functionFIR_coefficients
Calculates the FIR-filter coefficient vector from filter design parameters
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 |
|---|---|---|---|
| Modelica_Synchronous.WorkInProgress.Incubate.Types.FIR_FilterType | filterType | Modelica_Synchronous.WorkInProgress.Incubate.Types.FIR_FilterType.LowPass | Type of filter |
| Integer | order | 2 | Order of filter |
| Modelica.SIunits.Frequency | f_cut | 1 | Cut-off frequency |
| Modelica.SIunits.Time | Ts | Sampling period | |
| Modelica_Synchronous.WorkInProgress.Incubate.Types.FIR_Window | window | Modelica_Synchronous.WorkInProgress.Incubate.Types.FIR_Window.Rectangle | Type of window |
| Real | beta | 2.12 | Beta-Parameter for Kaiser-window |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real[order + 1] | a | Filter coefficient vector |