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

collapse all

Apply Transfer Function

Open Live Script

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

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

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 $1 + 0.2 x$ and $2 - 3 z^{- 1}$ .

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')

Figure contains an axes object. The axes object with title Time Series Plot:unnamed, xlabel Time (seconds), ylabel unnamed contains 2 objects of type line. These objects represent Original Data, Filtered Data.

Input Arguments

collapse all

`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).

More About

collapse all

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,

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

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,

$\begin{matrix} a (1) y (L) = b (1) x (L) + b (2) x (L - 1) + ... + b (n_{b} + 1) x (L - n_{b}) \\ - a (2) y (L - 1) - ... - a (n_{a} + 1) y (L - n_{a}) . \end{matrix}$

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

filter

Syntax

Description

Examples

Apply Transfer Function

Input Arguments

tsin — Input timeseries scalar

b — Numerator coefficients scalar | vector

a — Denominator coefficients scalar | vector

ind — Row or column indices scalar | vector

More About

Rational Transfer Function

References

Version History

See Also

`tsin` — Input `timeseries`
scalar

`b` — Numerator coefficients
scalar | vector

`a` — Denominator coefficients
scalar | vector

`ind` — Row or column indices
scalar | vector