filter

Modify frequency content of timeseries objects

Syntax

tsout = filter(tsin,b,a)

tsout = filter(tsin,b,a,ind)

Description

tsout = filter(tsin,b,a) applies the rational transfer function filter b(z⁻¹)/a(z⁻¹) to the uniformly-spaced data in the timeseries object tsin. The numerator b and denominator a are vectors containing the transfer function coefficients.

tsout = filter(tsin,b,a,ind) specifies the indices of the columns or rows to filter. ind is a vector of integers representing column indices for column-oriented data (tsin.IsTimeFirst is true) and representing row indices for row-oriented data (tsin.IsTimeFirst is false).

Examples

Apply Transfer Function

This example applies the following transfer function to a set of data:

$$H(z^{-1})=\frac{b(z^{-1})}{a(z^{-1})}=\frac{2+3z^{-1}}{1+0.2z^{-1}}$$

Create a timeseries object from the matrix count in count.dat.

load count.dat
tsin = timeseries(count(:,1),[1:24]);

Enter the coefficients for the denominator and numerator of the transfer function. Order the coefficients in ascending powers of $$z^{-1}$$ to represent $$1+0.2x$$ and $$2-3z^{-1}$$.

a = [1 0.2];
b = [2 3];

Apply the transfer function using filter, and compare the original data to the filtered data.

tsout = filter(tsin,b,a);
plot(tsin)
hold on
plot(tsout)
legend('Original Data','Filtered Data','Location','NorthWest')

Input Arguments

tsin — Input timeseries

scalar

Input timeseries, specified as a scalar. tsin must be uniformly sampled.

Data Types: timeseries

b — Numerator coefficients

scalar | vector

Numerator coefficients of the transfer function, specified as a scalar or vector.

a — Denominator coefficients

scalar | vector

Denominator coefficients of the transfer function, specified as a scalar or vector.

ind — Row or column indices

scalar | vector

Row or column indices, specified as a positive integer numeric scalar or vector. ind represents column indices for column-oriented data (tsin.IsTimeFirst is true) and represents row indices for row-oriented data (tsin.IsTimeFirst is false).

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

More About

Rational Transfer Function

The input-output description of the filter operation on a vector in the Z-transform domain is a rational transfer function. A rational transfer function is of the form,

$$Y(z)=\frac{b(1)+b(2)z^{-1}+\mathrm{...}+b(n_b+1)z^{-n_b}}{1+a(2)z^{-1}+\mathrm{...}+a(n_a+1)z^{-n_a}}X(z),$$

which handles both FIR and IIR filters [1]. n_a is the feedback filter order, and n_b is the feedforward filter order.

You also can express the rational transfer function as the following difference equation,

$$\begin{array}{c}a(1)y(L)=b(1)x(L)+b(2)x(L-1)+\mathrm{...}+b(n_b+1)x(L-n_b)\\ -a(2)y(L-1)-\mathrm{...}-a(n_a+1)y(L-n_a).\end{array}$$

Furthermore, you can represent the rational transfer function using its direct-form II transposed implementation, as in the following diagram. Here, n_a = n_b = n-1.

The operation of filter at sample m is given by the time domain difference equations

$$\begin{array}{l}y(m)=b(1)x(m)+w_1(m-1)\\ w_1(m)=b(2)x(m)+w_2(m-1)-a(2)y(m)\\ ⋮=⋮⋮\\ w_{n-2}(m)=b(n-1)x(m)+w_{n-1}(m-1)-a(n-1)y(m)\\ w_{n-1}(m)=b(n)x(m)-a(n)y(m).\end{array}$$

References

[1] Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1999.

Version History

Introduced before R2006a