Identification of Hammerstein model using cubic splines and FIR filtering

Abstract

Nonlinear models are exploited in the field of digital audio systems for modelling most of real-world devices that show a nonlinear behaviour. Among nonlinear models, Hammerstein systems are realized through a static nonlinearity cascaded with a linear filter. In this paper, the Hammerstein coefficients are estimated using an adaptive Catmull-Rom cubic spline for the static nonlinearity and an adaptive FIR filter for the dynamic linear system also introducing a pre-processing for the time delay estimation. Experimental results confirm the effectiveness of the proposed approach, making also comparisons with existing techniques of the state of the art.

A Swept-Sine-Type Single Measurement to Estimate Intermodulation Distortion in a Dynamic Range of Audio Signal Amplitudes

“…It is useful to note that, having chosen as input a signal x(t) for which the ω 1 and ω 2 angular frequency components have the same amplitude R, their role will be interchangeable, and the coefficients of the respective harmonics will be equal to each other. Consequently, to avoid linear dependence between equations of the system, the function g(t) related only to one of the two angular frequencies has been inserted in the vector (13). The matrix [A I MD ] therefore plays, in the case that the input signal is a double exponential swept-sine signal, a role similar to that played by [A c ] −1 T in the case of the single exponential swept-sine signal [23].…”

“…Even if the obtained model is highly accurate, a complete knowledge of the physical system is not always possible. For this reason the grey and black box approaches have been developed, which respectively require only a partial knowledge of the system, or only the knowledge of input and output signals [13], [14], [15]. Grey box approaches use the input/output (I/O) relationship to identify the system and then the model is improved using the block diagram of the circuit.…”

“…Among them, the Hammerstein and Wiener models rely on splitting the linear dynamic part from the static, non-linear one. Although less general than Volterra or Wiener filters, the Hammerstein and Wiener models provide an accurate modeling of even strong non-linearities, using a reduced number of parameters [13], [15]. Several efforts have been made in the literature to develop an algorithm for identifying such models, mainly exploiting a suitable input swept-sine signal [20], [21], [22], [23].…”

A study about Chebyshev nonlinear filters

“…The filters find application in speech [1], audio [2,3], telecommunication [4], image processing [1], biological system modeling [5], and many other fields. The LIP class includes truncated Volterra filters [1], still actively studied and used in applications [6][7][8][9][10], but also Wiener nonlinear filters [1], Hammerstein filters [1,[11][12][13][14], memory and generalized memory polynomial filters [15,16], filters based on functional expansions of the input samples, as functional link artificial neural networks (FLANN) [17][18][19][20] and radial basis function networks [21]. A review of finite-memory LIP nonlinear filters can be found in [22].…”

Introducing Legendre nonlinear filters

“…Among LIP filters, the most popular are the truncated Volterra filters [1], still actively studied and used in applications [2, 3,4,5,6,7,8,9]. Other elements of the class include particular cases of Volterra filters, as the Hammerstein filters [1, 10,11,12,13], and modified forms of Volterra filters, as memory and generalized memory polynomial filters [14,15]. Filters based on functional expansions of the input samples, as functional link artificial neural networks (FLANN) [16] and radial basis function networks [17], also belong to the LIP class.…”