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Analytical expressions of analog and digital α-spline filters with continuous transition bands are derived. Previous works based on β-spline functions consider the order of the spline function, which must be a natural number, as a parameter to sharpen the transition band. However, the inclusion of an α-spline model provides greater flexibility since its order can be a real number, it depends on three...
The use of transition functions to connect the passband and the stopband in the ideal amplitude frequency response of an FIR filter reduces the oscillations near the band edges caused by the Gibbs phenomenon in filters designed by windowing. To this end, several methods based on β-splines have been proposed, in which an integer order of the spline is used to properly shape the transition band of the...
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