Block: NotchBiQ


Inports

In	Input In(k)


Outports

Out	Output Out(k)


Mask Parameters

Name	ID	Description

method	1	Selection between bilinear and matched Z-transform discretization method

fn	2	Notching frequency in Hz

Q	3	Defines a quality factor of the filter

ts_fact	4	Multiplication factor of base sampling time (in integer format)

Description:

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

Second order transfer function used:

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

Calculation:

Out (k) = In(k) ⋅ H(z)

The transfer function H(z) of the filter is

- 1 - 2 H (z) = b0 +-b1z--+-b2z--- 1 + a1z-1 + a2z-2

with coefficients derived from the transfer function

s2 + ω2 H (s) = -2---ω0-0--2- s + Q + ω 0

Two methods of discretizing a continuous transfer function are available: bilinear and matching.

Warning: In some cases, the function is very sensitive to the accuracy of the coefficients. Therefore, using a fixed-point implementation can sometimes give inaccurate results.

To illustrate this issue, see step responses in figures 1 and 2 below. Filter settings are f_n = 50 Hz, Q = 10, f_s = 10 kHz.

Figure 1: Step response for ts_fact = 1.

Figure 2: Step response for t_fact = 10.

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