Filter

Filter RF complex baseband signals in Simulink

Since R2023a

• 

Libraries:
RF Blockset / Idealized Baseband

Description

Use the Idealized Baseband Filter block to filter RF complex baseband signals in Simulink. You can use the Butterworth, Chebyshev, or inverse Chebyshev design methods to design your filter. You can also model your filter either in the time- or frequency-domain and plot the filter characteristics.

To design an RF filter with impedance mismatches, use the Circuit Envelope Filter block.

Note

The Idealized Baseband Filter block replaces the Lowpass RF Filter, Highpass RF Filter, Bandpass RF Filter, and Bandstop RF Filter blocks.

Examples

Time Domain Filtering of RF Complex Baseband Signals in Simulink

Compare Idealized Baseband and Circuit Envelope Filter blocks.

• Open Script

Ports

Input

Port_1 — Time-dependent input signal

real scalar | real column | complex scalar | complex column

Time-dependent input signal, specified as a real scalar, real column, complex scalar, or complex column. A column represents consecutive points in time.

Data Types: double | single

Output

Port_1 — Time-dependent output signal

complex scalar | complex column

Time-dependent output signal, returned as a complex scalar or complex column. The output time-dependent signal is equal in size to the input time-dependent signal.

Data Types: double | single

Parameters

Main

Design method — Filter design method

Butterworth (default) | Chebyshev | Inverse Chebyshev

Filter design method, specified as one of the following:

• Butterworth

• Chebyshev

• Inverse Chebyshev

Filter type — Filter response type

Lowpass (default) | Highpass | Bandpass | Bandstop

Filter response type, specified as one of the following:

• Lowpass — Simulates a lowpass filter type with the design specified in Design method.

• Highpass — Simulates a highpass filter type with the design specified in Design method.

• Bandpass — Simulates a bandpass filter type with the design specified in Design method.

• Bandstop — Simulates a bandstop filter type with the design specified in Design method.

Implement using filter order — Implement using filter order

off (default) | on

Select this parameter to implement the filter order manually.

Filter order — Filter order

3 (default) | integer greater than 2

Filter order, specified as a integer greater than 2. If you set Filter design to Lowpass or Highpass, specify the number of lumped storage elements. If you set Filter design to Bandpass or Bandstop, specify twice the number of lumped storage elements.

Dependencies

To enable this parameter, select Implement using filter order.

Passband frequency (Hz) — Passband frequency

1e9 (default) | positive real scalar | positive ascending two-tuple vector

Passband frequency for lowpass, highpass, and bandpass filter types, specified as a positive real scalar or positive ascending two-tuple vector in Hz. Based on the Filter Type, accepted value types and default values differ as follows.

Filter Type	Value Type	Default Values (Hz)
Lowpass	Positive real scalar	1e9
Highpass	Positive real scalar	2000000000
Bandpass	Positive ascending two-tuple vector	[2000000000 3000000000]

Dependencies

To enable this parameter, set Filter type to Lowpass, Highpass, or Bandpass.

Passband attenuation (dB) — Passband attenuation

10*log10(2) (default) | positive real scalar

Passband attenuation of the filter, specified as a positive real scalar in dB. For bandpass filters, this value is applied equally to both edges of the passband.

Dependencies

To enable this parameter, set Filter type to Lowpass, Highpass, or Bandpass.

Stopband frequencies (Hz) — Stopband frequencies for bandstop filters

2000000000 (default) | positive real scalar | positive ascending two-tuple vector

Stopband frequencies for bandstop filters, specified as either a positive real scalar or positive ascending two-tuple vector in Hz. Based on the Filter Type and Implement using filter order parameters, accepted value types and default values differ as follows.

Filter Type	Value Type	Default Values (Hz)	To enable this parameter
Lowpass	Positive real scalar	2000000000	Set Filter type to Lowpass and clear Implement using filter order.
Highpass	Positive real scalar	1000000000	Set Filter type to Highpass and clear Implement using filter order.
Bandpass	Positive ascending two-tuple vector	[1500000000 3500000000]	Set Filter type to Bandpass and clear Implement using filter order.
Bandstop	Positive ascending two-tuple vector	[2100000000 2900000000]	Set Filter type to Bandstop and clear or select Implement using filter order.

Stopband attenuation (dB) — Stopband attenuation

40 (default) | positive real scalar

Stopband attenuation, specified as a positive real scalar greater than the Passband attenuation (dB) value in dB.

Dependencies

To enable this parameter, you can either:

• Set Filter type to Lowpass, Highpass, or Bandpass and clear Implement using filter order.

• Set Filter type to Bandstop, select Implement using filter order.

RF frequency (Hz) — Center of signal bandwidth

1000000000 (default) | positive real scalar

Center of the signal bandwidth with respect to the filter transfer function, specified as a positive real scalar in Hz. The signal bandwidth is $$\frac{1}{\text{Simulink Step Size}}$$.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

Type of simulation to run, specified as one of the following:

• Interpreted execution — Simulate the model using the MATLAB^® interpreter. This option shortens the startup time, but the speed of the subsequent simulations is slower than when you use the Code generation option. Use this mode to debug the source code of the block.

• Code generation — Simulate the 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 the speed of the subsequent simulations is faster than when you use the Interpreted execution option.

Modeling

Modeling domain — Modeling domain

Time (Fixed step) (default) | Time (Continuous) | Frequency (Digital filter)

Modeling domain, specified as one of the following:

• Time (Fixed step) — Model using fixed-step solvers (NDF2, Trapezoidal, and Backward Euler)

• Time(Continuous) — Model using continuous or stiff solvers (ode15s, ode23s, ode23t, and ode23tb)

• Frequency (Digital filter) — model using a 1-D digital filter.

Solver — Time-domain solvers

NDF2 (default) | Trapezoidal | Backward Euler | ode15s | ode23s | ode23t (trap) | ode23tb (trap+BE)

Fixed-step and continuous time-domain solvers, specified as one of the following:

Fixed-step Solvers

• NDF2 — Balance narrowband and wideband accuracy. This solver is suitable for situations where the frequency content of the signals in the system is unknown relative to the Nyquist rate.

• Trapezoidal — Perform narrowband simulations. Frequency warping and the lack of damping effects make this method inappropriate for most wideband simulations.

• Backward Euler — Simulate the largest class of systems and signals. Damping effects make this solver suitable for wideband simulation, but overall accuracy is low.

Continuous Solvers

• ode15s — Solve stiff differential equations and DAEs using a variable order method

• ode23s — Solve stiff differential equations using a low-order method

• ode23t (trap) — Solve moderately stiff ODEs and DAEs using a trapezoidal rule

• ode23tb (trap+BE) — Solve stiff differential equations using a trapezoidal rule and backward differentiation formula

Dependencies

To enable:

• Fixed-step time-domain solvers, set Modeling domain to Time (Fixed step).

• Continuous time-domain solvers, set Modeling domain to Time (Continuous).

FIR filter length — Filter length of 1-D digital filter

128 (default) | real positive integer

Filter length of the 1-D digital filter or impulse response duration, specified as a real positive integer.

Dependencies

To set this parameter, set Modeling domain to Frequency (Digital filter).

Visualization

First plot type — Plot type

S21 (default) | Phase delay | Group delay | Impulse response | Step response

Plot type of the first plot, specified as one of the following:

• S21

• Phase delay

• Group delay

• Impulse response

• Step response

Impulse response arguments — Input arguments to plot impulse response

[ 1e-11, 1e4] (default) | two-element vector

Input arguments to plot the impulse response, specified as a two-element vector. Plot the impulse response by specifying the sample time of the input signal and the number of samples in this parameter. For more information, see impulse.

Dependencies

To set this parameter, set First plot type or Second plot type to Impulse response.

Step response arguments — Input arguments to plot step response

[ 1e-11, 1e4, 1e-10 ] (default) | three-element vector

Input arguments to plot the step response, specified as a three-element vector. Plot the step response by specifying the sample time of the input signal, the number of samples, and the amount of time required for the step signal to reach the maximum value in this parameter. For more information, see stepresp.

Dependencies

To set this parameter, set First plot type or Second plot type to Step response.

First plot y-axis units — Y-axis units of first plot

Magnitude (dB) (default) | Magnitude (linear) | Angle (degrees) | Real | Imaginary

Y-axis units of the first plot, specified as one of the following:

• Magnitude (dB)

• Magnitude (linear)

• Angle (degrees)

• Real

• Imaginary

Dependencies

To set this parameter, set First plot type to S21.

Second Plot type — Plot type of second plot

None (default) | S21 | Phase delay | Group delay | Impulse response | Step response

Plot type of the second plot, specified as one of the following:

• None

• S21

• Phase delay

• Group delay

• Impulse response

• Step response

Second plot y-axis units — Y-axis units of second plot

Magnitude (dB) (default) | Magnitude (linear) | Angle (degrees) | Real | Imaginary

Y-axis units of the second plot, specified as one of the following:

• Magnitude (dB)

• Magnitude (linear)

• Angle (degrees)

• Real

• Imaginary

Dependencies

To set this parameter, set Second plot type to S21.

X-axis frequency points (Hz) — Frequency points to plot S-parameter data

logspace(8,10,2001) (default) | positive real vector

Frequency points to plot the S-parameter data, specified as a positive real vector in Hz.

X-axis scale — Linear or logarithmic X-axis scale

Linear (default) | Logarithmic

Select this parameter to plot your data on a linear or logarithmic X-axis scale. Specify Linear or Logarithmic.

Y-axis scale — Linear or logarithmic Y-axis scale

Linear (default) | Logarithmic

Select this parameter to plot your data in a linear or logarithmic Y-axis scale. Specify Linear or Logarithmic.

Plot Sparameter characteristics — Plot S-parameters data

button

Select this button to plot the characteristics of the S-parameters data.

Algorithms

Determine FIR Filter Coefficients

The software calculates the discrete FIR filter coefficients using the RF frequency (Hz) and FIR filter length parameters and the transfer function specified using the derived filter poles and zeros.

The following steps are followed to determine the Discrete FIR Filter block direct form coefficients:

1. Determine the frequency points contained in the bandwidth centered around the carrier frequency using this formula.

   $$\begin{array}{l}Freqs=\left[\left(\left(\frac{-ff{t}_{Len}}{2}\right):\left(\frac{ff{t}_{Len}}{2}-1\right)\right)\times \left(\frac{1}{t_{step}\times ff{t}_{Len}}\right)\right]+f_{carrier}\\ \text{where}\\ f_{carrier}-\text{Carrier frequency in Hz}\\ ff{t}_{Len}-\text{FIR filter length}\\ t_{step}-\text{Time step of the filter}\end{array}$$

2. Use the rffilter object and its functions to determine the rational analog filter transfer function from the mask parameters in [z,p,k] form.

3. Determine transfer function values for the frequency points in step one using this formula.

   $$Transf(Freqs)=k\times \frac{\prod \left(z-2\pi j\times Freqs\right)}{\prod \left(p-2\pi j\times Freqs\right)}$$

4. Determine the discrete FIR filter coefficients using this formula.

   $$Coeffs=\left(-1^{FilterOrder}\right)\times ifft\left(fftshift\left(Transf\left(Freqs\right)\right)\right)$$

Extended Capabilities

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

Version History

Introduced in R2023a

R2024b: Parameters of Filter block from idealized baseband library have been renamed

The following in the Filter block in the idealized baseband library have been renamed:

Parameter Name Before R2024b	Parameter Name Since R2024b
Carrier frequency (Hz)	RF frequency (Hz)

The following parameter values in the Filter block in the idealized baseband library have been changed.

Parameter	Values Before R2024b	Values Since R2024b
Modeling domain	Time domain (Fixed step)	Time (Fixed step)
	Time domain (Continuous)	Time (Continuous)
	Frequency domain (Digital filter)	Frequency (Digital filter)

When you open a model created before R2024b containing the S-parameters block, the software replaces the parameter names and values as shown in the table.

R2023a: Lowpass RF, Highpass RF, Bandpass RF, and Bandstop RF Filter blocks have been replaced

Starting in R2023a, the idealized baseband Filter block replaces the Lowpass RF Filter, Highpass RF Filter, Bandpass RF Filter, and Bandstop RF Filter blocks.

When you open a model created before R2023a containing the Lowpass RF Filter, Highpass RF Filter, Bandpass RF Filter, and Bandstop RF Filter Filter blocks, the software replace the old blocks with the new idealized baseband Filter block.