Splitting Magnitude Response into Real and Imaginary Parts

2017

The determination of real and imaginary parts from magnitude responses is studied for causal linear time-invariant systems having monotonic impulse responses. It is demonstrated that the problem can be interpreted as a special filtering task in the Mellin transform domain having a diffuse magnitude response bounded by the magnitude responses of the filters corresponding to zero and maximum imaginary parts prescribed by the Kronig-Kramers relations. Discrete-time filters processing geometrically sampled magnitude responses are designed for determining the real and imaginary parts. Testing results are presented verifying the performance of the filters.

Improving accuracy of FIR filters for computing convolution transforms for smooth non-bandlimited signals

2019

We propose to improve the accuracy of FIR filters for computing convolution transforms for smooth non-bandlimited (NBL) signals by designing filters by the identification method with using a pair of bandlimited portions of the chosen NBL input and output signals related with each other by the given transform. A design example of type IV linear phase differentiator is presented, where filter coefficients are calculated from the bandlimited portions of the Cauchy pulse and its derivative. The performance of the designed differentiator is evaluated by comparing the accuracy of computed derivatives for several smooth NBL test signals, such as the Cauchy pulse, the Hilbert transform of Cauchy pu…

DIGITAL EMULATION OF DIELECTRIC RELAXATION FUNCTIONS FOR CAPACITIVE SENSORS OF NON-DESTRUCTIVE DIELECTRIC SPECTROMETRY

2019

Digital estimators of relaxation spectra

2007

Determination of the distribution of relaxation times (DRT) from a wide variety of the time- and the frequency-domain material functions, such as polarization current and charge, real and imaginary parts of complex dielectric permittivity and complex dielectric modulus, the appropriate mechanical and magnetic counterparts is generalized as a filtering problem on a logarithmic time or frequency scale. Algorithms of the appropriate digital DRT estimators are derived. A novel regularization strategy is proposed based on choosing sampling rate for the input data, which ensures acceptably low random error of the recovered spectra. Optimum frequency ranges and sampling rates are found for determi…

Digital signal processing for relaxation data conversion

2005

Abstract The origins, philosophy and basic practical aspects are considered for an approach of digital data transformations for broadband dielectric relaxation spectroscopy and other relaxation experiments carrying out direct and inverse integral transforms with kernels depending on the ratio or product of arguments. The approach is based on the concept that the mentioned data transformations represent a filtering problem on a logarithmic scale allowing one to implement the transforms by digital functional filters with the logarithmic sampling. As an example, digital Kramers–Kronig transformers are considered.

FIR Kramers–Kronig transformers for relaxation data conversion

2006

It is shown that relaxation data conversion by the Kramers-Kronig (KK) relations can be treated as a filtering problem of band-unlimited relaxation signals in the Mellin transform domain. Based on this concept, KK relations are implemented in the form of FIR filters with the logarithmic sampling. It is demonstrated that KK transformers have sampling rate dependent impulse and frequency responses and only calculation of the imaginary part from the real part can be implemented by a computationally realisable filter. The performance of different types of transformers is studied.Approximately inversely proportional relationship is established between the error and the frequency range of input s…

Determination of relaxation and retardation spectrum by inverse functional filtering

2010

Abstract The article is devoted for the determination of the relaxation and retardation spectrum (RRS) from monotonic time- and frequency-domain material functions by the inverse functional filters executing discrete convolution algorithms for geometrically spaced data. It is shown that the problem of RRS determination from a wide variety of material functions leads to the three inverse filtering tasks on a logarithmic time or frequency scale with the three specific frequency responses concerning: (i) the time-domain functions, (ii) the real parts and (iii) the imaginary parts of the frequency-domain functions, and three algorithms (having the versions with even and odd number of coefficien…