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, 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, 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.

EXPMOVAVG

FILTEQ

LINAVG

MOVAVG