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Audio signal editing software for multi-speaker systems
Svěrák, Jan ; Schimmel, Jiří (referee) ; Sysel, Petr (advisor)
This master’s thesis focuses on creating audio editing software for multi-speaker systems which can be used for real-time signal processing, such as polarity inversion or delay ranging from one to several thousand samples. The thesis is split into three main chapters. The first chapter contains theoretical knowledge required for development of audio software, for example principles of digital signal processing. The second chapter comprises of an overview of the source files and descriptions of several significant classes and functions. The last chapter is intended as a user guide, therefore it contains instructions on how to operate the software via the user interface.
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Audio signal editing software for multi-speaker systems
Svěrák, Jan ; Schimmel, Jiří (referee) ; Sysel, Petr (advisor)
This master’s thesis focuses on creating audio editing software for multi-speaker systems which can be used for real-time signal processing, such as polarity inversion or delay ranging from one to several thousand samples. The thesis is split into three main chapters. The first chapter contains theoretical knowledge required for development of audio software, for example principles of digital signal processing. The second chapter comprises of an overview of the source files and descriptions of several significant classes and functions. The last chapter is intended as a user guide, therefore it contains instructions on how to operate the software via the user interface.
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Multivariate smooth interpolation that employs polyharmonic functions
Segeth, Karel
We study the problém of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomials therms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example is presented.
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A particular smooth interpolation that generates splines
Segeth, Karel
There are two grounds the spline theory stems from -- the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called $it smooth interpolation$ introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline with tension). We present the results of a 1D numerical example that characterize some properties of the tension spline.
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Smooth approximation spaces based on a periodic system
Segeth, Karel
A way of data approximation called smooth was introduced by Talmi and Gilat in 1977. Such an approach employs a (possibly infinite) linear combination of smooth basis functions with coefficients obtained as the unique solution of a minimization problem. While the minimization guarantees the smoothness of the approximant and its derivatives, the constraints represent the interpolating or smoothing conditions at nodes. In the contribution, a special attention is paid to the periodic basis system $exp(-ii kx)$. A 1D numerical example is presented.
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