sosfilt

Second-order (biquadratic) IIR digital filtering

Syntax

y = sosfilt(sos,x)

y = sosfilt(sos,x,dim)

Description

y = sosfilt(sos,x) applies the second-order section digital filter sos to the input signal x.

y = sosfilt(sos,x,dim) operates along the dimension dim.

Examples

Second-Order Section Filtering

Load chirp.mat. The file contains a signal, y, that has most of its power above Fs/4, or half the Nyquist frequency. The sample rate is 8192 Hz.

load chirp

t = (0:length(y)-1)/Fs;

Design a seventh-order Butterworth highpass filter to attenuate the components of the signal below Fs/4. Use a normalized cutoff frequency of 0.48π rad/sample. Express the filter coefficients in terms of second-order sections.

[zhi,phi,khi] = butter(7,0.48,'high');
soshi = zp2sos(zhi,phi,khi);

freqz(soshi)

Filter the signal. Display the original and highpass-filtered signals. Use the same y-axis scale for both plots.

outhi = sosfilt(soshi,y);

figure
subplot(2,1,1)
plot(t,y)
title('Original Signal')
ys = ylim;

subplot(2,1,2)
plot(t,outhi)
title('Highpass-Filtered Signal')
xlabel('Time (s)')
ylim(ys)

Design a lowpass filter with the same specifications. Filter the signal and compare the result to the original. Use the same y-axis scale for both plots. The result is mostly noise.

[zlo,plo,klo] = butter(7,0.48);
soslo = zp2sos(zlo,plo,klo);

outlo = sosfilt(soslo,y);

subplot(2,1,1)
plot(t,y)
title('Original Signal')
ys = ylim;

subplot(2,1,2)
plot(t,outlo)
title('Lowpass-Filtered Signal')
xlabel('Time (s)')
ylim(ys)

Input Arguments

sos — Second-order section digital filter

L-by-6 matrix

Second-order section digital filter, specified as an L-by-6 matrix, where L is the number of second-order sections. The matrix

$$\text{sos}=\left[\begin{array}{cccccc}{b}_{01}& b_{11}& b_{21}& 1& a_{11}& a_{21}\\ b_{02}& b_{12}& b_{22}& 1& a_{12}& a_{22}\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ b_{0L}& b_{1L}& b_{2L}& 1& a_{1L}& a_{2L}\end{array}\right]$$

represents the second-order section digital filter

$$H(z)={\displaystyle \prod _{k=1}^L{H}_k(z)={\displaystyle \prod _{k=1}^L\frac{b_{0k}+b_{1k}{z}^{-1}+b_{2k}{z}^{-2}}{1+a_{1k}{z}^{-1}+a_{2k}{z}^{-2}}}}.$$

Example: [b,a] = butter(3,1/32); sos = tf2sos(b,a) specifies a third-order Butterworth filter with a normalized 3 dB frequency of π/32 rad/sample.

Data Types: single | double

x — Input signal

vector | matrix | N-D array

Input signal, specified as a vector, matrix, or N-D array.

Example: x = [2 1].*sin(2*pi*(0:127)'./[16 64]) specifies a two-channel sinusoid.

Data Types: single | double
Complex Number Support: Yes

dim — Dimension to operate along

positive integer scalar

Dimension to operate along, specified as a positive integer scalar. By default, sosfilt operates along the first array dimension of x with size greater than 1.

Data Types: single | double

Output Arguments

y — Filtered signal

vector | matrix | N-D array

Filtered signal, returned as a vector, matrix, or N-D array. y has the same size as x.

References

[1] Bank, Balázs. "Converting Infinite Impulse Response Filters to Parallel Form". IEEE Signal Processing Magazine. Vol. 35, Number 3, May 2018, pp. 124-130.

[2] Orfanidis, Sophocles J. Introduction to Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1996.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• Input filter sos must be stable. Use isstable to check for filter stability.

• All second-order subsections of the input filter must be IIR.

• The gpuArray version of sosfilt uses a parallel algorithm [1] which is different from the MATLAB^® version. The algorithms give different results for complex-valued input with NaN or Inf values:

  • In the MATLAB version, the NaNs and Infs propagate only in the real part.

  • In the gpuArray version, the NaNs and Infs propagate in both the real part and the imaginary part.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).