# Documentation

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# filter

Class: timeseries

Shape frequency content of time-series

## Syntax

```ts1 = filter(ts, numerator, denominator) ts1=filter(ts, numerator, denominator, index) ```

## Description

`ts1 = filter(ts, numerator, denominator) ` applies the transfer function filter b(z−1)/a(z−1) to the data in the `timeseries` object `ts`. `b` and `a` are the coefficient arrays of the transfer function numerator and denominator, respectively.

`ts1=filter(ts, numerator, denominator, index) ` uses the optional `index` integer array to specify either the columns or rows to filter, depending on the value of `ts.IsTimeFirst`.

## Input Arguments

 `ts` The first `timeseries` object for which you want to shape the frequency content. `numerator` The coefficient array of the transfer function numerator. `denominator` The coefficient array of the transfer function denominator. `index` An integer array that specifies the columns or rows to filter when `ts.IsTimeFirst` is true.

## Output Arguments

 `ts1` The `timeseries` object that results from filtering the input `timeseries` object.

## Examples

expand all

This example applies the following transfer function to the data in `count.dat`:

Load the matrix `count` into the workspace:

`load count.dat`

Create a time-series object based on this matrix:

`count1 = timeseries(count(:,1),[1:24]);`

Enter the coefficients of the denominator ordered in ascending powers of to represent :

`a = [1 0.2];`

Enter the coefficients of the numerator to represent :

`b = [2 3];`

Call the filter method:

`filter_count = filter(count1, b, a);`

Compare the original data and the shaped data with an overlaid plot of the two curves:

```figure plot(count1,'-.') grid on hold on plot(filter_count,'-') legend('Original Data','Shaped Data','Location','NorthWest')```

## Tips

• The time-series data must be uniformly sampled to use this filter.

• The following function

```y = filter(b,a,x) ```

creates filtered data `y` by processing the data in vector `x` with the filter described by vectors `a` and `b`.

• The `filter` function is a general tapped delay-line filter, described by the difference equation:

a(1)y(n) = b(1)x(n) + b(2)x(n − 1) + ... + b(nb)x(nnb + 1) − a (2)y(n − 1) − ... − a(Na)y(nNb + 1).

Here, n is the index of the current sample, Na is the order of the polynomial described by vector `a`, and Nb is the order of the polynomial described by vector `b`. The output y(n) is a linear combination of current and previous inputs, x(n) x(n −1)..., and previous outputs, y(n − 1) y(n − 2)... .

• You use the discrete filter to shape the data by applying a transfer function to the input signal.

Depending on your objectives, the transfer function you choose might alter both the amplitude and the phase of the variations in the data at different frequencies to produce either a smoother or a rougher output.

• In digital signal processing (DSP), it is customary to write transfer functions as rational expressions in z−1 and to order the numerator and denominator terms in ascending powers of z−1.

Taking the z-transform of the difference equation

a(1)y(n) = b(1)x(n) + b(2)x(n −1) + ... + b(nb)x(nnb + 1) − a (2)y(n − 1) − ... − a(na)y(na + 1),

results in the transfer function

`$Y\left(z\right)=H\left({z}^{-1}\right)X\left(z\right)=\frac{b\left(1\right)+b\left(2\right){z}^{-1}+...+b\left(nb\right){z}^{-nb+1}}{a\left(1\right)+a\left(2\right){z}^{-1}+...+a\left(na\right){z}^{-na+1}}X\left(z\right),$`

where Y(z) is the z-transform of the filtered output y(n). The coefficients b and a are unchanged by the z-transform.