Novel necessary and sufficient existence conditions for convolution inverses of real finite sequences are derived. These conditions are obtained with the aid of well known…
Abstract
Novel necessary and sufficient existence conditions for convolution inverses of real finite sequences are derived. These conditions are obtained with the aid of well known conditions expressed in terms of the Fourier and z‐transforms. The conditions given in the paper imply suitable algorithms, which are convenient for checking the existence of convolution inverses of any real finite sequences.
Henryk UGOWSKI and Andrzej DYKA
The aim of this paper is to prove the existence and unicity of the convolution inverse for a certain class of real functions of the discrete argument. The properties of these…
Abstract
The aim of this paper is to prove the existence and unicity of the convolution inverse for a certain class of real functions of the discrete argument. The properties of these inverses, in particular the errors that arise from the truncation of the infinite sequences that represent them, are examined. In the second part of this paper subtitled “Application in solving convolution equations” the possibility of using convolution inverses for determining the solution to the Fredholm equations of the first kind is discussed.
Andrzej DYKA and Henryk UGOWSKI
The aim of this paper is to show that in the case of even input signals with sidelobes of equal amplitude and arbitrary sign the D‐algorithm introduced in the first part of this…
Abstract
The aim of this paper is to show that in the case of even input signals with sidelobes of equal amplitude and arbitrary sign the D‐algorithm introduced in the first part of this paper subtitled “Theory”, may give a solution which is equal to that with the Chebyshev minimax norm for the approximation error. It is proved that, with some restrictions, in the case of two, four, and six sidelobe even input signals, the algorithm discussed gives exactly the Chebyshev minimax solution—CMS. Also, properties of the algorithm in the case of more general input signal are discussed.
Andrzej DYKA and Henryk UGOWSKI
A new computational noniterative algorithm which gives the solution to a linear deconvolution‐inverse filtering problem is proposed and its properties are studied. It is proved…
Abstract
A new computational noniterative algorithm which gives the solution to a linear deconvolution‐inverse filtering problem is proposed and its properties are studied. It is proved, in some specific cases of input signal, that the algorithm discussed gives the solution, which is equal to that with the Chebyshev minimax norm for the approximation error. In a general case of input signal the solution obtained provides a good prompt for determining an “appropriate subsystem” of n + 1 linear equations of n unknowns, which directly gives the Chebyshev minimax norm based solution.
H. UGOWSKI and A. DYKA
A solution of a discrete minimax problem is derived, using the standard methods of approximation theory. It represents a problem of the deconvolution‐inverse filtering of a…
Abstract
A solution of a discrete minimax problem is derived, using the standard methods of approximation theory. It represents a problem of the deconvolution‐inverse filtering of a three‐element discrete even signal, subject to a constraint on the output signal sidelobe level. Consequently, properties of this solution, in particular the asymptotic behaviour of the parameter, which represents the degradation of signal‐to‐noise ratio due to the filtering are examined.
Henryk UGOWSKI and Andrzej DYKA
In the first part of this paper subtitled ‘Theory and estimation of the truncation error’ we have examined the existence and unicity of the convolution inverse. In this part of…
Abstract
In the first part of this paper subtitled ‘Theory and estimation of the truncation error’ we have examined the existence and unicity of the convolution inverse. In this part of the paper we discuss the application of convolution inverses for determining the solution to the Fredholm equation of the first kind. Particular attention is paid to the errors that arise from both the truncation of the infinite sequence that represents the inverse and the inaccuracy in input data.
In this note we correct the flow diagram of the ascent algorithm for the linear minimax problem which was shown by Cheney on p. 50.
Abstract
In this note we correct the flow diagram of the ascent algorithm for the linear minimax problem which was shown by Cheney on p. 50.
This paper presents a closed form analytic solution for the impulse response of an optimum FIR deconvolution filter intended for a pair of discrete pulses of arbitrary amplitude…
Abstract
This paper presents a closed form analytic solution for the impulse response of an optimum FIR deconvolution filter intended for a pair of discrete pulses of arbitrary amplitude and sign, subject to the minimisation of Chebyshev maximum norm for the approximation error. The tradeoff between the approximation error and the degradation of signal‐to‐noise ratio, is examined.