scaleFilterSections

R2026b

Scale cascaded transfer functions with scale values

Since R2023b

Syntax

Bg = scaleFilterSections(B,g)

Description

Bg = scaleFilterSections(B,g) scales the sections of the numerator filter coefficients B represented with Cascaded Transfer Functions (CTF) by applying the scale values specified in g.

Examples

Scale Second-Order Section Matrix

Design a 14th-order elliptic bandpass digital filter with a lower passband frequency of $\pi /5$ rad/sample and a higher passband frequency of $3\pi /5$ rad/sample. Specify 10 dB of passband ripple and 40 dB of stopband attenuation. Represent the filter using cascaded transfer functions.

N = 14;
[B,A] = ellip(N/2,10,40,[0.2 0.6],"ctf")

B = 4×5

    0.4184    0.0000   -0.4184         0         0
    0.4184   -0.3351    0.1684   -0.3351    0.4184
    0.4184   -0.4070    0.3842   -0.4070    0.4184
    0.4184   -0.4158    0.4107   -0.4158    0.4184

A = 4×5

    1.0000   -0.7094    0.8572         0         0
    1.0000   -1.1435    1.4172   -1.0733    0.9081
    1.0000   -1.0196    1.0568   -1.0091    0.9862
    1.0000   -1.0010    1.0029   -0.9998    0.9984

Define scale values as a vector with incremental gains (1, 2, ..., $L$) for each of the $L$ sections, and append the overall system gain as ${0.5}^L$. This vector makes the numerator coefficients be scaled by 0.5, 1, ..., $0.5L$.

numSections = size(B,1);
g = [1:numSections 0.5^(numSections)];

Use scaleFilterSections to scale the filter numerator coefficients so that the gain is uniformly distributed across all sections.

Bg = scaleFilterSections(B,g)

Bg = 4×5

    0.2092    0.0000   -0.2092         0         0
    0.4184   -0.3351    0.1684   -0.3351    0.4184
    0.6276   -0.6105    0.5764   -0.6105    0.6276
    0.8367   -0.8317    0.8215   -0.8317    0.8367

Visualize the frequency response.

freqz(Bg,A,4096,"ctf")

Input Arguments

B — Unscaled CTF numerator filter coefficients

matrix

Unscaled CTF numerator filter coefficients, specified as a matrix.

• The number of rows in B equals L, where L is the number of filter sections in the cascade.

• The number of columns in B equals m + 1, where m is the section order.

• If you specify B as a vector, scaleFilterSections treats B as a matrix, determining the number of sections and the numerator order depending on vector size:

  • Row vector — The function treats B as a one-section transfer function with numerator order m, where m + 1 is the number of columns. The ith column of B corresponds to the z^{-(i - 1)} numerator coefficient.

  • Column vector — The function treats B as an L-section transfer function with scalar numerators. Each row of B corresponds to a numerator in each corresponding section.

Data Types: single | double
Complex Number Support: Yes

g — Scale values

scalar | vector

Scale values, specified as a scalar or a vector with L + 1 elements, where L is the number of filter sections in the cascade.

• If g is a scalar, scaleFilterSections applies the value uniformly to all the cascade filter sections.

• If g is a vector, scaleFilterSections applies each of the first L scale values to the corresponding filter section and the last scale value uniformly to all the filter sections.

Data Types: single | double

Output Arguments

Bg — Scaled CTF numerator filter coefficients

matrix

Scaled CTF numerator filter coefficients, returned as a matrix of the same size as B.

See Algorithms for more information.

Algorithms

The scaleFilterSections function scales the matrix B with a scalar or vector g and returns Bg as one of these:

• If g is a scalar:

  L = size(B,1);
  gL = (abs(g))^(1/L);
  Bg = B*gL;
  Bg(L,:) = sign(g)*Bg(L,:);

• If g is a vector with L+1 samples, given L sections:

  L = size(B,1);
  gS = g(end);
  gL = (abs(gS))^(1/L);
  gl = g(1:end-1);
  Bg = B.*gl(:)*gL;
  Bg(L,:) = sign(gS)*Bg(L,:);

Extended Capabilities

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The scaleFilterSections function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2023b

R2026b: Use thread-based environments

You can use scaleFilterSections in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.