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sosfilt

Second-order (biquadratic) IIR digital filtering

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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.

  • If x is a matrix, then the function operates along the first dimension and returns the filtered data for each column.

  • If x is a multidimensional array, then the function operates along the first array dimension with size greater than 1.

example

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

Examples

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Open Live Script

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)

Figure contains 2 axes objects. Axes object 1 with title Phase, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Phase (degrees) contains an object of type line. Axes object 2 with title Magnitude, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Magnitude (dB) contains an object of type line.

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)

Figure contains 2 axes objects. Axes object 1 with title Original Signal contains an object of type line. Axes object 2 with title Highpass-Filtered Signal, xlabel Time (s) contains an object of type line.

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)

Figure contains 2 axes objects. Axes object 1 with title Original Signal contains an object of type line. Axes object 2 with title Lowpass-Filtered Signal, xlabel Time (s) contains an object of type line.

Input Arguments

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

sos=[b01b11b211a11a21b02b12b221a12a22⋮⋮⋮⋮⋮⋮b0Lb1Lb2L1a1La2L]

represents the second-order section digital filter

H(z)=∏k=1LHk(z)=∏k=1Lb0k+b1kz−1+b2kz−21+a1kz−1+a2kz−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

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

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

Data Types: single | double

Output Arguments

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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™.

Version History

Introduced before R2006a

See Also

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