Block: BandstopBiQ

Description:

Calculates the filter coefficients for a second order bandstop and performs filtering on input signal.

Second order transfer function used:

H(z) = (b0.z² + b1.z + b2) / (z² + a1.z + a2)

Butterworth

• center frequency f_c

  • center frequency f_c is given by f_c² = f _c1² * f _c2²

  • phase discontinuity @center frequency f_c

• @lower cut-off frequency  f_c1

  • -3dB attenuation

  • -45 degree phaseshift

• @upper cut-off frequency f_c2

  • -3dB attenuation

  • 45 degree phaseshift

• passband

  • roll-off dynamics are constant and not adjustable

E.g.:
The cut-off frequencies are f_c1 = 100Hz and f_c2 = 300Hz.
The bodeplot is shown in the figure 1 below.

Chebyshev
Note: A second order Chebyshev I bandstop has the same bodeplot as a second order Chebyshev II bandstop. Hence, only the ’Chebyshev’ option is given.

• center frequency f_c

  • center frequency f_c is given by f_c² = f _c1² * f _c2²

  • phase discontinuity @center frequency f_c

• @lower cut-off frequency  f_c1

  • -rcdB attenuation

  • -phaseshift proportional to rc

• @upper cut-off frequency f_c2

  • -rcdB attenuation

  • phaseshift proportional to rc

• passband

  • roll-off dynamics are adjustable using parameter rc

E.g.:
The cut-off frequencies are f_c1 = 100Hz and f_c2 = 300Hz.
The parameter rc is set to 10dB.
The bodeplot is shown in the figure 2 below.

Bessel
Note: A second order Bessel bandstop behaves exactly like a second order Butterworth bandstop. Hence, no ’Bessel’ option is given.

Implementations:

Implementation: FiP16

16 Bit Fixed Point Implementation

Implementation: FiP32

32 Bit Fixed Point Implementation

Implementation: Float32

32 Bit Floating Point Implementation

Implementation: Float64

64 Bit Floating Point Implementation