Tunable Bandpass IIR Filter

Design IIR bandpass filter with tunable filter specifications

Since R2023a

• 

Libraries:
DSP System Toolbox / Filtering / Filter Sources

Description

Use the Tunable Bandpass IIR Filter block to design an IIR bandpass filter using the Butterworth, Chebyshev Type I and Chebyshev Type II design methods. You can tune the filter design specifications such as the filter order, 3-dB cutoff frequencies, passband ripple, and stopband attenuation while the simulation is running. When the values of these parameters change, the block redesigns the filter and outputs the numerator and denominator coefficients in the fourth-order section form.

Examples

Filter Noisy Signal Using Fourth-Order Section (FOS) Filter in Simulink

Filter a noisy sinusoidal signal using the Fourth-Order Section Filter block. The numerator and denominator coefficients of the fourth-order section filter are obtained using the Tunable Bandpass IIR Filter block. You can tune the frequency specifications of this filter during simulation.

Open and Run the Model

The input signal is a sum of two sine waves with the frequencies of 100 Hz and 350 Hz. The sample rate is 1000 Hz and the number of samples in each frame is 1024. Add zero-mean white Gaussian noise with a variance of 1e-4 to the sum of the sine waves.

The Tunable Bandpass IIR Filter block designs a sixth order bandpass IIR filter with the first and second 3-dB cutoff frequencies at 0.25 rad/sample and 0.75 rad/sample, respectively. Visualize the frequency response of the filter using Filter Visualizer.

Filter the noisy sinusoidal signal using the Fourth-Order Section Filter block. Visualize the original sinusoidal signal and the filtered signal using the Spectrum Analyzer.

Tuning Frequency Specification of FOS Filter

During simulation, you can tune the frequency specifications of the FOS filter by tuning the frequency parameters in the Tunable Bandpass IIR Filter block. The filter response updates accordingly.

Change the first 3-dB cutoff frequency to 0.65 rad/sample in the Tunable Bandpass IIR Filter block. The first tone of the sinusoidal signal is attenuated as it no longer falls in the passband frequency of the filter.

Ports

Input

N — Filter order

even positive integer

Specify the filter order as an even positive integer.

Dependency

To enable this port, select the Specify filter order from input port parameter.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Fc1 — First 3-dB cutoff frequency

nonnegative scalar ≤ Fc2

Specify the first 3-dB cutoff frequency Fc1 of the filter in normalized frequency units as a nonnegative scalar less than or equal to the second 3-dB cutoff frequency Fc2.

Dependency

To enable this port, select the Specify first 3-dB cutoff frequency from input port parameter.

Data Types: single | double

Fc2 — Second 3-dB cutoff frequency

Fc1 ≤ positive scalar ≤ 1

Specify the second 3-dB cutoff frequency of the filter in normalized frequency units as a positive scalar greater than or equal to Fc1 and less than or equal to 1.

Dependency

To enable this port, select the Specify second 3-dB cutoff frequency from input port parameter.

Data Types: single | double

Ap — Passband ripple in dB

nonnegative scalar

Specify the passband ripple of the Chebyshev Type I filter as a nonnegative scalar in dB.

Dependency

To enable this port:

• Set the Design method parameter to Chebyshev Type I.

• Select the Specify the passband ripple from input port parameter.

Data Types: single | double

Ast — Stopband attenuation in dB

nonnegative scalar

Specify the stopband attenuation of the Chebyshev Type II filter as a nonnegative scalar in dB.

Dependency

To enable this port:

• Set the Design method parameter to Chebyshev Type II.

• Select the Specify the stopband attenuation from input port parameter.

Data Types: single | double

Output

Num — Numerator coefficients

P-by-5 matrix

Numerator coefficients b, returned as a P-by-5 matrix (fourth-order section form), where P is the number of filter sections.

$$b=\left[\begin{array}{ccccc}{b}_{01}& b_{11}& b_{21}& b_{31}& b_{41}\\ b_{02}& b_{12}& b_{22}& b_{32}& b_{42}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ b_{0P}& b_{1P}& b_{2P}& b_{3P}& b_{4P}\end{array}\right]$$

This equation represents the fourth-order section filter in the transfer function form.

$$H(z)={\displaystyle \prod _{k=1}^P{H}_k}(z)={\displaystyle \prod _{k=1}^P\frac{b_{0k}+b_{1k}{z}^{-1}+b_{2k}{z}^{-2}+b_{3k}{z}^{-3}+b_{4k}{z}^{-4}}{a_{0k}+a_{1k}{z}^{-1}+a_{2k}{z}^{-2}+a_{3k}{z}^{-3}+a_{4k}{z}^{-4}}}$$

where,

• a –– Denominator coefficients matrix. For more details on how to specify this matrix, see the Den output port.

• k –– Row index.

The maximum number of filter sections equals ceil(N_max/4), where N_max is the value of the Filter maximum order (must be even) parameter.

When the actual filter order N is less than the maximum filter order N_max, the last ceil(N_max/4) − ceil(N/4) sections are trivial with coefficients [b₀, b₁, b₂, b₃, b₄] = [1, 0, 0, 0, 0].

The data type of this port depends on the value of the Output data type parameter.

Data Types: single | double

Den — Denominator coefficients

P-by-5 matrix

Denominator coefficients a, returned as a P-by-5 matrix (fourth-order section form), where P is the number of filter sections.

$$a=\left[\begin{array}{ccccc}{a}_{01}& a_{11}& a_{21}& a_{31}& a_{41}\\ a_{02}& a_{12}& a_{22}& a_{32}& a_{42}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ a_{0P}& a_{1P}& a_{2P}& a_{3P}& a_{4P}\end{array}\right]$$

This equation represents the fourth-order section filter in the transfer function form.

$$H(z)={\displaystyle \prod _{k=1}^P{H}_k}(z)={\displaystyle \prod _{k=1}^P\frac{b_{0k}+b_{1k}{z}^{-1}+b_{2k}{z}^{-2}+b_{3k}{z}^{-3}+b_{4k}{z}^{-4}}{a_{0k}+a_{1k}{z}^{-1}+a_{2k}{z}^{-2}+a_{3k}{z}^{-3}+a_{4k}{z}^{-4}}}$$

where,

• b –– Numerator coefficients matrix. For more details on how to specify this matrix, see the Num output port.

• k –– Row index.

The maximum number of filter sections equals ceil(N_max/4), where N_max is the value of the Filter maximum order (must be even) parameter.

The leading denominator coefficient a₀ is always 1.

When the actual filter order N is less than the maximum filter order N_max, the last ceil(N_max/4) − ceil(N/4) sections are trivial with coefficients [a₀, a₁, a₂, a₃, a₄] = [1, 0, 0, 0, 0].

The data type of this port depends on the value of the Output data type parameter.

Data Types: single | double

Parameters

Design method — Filter design method

Butterworth (default) | Chebyshev Type I | Chebyshev Type II

Specify the filter design method as:

• Butterworth

• Chebyshev Type I

• Chebyshev Type II

Specify filter order from input port — Flag to specify filter order from input port

off (default) | on

Select this parameter to specify the filter order from the input port N. When you clear this parameter, you can specify the filter order in the block dialog box using the Filter order (must be even) parameter.

Filter order (must be even) — Filter order

6 (default) | even positive integer

Specify the filter order as an even positive integer less than or equal to the value of the Filter maximum order (must be even) parameter.

Tunable: Yes

Dependency

To enable this parameter, clear the Specify filter order from input port parameter.

Filter maximum order (must be even) — Maximum order of filter

10 (default) | even positive integer

Specify the maximum order of the filter as an even positive integer. The value you specify in the Filter order (must be even) parameter must be less than or equal to the value you specify in the Filter maximum order (must be even) parameter.

Specify first 3-dB cutoff frequency from input port — Specify first 3-dB cutoff frequency from input port

off (default) | on

Select this parameter to specify the first 3-dB filter cutoff frequency from the input port Fc1. When you clear this parameter, you can specify the first 3-dB cutoff frequency in the block dialog box using the First 3-dB cutoff frequency parameter.

First 3-dB cutoff frequency — First 3-dB cutoff frequency

0.25 (default) | positive scalar

Specify the first 3-dB cutoff frequency of the filter in normalized frequency units as a positive scalar less than or equal to the second 3-dB cutoff frequency.

Tunable: Yes

Dependency

To enable this parameter, clear the Specify first 3-dB cutoff frequency from input port parameter.

Specify second 3-dB cutoff frequency from input port — Specify second 3-dB cutoff frequency from input port

off (default) | on

Select this parameter to specify the second 3-dB filter cutoff frequency from the input port Fc2. When you clear this parameter, you can specify the second 3-dB cut-off frequency in the block dialog box using the Second 3-dB cutoff frequency parameter.

Second 3-dB cutoff frequency — Second 3-dB cutoff frequency

0.75 (default) | positive scalar

Specify the second 3-dB cutoff frequency of the filter in normalized frequency units as a positive scalar greater than or equal to the first 3-dB cutoff frequency and less than or equal to 1.

Tunable: Yes

Dependency

To enable this parameter, clear the Specify second 3-dB cutoff frequency from input port parameter.

Specify the passband ripple from input port — Specify passband ripple from input port

off (default) | on

Select this parameter to specify passband ripple from the input port Ap. When you clear this parameter, you can specify the passband ripple in the block dialog box using the Passband ripple (dB) parameter.

Dependency

To enable this parameter, set the Design method parameter to Chebyshev Type I.

Passband ripple (dB) — Passband ripple in dB

1 (default) | positive scalar

Specify the passband ripple of the Chebyshev Type I filter as a positive scalar in dB.

Tunable: Yes

Dependency

To enable this parameter:

• Set the Design method parameter to Chebyshev Type I.

• Clear the Specify the passband ripple from input port parameter.

Specify the stopband attenuation from input port — Specify stopband attenuation from input port

off (default) | on

Select this parameter to specify stopband attenuation from the input port Ast. When you clear this parameter, you can specify the stopband attenuation in the block dialog box using the Stopband attenuation (dB) parameter.

Dependency

To enable this parameter, set the Design method parameter to Chebyshev Type II.

Stopband attenuation (dB) — Stopband attenuation in dB

60 (default) | positive scalar

Specify the stopband attenuation of the Chebyshev Type II filter as a positive scalar in dB.

Tunable: Yes

Dependency

To enable this parameter:

• Set the Design method parameter to Chebyshev Type II.

• Clear the Specify the stopband attenuation from input port parameter.

Sample time — Sample time in seconds

-1 (default) | positive scalar | Inf

Specify the sample time as -1 (inherited), Inf (constant sample time), or a positive scalar. This parameter indicates when during the simulation the block produces the output and updates its internal state. For more details, see What Is Sample Time? (Simulink).

Output data type — Data type of filter coefficients

double (default) | single

Specify the data type of the filter coefficients that the block outputs through the Num and Den ports as double or single.

Simulate using — Type of simulation to run

Code generation (default) | Interpreted execution

Specify the type of simulation to run as one of the following:

• Code generation –– Simulate model using generated C code. The first time you run a simulation, Simulink^® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time but provides faster simulation speed than Interpreted execution.

• Interpreted execution –– Simulate model using the MATLAB^®  interpreter. This option shortens startup time but has slower simulation speed than Code generation.

Block Characteristics

Data Types	double | integer | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

References

[1] Orfanidis, Sophocles J. Introduction to Signal Processing. Prentice Hall, 1996.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023a