Block: HighpassBiQ


Inports

In	Input In(k)


Outports

Out	Output Out(k)


Mask Parameters

Name	ID	Description

characteristic	1	The filter characteristic is one of Butterworth, Chebyshev I, Chebyshev II (also known as inverse Chebyshev) or Bessel

fc	2	Cut-off frequency in Hz

rp	3	The passband ripple is only used and verified with ’Chebyshev I’ filters. Must be a positive number

rs	4	The stopband ripple is only used and verified with ’Chebyshev II’ filters. Must be a positive number

ts_fact	5	Multiplication factor of base sampling time (in integer format)

Description:

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

Second order transfer function used:

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

Butterworth

passband
- maximal flat
@cut-off frequency:
- -3dB attenuation
- -90 degree phaseshift
stopband
- monotonic -40dB decline per decade
- approx. -37dB decline within fist decade

E.g.: Cut-off frequency is 10Hz. The bodeplot is shown in the figure 1 below.

Figure 1: Bodeplot Butterworth highpass.

Chebyshev I

passband:
- N/2=1 ripple in the passband.
- attenuation from 0 to rp [dB].
@cut-off frequency: attenuation is bigger than or equal rp [dB].
stopband:
- monotonic -40dB decline per decade
Trade-off:
- the bigger passband ripple rp is choosen, the steeper is the magnitude cut-off within the first decade in stopband
- the bigger the passband ripple rp is choosen, the bigger is the overall passband attenuation!

E.g.:
Cut-off frequency is 10Hz.
The maximal ripple in the passband rp must be given in [dB].
To show the mentioned trade-off, two bodelplots are shown. One with a small and one with a bigger rp. The bodeplot is shown in the figures 2 and 3 below.

Figure 2: Bodeplot Chebyshev I highpass. rp = 5dB

Figure 3: Bodeplot Chebyshev I highpass. rp = 20dB

Chebyshev II
Also known as inverse Chebyshev filter.

passband
- flat, no ripples
@cut-off frequency: attenuation is rs [dB].
stopband
- N/2=1 ripple in the stopband
- attenuation is smaller than or equal rs [dB].
Trade-off:
- the lower rs is choosen, the sharper is the magnitude cut-off
- the lower rs is choosen, the lower is the over all stopband attenuation

E.g.:
Cut-off frequency is 10Hz.
The maximal ripple in the stopband rs must be given in [dB].
To show the mentioned trade-off, two bodelplots are shown. One with a small and one with a bigger rs. The bodeplot is shown in the figures 4 and 5 below.

Figure 4: Bodeplot Chebyshev II highpass. rs = 5dB

Figure 5: Bodeplot Chebyshev II highpass. rs = 20dB

Bessel

passband
- constant group-delay in passband.
- least sharp magnitude roll-off.
@cut-off frequency:
- approx. -1.6 dB attenuation
- approx. -56 degree phaseshift
stopband
- monotonic -40dB decline per decade
- approx. -30dB decline within first decade

E.g.:
Cut-off frequency is 10Hz.
The bodeplot is shown in the figure 6 below.

Figure 6: Bodeplot Bessel highpass.

Implementations:

FiP16	16 Bit Fixed Point Implementation
FiP32	32 Bit Fixed Point Implementation
Float32	32 Bit Floating Point Implementation
Float64	64 Bit Floating Point Implementation

Implementation: FiP16

16 Bit Fixed Point Implementation


Inports Data Type

In	int16


Outports Data Type

Out	int16

Implementation: FiP32

32 Bit Fixed Point Implementation


Inports Data Type

In	int32


Outports Data Type

Out	int32

Implementation: Float32

32 Bit Floating Point Implementation


Inports Data Type

In	float32


Outports Data Type

Out	float32

Implementation: Float64

64 Bit Floating Point Implementation


Inports Data Type

In	float64


Outports Data Type

Out	float64