# sosfilt

Second-order (biquadratic) IIR digital filtering

## Description

example

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

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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

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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

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

represents the second-order section digital filter

$H\left(z\right)=\prod _{k=1}^{L}{H}_{k}\left(z\right)=\prod _{k=1}^{L}\frac{{b}_{0k}+{b}_{1k}{z}^{-1}+{b}_{2k}{z}^{-2}}{1+{a}_{1k}{z}^{-1}+{a}_{2k}{z}^{-2}}.$

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

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

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