A constrained iterative deconvolution technique with an optimal filtering: application to a hydrocarbon concentration sensor

"Self-Wiener" Filtering: Data-Driven Deconvolution of Deterministic Signals

“…It is important to bear in mind that, in practice, since the input signal is unknown, and therefore the per frequency SNRs are unknown as well, the MSE cannot be evaluated, hence it is not clear how one chooses 3 the tuning parameter q, which clearly affects the resulting performance considerably. In contrast, since our proposed SW estimator is free of such a tuning parameter, in some sense, it implicitly chooses the proper "weighting", according to the per frequency estimated output SNR (22).…”

“…Note that in our setting, where no assumptions on the input signal's DFT X[k] are made, (46) is generally biased and overestimated. Therefore, the estimated output SNR (22) will now be lower. In turn, this will cause performance degradation at frequencies with high and intermediate SNR, since a higher shrinkage value (20) will be wrongfully used.…”

“…Nevertheless, this "defense mechanism" is of course limited due to the fact that X is unknown. Indeed, the SW estimator, as any other estimator in this setup, cannot accurately distinguish between the presence of a dominant signal and a highly "energized" realization of noise, which is manifested as a large estimated output SNR (22). Consequently, in the later case, |Z| will be above the threshold, causing an erroneous estimate.…”

Optical Waveguiding and Applied Photonics

“…Consequently, a pre-low-pass filtering of observed data can be very useful in some cases. The aim is to propose a new advanced filtering scheme with an adaptive noise canceller (ANC), which, with a knowledge of a priori noise statistics and the lidar profile, optimizes a set of digital filter coefficients to adapt its impulse response to improve the SNR (Neveux et al 2000). The choice of adaptive algorithm in a normalized least mean square (N-LMS) that updates the filter weight looking up to input signal power, making a fine tuning of impulse response.…”

On teaching measurement applications of digital signal processing

“…• in [11], the forward-model-based calibration is applied for compensation of the dynamic imperfections of a Fabry-Perot fibre-optic sensor of temperature, under an assumption that the sensor can be adequately modelled by means of a linear ordinary differential equation with constant coefficients; an iterative method is used for estimation of those coefficients; • in [12], the inverse-model-based calibration is applied for compensating the inertia of a sensor, under an assumption that the sensor can be adequately modelled by means of a linear ordinary differential equations with constant coefficients; an inverse linear filter, compensating the zeros and poles of the corresponding transfer function, is designed on the basis of the sensor responses to appropriately selected polynomial and sinusoidal test signals; • in [13], an iterative method of deconvolution, based on the use of a conjugate-gradient algorithm of constrained optimization combined with a linear Wiener-type filter, is used for reconstruction of time-varying concentrations of polluting agents, emitted by a boiler during its cracking, on the basis of data provided by a hydrocarbon sensor.…”