### Block: LowpassBiQ

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 lowpass 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 lowpass.

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 lowpass. rp = 5dB

Figure 3: Bodeplot Chebyshev I lowpass. 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 lowpass. rs = 20dB

Figure 5: Bodeplot Chebyshev II lowpass. rs = 5dB

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 lowpass.

##### 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