functionFIR_coefficients
Information
The 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. The beta parameter is only needed by the Kaiser window.
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| FIRspec | specType | Modelica_LinearSystems2.Controller.Types.FIRspec.MeanValue | Specification type of FIR filter |
| Integer | L | 2 | Length of mean value filter |
| Modelica_LinearSystems2.Utilities.Types.FilterType | filterType | Modelica_LinearSystems2.Utilities.Types.FilterType.LowPass | Type of filter |
| Integer | order | 2 | Order of filter |
| Modelica.Units.SI.Frequency | f_cut | 1 | Cut-off frequency |
| Modelica.Units.SI.Time | Ts | Sampling time | |
| Types.Window | window | Modelica_LinearSystems2.Controller.Types.Window.Rectangle | Type of window |
| Real | beta | 2.12 | Beta-Parameter for Kaiser-window |
| Real[:] | a_desired | {1, 1} | FIR filter coefficients |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real[if specType == FIRspec.MeanValue then L else (if specType == FIRspec.Window then if mod(order, 2) > 0 and filterType == FilterType.HighPass then order + 2 else order + 1 else size(a_desired, 1))] | a | Filter coefficients |