Direct-Form II Transpose Filter (DSP Blockset)

DSP Blockset

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Direct-Form II Transpose Filter

See Also

Apply an IIR filter to the input.

Library

Filter Realizations, in Filtering

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.

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)]

Note that 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.

The Frame-based inputs parameter allows you to choose between sample-based and frame-based operation.

Sample-Based Operation

When the check box is not selected (default), the block assumes that the input is a 1-by-N sample vector or M-by-N sample matrix. Each of the N vector elements (or M*N matrix elements) is treated as an independent channel, and the block filters each channel over time.

Frame-Based Operation

When the Frame-based inputs check box is selected, the block assumes that the input is an M-by-N frame matrix. Each of the N frames in the matrix contains M sequential time samples from an independent signal. The illustration below shows a 6-by-4 matrix input:

The Number of channels parameter specifies the number of independent channels (columns), N, in the matrix, and the block filters each channel independently over time. Frame-based operation provides substantial increases in throughput rates, at the expense of greater model latency.

Note
If you expect to generate code for the Direct-Form II Transpose Filter block using the Real-Time Workshop, you should ensure that inputs are contiguous in memory. See the Contiguous Copy block for more information.

Dialog Box

Numerator: The filter numerator.
Denominator: The filter denominator.
Initial conditions: The filter's initial conditions, a scalar, vector, or matrix.
Frame-based inputs: Selects frame-based operation.
Number of channels: For frame-based operation, the number of columns (channels) in the input 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.