Compute output, error, and coefficients using frequency domain FIR adaptive filter

Libraries:
DSP System Toolbox / Filtering / Adaptive Filters

Description

The Frequency-Domain Adaptive Filter block implements an adaptive finite impulse response (FIR) filter in the frequency domain using the fast block least mean squares (LMS) algorithm. The Filter length and the Block length parameters specify the filter length and the block length values the algorithm uses. When you select the Output filter FFT coefficients check box, the block outputs the discrete Fourier transform of the current filter coefficients. The block offers the constrained and unconstrained versions of the algorithm with partitioned and nonpartitioned modes. For details, see Algorithms.

Ports

Input

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The signal to be filtered by the frequency-domain FIR adaptive filter. The data input and the desired signal input must have the same size and data type. The length of the input vector must be divisible by the Block length parameter value.

The data input can be a variable-size signal as long as the frame length is a multiple of the Block length. You can change the number of elements in the column vector during the model simulation.

Data Types: single | double
Complex Number Support: Yes

The frequency-domain adaptive filter adapts its filter weights to minimize the error, Error, and converge the input signal to match the desired signal as closely as possible.

The data input and the desired signal must have the same size and data type. The length of the desired signal vector must be divisible by the Block length parameter value.

The desired signal can be a variable-size signal as long as the frame length is a multiple of the Block length. You can change the number of elements in the column vector during the model simulation.

Data Types: single | double
Complex Number Support: Yes

Adaptation step size factor, specified as a real scalar in the range (0,1]. Using a small step size ensures a small steady-state error. However, a small step size decreases the resulting convergence speed of the adaptive filter. Increasing the step size improves the convergence speed, at the cost of increased steady-state mean squared error. When the step size value is 1, the algorithm provides the optimal tradeoff between the convergence speed and the steady-state mean squared error.

Dependencies

This port appears when you select the Specify step size from port parameter.

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

Leakage factor used in leaky adaptive filter, specified as a real scalar in the range (0,1]. When the value is less than 1, the block implements a leaky adaptive algorithm. When the value is 1, the block provides no leakage in the adapting method.

Dependencies

This port appears when you select the Specify leakage factor from port check box.

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

Averaging factor used to compute the exponentially windowed fast Fourier transform (FFT) input signal powers for the coefficient updates, specified as a real scalar in the range (0,1].

Dependencies

This port appears when you select the Specify averaging factor from port check box.

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

Offset for the normalization terms in the coefficient updates, specified as a nonnegative real scalar value. Use this value to avoid division by zero or division by very small numbers if any of the FFT input signal powers become very small.

Dependencies

This port appears when you select the Specify offset from port check box.

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

If you input a nonzero scalar value through this port, the block continuously updates its filter coefficients. If you input a zero through this port, the filter coefficients do not update, and their values remain at the current value.

Dependencies

This port appears when you select the Enable adapt port check box.

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

If you input a nonzero scalar value through this port, the block resets all internal states. If you input a zero through this port, the internal states are not reset.

Dependencies

This port appears when you select the Enable reset port check box.

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

Output

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Filtered output, returned as a column vector. The block adapts its filter weights to converge the input signal to match the desired signal as closely as possible. The filter outputs the converged signal.

Data Types: single | double
Complex Number Support: Yes

Difference between the output signal and the desired signal, returned as a column vector. The objective of the adaptive filter is to minimize this error. The block adapts its weights to converge towards optimal filter weights which produce an output signal that matches the desired signal as closely as possible. For more details on how Error is computed, see References.

Data Types: single | double
Complex Number Support: Yes

Current discrete Fourier transform of the filter coefficients, returned as a row vector. For Constrained FDAF and Unconstrained FDAF algorithms, the length of this vector is equal to the sum of the Filter length value and the Block length value. This port initially outputs the FFT values of the Initial time-domain coefficients parameter. During the model simulation, this port outputs the FFT values of the current filter coefficients.

Dependencies

This port appears when you select the Output filter FFT coefficients check box.

Data Types: single | double
Complex Number Support: Yes

Parameters

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Method used to calculate the filter coefficients, specified as::

• Constrained FDAF –– Imposes a gradient constraint on the filter tap weights.

• Partitioned constrained FDAF –– Partitions the impulse response of the filter to reduce latency.

• Unconstrained FDAF –– No gradient constraint is imposed on the filter tap weights.

• Partitioned unconstrained FDAF –– Partitions the impulse response of the filter to reduce latency. No gradient constraint is imposed on the filter tap weights.

For more details, see Algorithms.

Length of the FIR filter coefficients vector, specified as a positive, integer-valued scalar.

Block length for the coefficients update, specified as a positive, integer-valued scalar. The adaptive filter processes the input data and the desired signal as a block of samples of length set by this parameter. For details on how this data is processed by the filter, see Algorithms. The length of the input vector must be divisible by the Block length parameter value. The default value of the Block length parameter is set to the value of the Filter length parameter.

When you select this check box, the adaptation step size is input through the Mu port. When you clear this check box, the step size is specified on the block dialog through the Step size parameter.

Adaptation step size factor, specified as a real scalar in the range (0,1]. Setting the Step size parameter to 1 provides the fastest convergence during adaptation.

Tunable: Yes

Dependencies

This parameter appears when you clear the Specify step size from port check box.

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

When you select this check box, the leakage factor is input through the Leak port. When you clear this check box, the leakage factor is specified on the block dialog through the Leakage factor parameter.

Leakage factor used in leaky adaptive filter, specified as a real scalar in the range (0,1]. When the value is less than 1, the block implements a leaky adaptive algorithm. When the value is 1, the block provides no leakage in the adapting method.

Tunable: Yes

Dependencies

This parameter appears when you clear the Specify leakage factor from port check box.

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

When you select this check box, the averaging factor for signal power is input through the Avrg port. When you clear this check box, the averaging factor is specified on the block dialog through the Averaging factor parameter.

Averaging factor used to compute the exponentially windowed FFT input signal powers for the coefficient updates, specified as a real scalar in the range (0,1].

Tunable: Yes

Dependencies

This parameter appears when you clear the Specify averaging factor from port check box.

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

When you select this check box, the offset for the normalization terms in the coefficient updates is input through the Offset port. When you clear this check box, the offset is specified on the block dialog through the Offset parameter.

Offset for the normalization terms in the coefficient updates, specified as a nonnegative real scalar value. Use this value to avoid division by zero or division by very small numbers if any of the FFT input signal powers become very small.

Tunable: Yes

Dependencies

This parameter appears when you clear the Specify offset from port check box.

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

Initial common value of all of the FFT input signal powers, specified as a positive numeric scalar value.

If you change this value during the simulation, the change takes effect only after a reset event occurs.

Tunable: Yes

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

Initial time-domain coefficients of the adaptive filter, specified as a scalar or a vector of length equal to the value you specify in the Filter length parameter. The adaptive filter block uses these coefficients to compute the initial frequency-domain filter coefficients.

If you change this value during the simulation, the change takes effect only after a reset event occurs.

Tunable: Yes

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

When you select this check box, the Adapt input port is enabled. If you input a nonzero scalar value through this port, the block continuously updates its filter coefficients. If you input a zero through this port, the filter coefficients do not update and their values remain at the current value.

When you select this check box, the Reset input port is enabled. If you input a nonzero scalar value through this port, the block resets all internal states. If you input a zero through this port, the internal states are not reset.

When you select this check box, the FFTCoeffs output port is enabled. Through this port, the block outputs the discrete Fourier transform of the current filter coefficients.

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. Simulink reuses the C code in subsequent simulations as long as the model does not change. This option requires additional startup time but subsequent simulations are faster compared to Interpreted execution.

• Interpreted execution –– Simulate model using the MATLAB®  interpreter. This option shortens startup time but subsequent simulations are slower compared to Code generation.

Block Characteristics

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

Algorithms

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Frequency-domain adaptive filtering consists of three steps - filtering, error estimation, and tap-weight adaptation. This algorithm implements FIR filtering in the frequency domain using the overlap-save or overlap-add method. For more implementation details of these two methods, see the Algorithms section in the dsp.FrequencyDomainFIRFilter object page. The error estimation and the tap-weight adaptation are implemented using the fast block LMS algorithm (FBLMS).

References

[1] Shynk, J.J."Frequency-Domain and Multirate Adaptive Filtering." IEEE Signal Processing Magazine, Vol. 9, No. 1, pp. 14–37, Jan. 1992.

[2] Farhang-Boroujeny, B., Adaptive Filters: Theory and Applications, Chichester, England, Wiley, 1998.

[3] Stockham, T. G., Jr. "High Speed Convolution and Correlation." Proceedings of the 1966 Spring Joint Computer Conference, AFIPS, Vol 28, 1966, pp. 229–233.

Version History

Introduced in R2018a