Filter

Filter complex RF broadband signals.

blockType: Filter

Path in the library:

/RF/Idealized Baseband/Filter

Description

Block Filter It is a filter of complex radio frequency (RF) broadband signals. To design a filter, you can use the Butterworth, Chebyshev methods, or the Chebyshev inverse method. You can also simulate a filter in the time or frequency domain and plot its characteristics.

Ports

Input

# In — time-dependent input signal
the real scalar | the real column | the complex scalar | the complex column

Details

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

Data types	`Float64`, `Float32`
Complex numbers support	Yes

Output

# Out — time-dependent output signal
the complex scalar | the complex column

Details

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

Data types	`Float64`, `Float32`
Complex numbers support	Yes

Parameters

Main

# Design method — filter design method
Butterworth | Chebyshev | InverseChebyshev

Details

The filter construction method. Set as:

Butterworth
Chebyshev
InverseChebyshev

Values	`Butterworth` \| `Chebyshev` \| `InverseChebyshev`
Default value	`Butterworth`
Program usage name	`DesignMethod`
Tunable	No
Evaluatable	No

# Filter type — filter response type
Lowpass | Highpass | Bandpass | Bandstop

Details

The type of filter response. Set as:

Lowpass – simulates the type of low-pass filter with the design specified in Design method.
Highpass – simulates the type of high-pass filter with the method specified in Design method.
Bandpass – simulates the type of bandpass filter with the method specified in Design method.
Bandstop – simulates the type of bandpass filter with the method specified in Design method.

Values	`Lowpass` \| `Highpass` \| `Bandpass` \| `Bandstop`
Default value	`Lowpass`
Program usage name	`ResponseType`
Tunable	No
Evaluatable	No

# Implement using filter order — enable the implementation using the filter order
Logical

Details

Check this box to implement the filter order manually.

Default value	`true (switched on)`
Program usage name	`UseFilterOrder`
Tunable	No
Evaluatable	No

# Filter order — filter order
Real number

Details

The filter order, specified as an integer, . If for Filter type value selected Lowpass or Highpass, specify the number of single storage items. If for the parameter Filter type value selected Bandpass or Bandstop, specify twice as many elements.

Dependencies

To use this option, select the option checkbox. Implement using filter order.

Default value	`3`
Program usage name	`FilterOrder`
Tunable	No
Evaluatable	Yes

# Passband frequency (Hz) — bandwidth frequency
Real number

Details

The bandwidth frequency for the low pass filter Lowpass in Hz, given as a positive real scalar.

Dependencies

To use this parameter, set for the parameter Filter type meaning Lowpass.

Default value	`1.0e9`
Program usage name	`PassFreq_lp`
Tunable	No
Evaluatable	Yes

# Passband frequency (Hz) — bandwidth frequency
Real number

Details

The bandwidth frequency for the high pass filter Highpass in Hz, given as a positive real scalar.

Dependencies

To use this parameter, set for the parameter Filter type meaning Highpass.

Default value	`2.0e9`
Program usage name	`PassFreq_hp`
Tunable	No
Evaluatable	Yes

# Passband frequencies (Hz) — bandwidth frequencies

Details

Bandwidth frequencies for a bandpass filter Bandpass in Hz, set as a positive ascending vector of two values.

Dependencies

To use this parameter, set for the parameter Filter type meaning Bandpass.

Default value	`[2.0e9 3.0e9]`
Program usage name	`PassFreq_bp`
Tunable	No
Evaluatable	Yes

# Passband frequencies (Hz) — bandwidth frequencies

Details

Bandwidth frequencies for a bandpass filter Bandstop in Hz, set as a positive ascending vector of two values.

Dependencies

To use this parameter, set for the parameter Filter type meaning Bandstop and uncheck the box Implement using filter order.

Default value	`[1.0e9 4.0e9]`
Program usage name	`PassFreq_bs`
Tunable	No
Evaluatable	Yes

# Passband attenuation (dB) — bandwidth attenuation
Real number

Details

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

Dependencies

To use this parameter, set for the parameter Filter type meaning Lowpass, Highpass or Bandpass.

Default value	`10log10(2)`
Program usage name	`PassAtten`
Tunable	No
Evaluatable	Yes

# Stopband frequency (Hz) — delay band frequencies for bandpass filters
Real number

Details

The frequency of the delay band for filters Lowpass in Hz, given as a positive real scalar.

Dependencies

To use this parameter, set for the parameter Filter type meaning Lowpass.

Default value	`2.0e9`
Program usage name	`StopFreq_lp`
Tunable	No
Evaluatable	Yes

# Stopband frequency (Hz) — delay band frequencies for bandpass filters
Real number

Details

The frequency of the delay band for filters Highpass in Hz, given as a positive real scalar.

Dependencies

To use this parameter, set for the parameter Filter type meaning Highpass.

Default value	`1.0e9`
Program usage name	`StopFreq_hp`
Tunable	No
Evaluatable	Yes

# Stopband frequencies (Hz) — delay band frequencies for bandpass filters

Details

Delay band frequencies for bandpass filters Bandpass in Hz, set as a positive increasing vector of two values.

Dependencies

To use this parameter, set for the parameter Filter type meaning Bandpass and uncheck the box Implement using filter order..

Default value	`[1.5e9 3.5e9]`
Program usage name	`StopFreq_bp`
Tunable	No
Evaluatable	Yes

# Stopband frequencies (Hz) — delay band frequencies for bandpass filters

Details

Delay band frequencies for bandpass filters Bandstop in Hz, set as a positive increasing vector of two values.

Dependencies

To use this parameter, set for the parameter Filter type meaning Bandstop.

Default value	`[2.1e9 2.9e9]`
Program usage name	`StopFreq_bs`
Tunable	No
Evaluatable	Yes

# Stopband attenuation (dB) — attenuation in the delay band
Real number

Details

Attenuation in the delay band in dB, specified as a positive real scalar greater than the value of the parameter Passband attenuation (dB).

Dependencies

To use this parameter:

Set for the parameter Filter type meaning Lowpass, Highpass or Bandpass and uncheck the box Implement using filter order.
Install Filter type meaning Bandstop and check the box Implement using filter order.

Default value	`40`
Program usage name	`StopAtten`
Tunable	No
Evaluatable	Yes

# RF frequency (Hz) — the center of the frequency band of the signal
Real number

Details

The center of the frequency band of the signal relative to the transfer function of the filter is given as a positive real scalar, in Hz.

Default value	`1.0e9`
Program usage name	`RF`
Tunable	No
Evaluatable	Yes

Main

# Modeling domain — the field of modeling
Time (Fixed step) | Frequency (Digital filter)

Details

The field of modeling. Set as:

Time (Fixed step) – simulation using fixed-step solvers (NDF2, Trapezoidal, Backward Euler)
Frequency (Digital filter) – simulation using a 1-D digital filter.

Values	`Time (Fixed step)` \| `Frequency (Digital filter)`
Default value	`Time (Fixed step)`
Program usage name	`ModelingDomain`
Tunable	No
Evaluatable	No

# Solver — time domain solvers
NDF2 | Trapezoidal | Backward Euler

Details

Fixed-step solvers. Set as:

NDF2 – a balance of narrowband and broadband accuracy. This solver is suitable for situations where the frequency content of the signals in the system is unknown relative to the Nyquist frequency.
Trapezoidal – performs narrow-band modeling. The frequency distortion and lack of damping effect make this method unsuitable for most broadband simulations.
Backward Euler – modeling of the largest class of systems and signals. The damping effects make this solver suitable for broadband modeling, but the overall accuracy is low.

Dependencies

To use this parameter, set for the parameter Modeling domain meaning Time (Fixed step).

Values	`NDF2` \| `Trapezoidal` \| `Backward Euler`
Default value	`NDF2`
Program usage name	`SolverFixedStep`
Tunable	No
Evaluatable	No

# FIR filter length — length of 1-D digital filter
Real number

Details

The length of a 1-D digital filter or the pulse response duration, set as a positive integer.

Dependencies

To use this parameter, set for the parameter Modeling domain meaning Frequency (Digital filter).

Default value	`128`
Program usage name	`LengthFir`
Tunable	No
Evaluatable	Yes

Additional information

Algorithms

Determination of FIR filter coefficients

The program calculates the coefficients of a discrete FIR filter using the parameters RF frequency (Hz) and FIR filter length, as well as the transfer function specified using the obtained poles and zeros of the filter.

To determine the coefficients of the direct form of the Discrete FIR Filter block, the following steps are performed:

The frequency points located in the passband centered around the carrier frequency are determined by the formula:

Where
- – carrier frequency, in Hz;
- – FIR filter length;
- – time step of the filter.
The values of the transfer functions for the frequency points specified in step 1 are determined by the formula:
The coefficients of a discrete FIR filter are determined by the formula: