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Second-order (biquadratic) IIR digital filtering

`y = sosfilt(sos,x)`

y = sosfilt(sos,x,dim)

`y = sosfilt(sos,x)`

applies
the second-order section digital filter `sos`

to
the vector `x`

. The output, `y`

,
is the same length as `x`

.

If either input to `sosfilt`

is single precision,
filtering is implemented using single-precision arithmetic. The output, `y`

,
is single precision.

`sos`

represents the second-order section digital
filter *H*(*z*)

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

by an *L*-by-6 matrix containing the coefficients
of each second-order section in its rows.

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

If `x`

is a matrix, `sosfilt`

applies
the filter to each column of `x`

independently. The
output `y`

is a matrix of the same size, containing
the filtered data corresponding to each column of `x`

.

If `x`

is a multidimensional array, `sosfilt`

filters
along the first nonsingleton dimension. The output `y`

is
a multidimensional array of the same size as `x`

,
containing the filtered data corresponding to each row and column
of `x`

.

The second order sections matrix, `sos`

, the
input signal, `x`

, or both can be double or single
precision. If at least one input is single precision, filtering is
done with single precision arithmetic.

`y = sosfilt(sos,x,dim)`

operates
along the dimension `dim`

.

[1] Orfanidis, S.J., *Introduction
to Signal Processing*, Prentice-Hall, Englewood Cliffs,
NJ, 1996.

`filter`

| `medfilt1`

| `sgolayfilt`