DSP Blockset

Direct-Form II Transpose Filter

Apply an IIR filter to the input.

Library

Filtering / Filter Structures

Description

The Direct-Form II Transpose Filter block applies a transposed direct-form II IIR filter to the input.

This is a canonical form that has the minimum number of delay elements. The filter order is max(m,n)-1.

An M-by-N sample-based matrix input is treated as M*N independent channels, and an M-by-N frame-based matrix input is treated as N independent channels. In both cases, the block filters each channel independently over time, and the output has the same size and frame status as the input.

The filter is specified in the parameter dialog box by its transfer function,

where the Numerator parameter specifies the vector of numerator coefficients,

[b(1) b(2) ... b(m)]

and the Denominator parameter specifies the vector of denominator coefficients,

[a(1) a(2) ... a(n)]

The filter coefficients are normalized by a₁.

Initial Conditions

In its default form, the filter initializes the internal filter states to zero, which is equivalent to assuming past inputs and outputs are zero. The block also accepts optional nonzero initial conditions for the filter delays. Note that the number of filter states (delay elements) per input channel is

max(m,n)-1

The Initial conditions parameter may take one of four forms:

• Empty matrix

The empty matrix, [], causes a zero (0) initial condition to be applied to all delay elements in each filter channel.

• Scalar

The scalar value is copied to all delay elements in each filter channel. Note that a value of zero is equivalent to setting the Initial conditions parameter to the empty matrix, [].

• Vector

The vector has a length equal to the number of delay elements in each filter channel, max(m,n)-1, and specifies a unique initial condition for each delay element in the filter channel. This vector of initial conditions is applied to each filter channel.

• Matrix

The matrix specifies a unique initial condition for each delay element, and can specify different initial conditions for each filter channel. The matrix must have the same number of rows as the number of delay elements in the filter, max(m,n)-1, and must have one column per filter channel.

Dialog Box

Numerator

The filter numerator vector. Tunable; the numerator coefficients can be adjusted while the simulation runs, but the vector length (i.e., the filter order) must remain the same.

Denominator

The filter denominator vector. Tunable; the denominator coefficients can be adjusted while the simulation runs, but the vector length (i.e., the filter order) must remain the same.

Initial conditions

The filter's initial conditions, a scalar, vector, or matrix.

References

Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1989.

Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.

See Also

Biquadratic Filter	DSP Blockset
Discrete Filter	Simulink
Filter Realization Wizard	DSP Blockset
Time-Varying Direct-Form II Transpose Filter	DSP Blockset
filter	MATLAB

See Filter Structures for related information.

Digital IIR Filter Design

Discrete Impulse