Biquadratic Filter (DSP Blockset)

Apply a cascade of biquadratic (second-order section) filters to the input.

Library

Filter Realizations, in Filtering

Description

The Biquadratic Filter block applies a cascade of biquadratic filters independently to each input channel. The filter is constructed from L second-order sections, each having a quadratic numerator and denominator. The biquadratic filter is useful for reduced precision implementations because the coefficients are bounded between ±2 for typical minimum-phase designs. This reduces scaling and coefficient sensitivity problems.

The SOS matrix parameter specifies the filter coefficients as a second-order section matrix of the type produced by the tf2sos and ss2sos functions in the Signal Processing Toolbox. This is an L-by-6 matrix,

whose rows contain the numerator and denominator coefficients b_ik and a_ik of each second-order section in H(z):

Use the ss2sos and tf2sos functions to convert a state-space or transfer-function description of the filter into the second-order section description used by this block.

The Initial conditions parameter sets the initial filter states, and can be specified in the following different forms:

Scalar to be repeated for all filter states in all channels. An empty vector, [], is the same as the scalar value 0.
Vector of length 2*L to initialize the filter states for all channels. Each pair of elements in the vector specifies z^-1 and z^-2 for a particular second-order section. For example, ic(1) and ic(2) respectively specify z^-1 and z^-2 for H₁(z) in every channel, where ic is the initial condition vector.
Matrix of dimension (2*L)-by-N containing the initial filter states for each of the N channels. Each pair of elements in a column specifies z^-1 and z^-2 for a particular second-order section of the corresponding channel. For example, ic(1,3) and ic(2,3) respectively specify z^-1 and z^-2 for H₁(z) in the third channel, where ic is the initial condition matrix.

You can choose frame-based or sample-based operation by selecting (or deselecting, respectively) the Frame-based inputs check box.

Sample-Based Operation

When the Frame-based inputs 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 Number of channels parameter specifies the number of independent signals, N, in the matrix. The block independently applies the filter to each channel.

In both sample-based and frame-based modes, the output is the same size as the input.

Note
If you expect to generate code for the Biquadratic 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

SOS matrix: The second-order section matrix specifying the filter's coefficients. This matrix can be generated from state-space or transfer-function descriptions by using the Signal Processing Toolbox functions ss2sos and tf2sos.
Frame-based inputs: Selects frame-based operation.
Number of channels: For frame-based operation, the number of columns (frames) in the input matrix.