# LINEXPAVG

## Purpose:

Computes the exponential moving average
with zero phase shift.

## Syntax:

LINEXPAVG(series,
a, yi)

series |
- |
A series or table. |

a |
- |
Optional. A real, the smoothing factor where
0 <= **a** <= 1.
Defaults to 1.0, no averaging. |

yi |
- |
Optional. A real, the initial value. Defaults
to **series[1]**, the first input
value. |

##

## Alternate Syntax:

LINEXPAVG(series, N, yi)

series |
- |
A series or table. |

N |
- |
Optional. An integer, the effective number
of points to average where **N**
>= 1. Defaults to 1, no averaging. |

yi |
- |
Optional. A real, the initial value. Defaults
to **series[1]**, the first input
value. |

## Returns:

A series, the zero phase exponential moving
average.

## Example:

W1: 1..5

W2: linexpavg(w1, 0.5)

W2 == {1.40625, 2.015625, 2.632813, 3.066406, 3.033203}

The XOFFSET of the result is 1.0.

## Example:

W1: 1..5

W2: linexpavg(w1, 3)

W2 == {1.40625, 2.015625, 2.632813, 3.066406, 3.033203}

Same as above except the smoothing factor is in the form of the effective
number of points to smooth. The effective number of points, **N**
is related to **a**, the smoothing
factor by:

*N* = (2 / *a*)
- 1

## Example:

W1: integ(gnorm(1000, 1/100))

W2: expavg(w1, 0.3)

W3: linexpavg(w1, 0.3);overp(w1, lred);overp(w2,
lgreen)

W1 contains 1000
samples of synthesized data.

W2 performs a standard
exponential moving average with a
smoothing factor of 0.3.

W3 performs zero
phase exponential moving average by reversing the original data, computing
an exponential moving average, reversing the result and computing another
exponential point moving average.

Compared to the standard exponential moving
average, the peaks of the resulting smoothed series line up with the original
data.

## Remarks:

LINEXPAVG computes zero phase exponential
moving average by reversing the input series, computing the exponential
point moving average, reversing the result and computing another exponential
moving average. The reversal steps help ensure the peak locations of the
original data are preserved.

The effective number of points to average,
**N**, is related to the smoothing
factor **a**, by:

*N* = (2 / *a*)
- 1

where **N**
is similar to the number of points to average as with the standard moving
average. If the smoothing parameter of LINEXPAVG is an integer greater
or equal to 1, it is assumed to be the effective number of points as determined
above.

See EXPMOVAVG
for more details on the exponential moving average.

See LINAVG
to compute a zero phase moving average.

## See Also:

EXPMOVAVG

FILTEQ

LINAVG

MOVAVG