizing observation is that Kims cite{kim2010} characterization of feedback capacity which is developed for stable ARMA noise, if applied to the unstable ARMA noise, gives a lower value of feedback capacity compared to our feedback capacity formula.
In this paper, we incorporate a graph filter deconvolution step into the classical geometric convolutional neural network pipeline. More precisely, under the assumption that the graph domain plays a role in the generation of the observed graph signals, we pre-process every signal by passing it through a sparse deconvolution operation governed by a pre-specified filter bank. This deconvolution operation is formulated as a group-sparse recovery problem, and convex relaxations that can be solved efficiently are put forth. The deconvolved signals are then fed into the geometric convolutional neural network, yielding better classification performance than their unprocessed counterparts. Numerical experiments showcase the effectiveness of the deconvolution step on classification tasks on both synthetic and real-world settings.
This paper presents a case study on short-term load forecasting for France, with emphasis on special days, such as public holidays. We investigate the generalisability to French data of a recently proposed approach, which generates forecasts for normal and special days in a coherent and unified framework, by incorporating subjective judgment in univariate statistical models using a rule-based methodology. The intraday, intraweek, and intrayear seasonality in load are accommodated using a rule-based triple seasonal adaptation of a seasonal autoregressive moving average (SARMA) model. We find that, for application to French load, the method requires an important adaption. We also adapt a recently proposed SARMA model that accommodates special day effects on an hourly basis using indicator variables. Using a rule formulated specifically for the French load, we compare the SARMA models with a range of different benchmark methods based on an evaluation of their point and density forecast accuracy. As sophisticated benchmarks, we employ the rule-based triple seasonal adaptations of Holt-Winters-Taylor (HWT) exponential smoothing and artificial neural networks (ANNs). We use nine years of half-hourly French load data, and consider lead times ranging from one half-hour up to a day ahead. The rule-based SARMA approach generated the most accurate forecasts.
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