Measurement of distorted exponential signal components using maximum likelihood estimation

• Published in: Measurement : journal of the International Measurement Confederation Vol. 58; pp. 503 - 510
• Main Authors: Michaeli, Linus, Šaliga, Ján, Liptak, Jozef, Godla, Marek, Kollár, István
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-12-2014
• Subjects: Dynamic ADC testing; Exponential testing stimulus signal; Maximum likelihood method; Signal decomposition; Exponential testing stimulus signal; Dynamic ADC testing; Maximum likelihood method; Signal decomposition
• ISSN: 0263-2241; 1873-412X
• DOI: 10.1016/j.measurement.2014.09.024

•The maximum likelihood method for the measurement of signal components is presented.•Prony’s method serves for initiating of the differential evolution procedure.•The robustness on ADC nonlinearities, quantization and clopping noise is analyzed.•Simulation and experimental data approved the effectiveness of the method.
Exponential signal is a suitable stimulus for dynamic ADC testing because of the simplicity of the generating RC circuit. A potential distortion source of the ideal exponential shape is the dielectric absorption of the capacitor, whose effect can be represented by additional superimposed exponential components with longer time constant and smaller peak value. Measurement of the distortion of the exponential signal by using a reference waveform recorder with known nonlinearity is the initial step in the calibration of an ADC testing stand with exponential stimulus, along with the assessment of its uncertainty. Lack of the orthogonality of stimulus signal components makes classical analysis methods difficult to apply.
This paper presents a method for measurement of multiexponential signal components as an example of the more general task of signal decomposition where signal components are non-orthogonal. The proper optimization procedure based on the ML method will be presented, which usually reaches the global minimum of the cost function. Effectiveness will be shown by simulation, and by application to measurement of a multiexponential signal acquired by a reference waveform recorder with known error parameters.