.Modelica_Synchronous.WorkInProgress.Incubate.Internal.FIR_coefficients .Modelica_Synchronous.WorkInProgress.Incubate.Internal.FIR_coefficientsThe FIR-filter synthesis based on the window method. The coefficients are calculated through a fourier series approximation of the desired amplitude characteristic. Due to the fact that the Fourier series is truncated, there will be discontinuities in the magnitude of the filter. Especial at the edge of the filter the ripple is concentrated (Gibbs-effect). To counteract this, the filter coefficients are convolved in the frequency domain with the spectrum of a window function, thus smoothing the edge transitions at any discontinuity. This convolution in the frequency domain is equivalent to multiplying the filter coefficients with the window coefficients in the time domain.
The filter equation
y(k) = a0*u(k) + a1*u(k-1) + a2*u(k-2) + ... + an*u(k-n)
implies that the function outputs n+1 coefficients for a n-th order filter. The
coefficients can be weightened with different kind of windows: Rectangle, Bartlett,
Hann, Hamming, Blackman, Kaiser function FIR_coefficients
import FilterType = Modelica_Synchronous.WorkInProgress.Incubate.Types.FIR_FilterType;
input Modelica_Synchronous.WorkInProgress.Incubate.Types.FIR_FilterType filterType = Modelica_Synchronous.WorkInProgress.Incubate.Types.FIR_FilterType.LowPass "Type of filter";
input Integer order(min = 1) = 2 "Order of filter";
input Modelica.SIunits.Frequency f_cut = 1 "Cut-off frequency";
input Modelica.SIunits.Time Ts(min = 0) "Sampling period";
input Modelica_Synchronous.WorkInProgress.Incubate.Types.FIR_Window window = Modelica_Synchronous.WorkInProgress.Incubate.Types.FIR_Window.Rectangle "Type of window";
input Real beta = 2.12 "Beta-Parameter for Kaiser-window" annotation(
Dialog(enable = window == Modelica_Synchronous.Types.Window.Kaiser));
output Real a[order + 1] "Filter coefficient vector";
end FIR_coefficients;