XxYxZ Statistic

This operator applies an XxYxZ statistic filter to the multibeam echogram.

You can define the statistic and the size of the window on the XxYxZ Statistic page of the Variable Properties dialog box.

Echoview accepts operands with the following data types:

Multibeam magnitude
Multibeam phase
Multibeam Sv
Multibeam TS
Multibeam unspecified dB

This operator may be of use with edge detection, intermittent noise removal and other signal processing tasks.

Note: Under live viewing, the Live Export based on a convolution variable may be limited.

Settings

The XxYxZ Statistic Variable Properties dialog box pages include (common) Variable Properties pages and these operator pages:

Operands page

XxYxZ Statistic page

This page is used to specify the filter statistic and the size of the filter window (see Sliding window and kernel).

Setting	Description
Statistic	Mean Minimum Maximum Median Percentile Standard deviation Variance Mean absolute deviation Coefficient of variation Kurtosis
Percentile (%)	Specifies the Nth Percentile (0 to 100%).
Rows (samples)	An odd number between 1 and 999 specifying the number of rows (X) for the window.
Columns (beams)	An odd number between 1 and 999 specifying the number of columns (Y) for the window.
Layers (pings)	An odd number between 1 and 999 specifying the number of layers (Z) for the window.
Input samples per calculation	The number of values per calculation = Rows × Columns × Layers The larger the number, the longer it takes for the operator to execute.

Algorithm

Available XxYxZ Statistic filter kernel algorithms.

Statistic

Value

Mean

Mean equation

Where:

n is the number of samples within the XxYxZ window.

xj is the jth sample value in the XxYxZ window.

Echoview computes the mean in the linear domain.

Minimum

The minimum of the values in the XxYxZ window.

Maximum

The maximum of the values in the XxYxZ window.

Median

The median of the values in the XxYxZ window. The median is the sample value of the 50th percentile.

Percentile (%)

The Nth percentile score of the values in the XxYxZ window.

yI, J (window) = Wk + (Wk+1 - Wk) (k' - k)

Where:

yI, J (window) = the Nth percentile score of the values in the XxYxZ window

Wk = the value of sample k in the list W — (defined below)

k = ëk'û *

k' = N x P/100

N = the number of samples in the list W.

P = the Percentile entered on the XxYxZ Statistic page of the Variable properties dialog box

W = the ordered list of sample values in the window where (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

*Floor function ëxû, gives the largest integer less than or equal to x.

Standard deviation

See Mean above for the definition of n, xj and .

Echoview computes the standard deviation of the values in the window in the linear domain.

¹Not referring to the ping sample.

Variance

The variance s2. See Standard deviation above for the definition of s.

Echoview computes the variance of the values in the window in the linear domain.

Mean absolute deviation

See Mean above for the definition of n, xj and .

Echoview computes the MAD of the values in window in the linear domain.

Coefficient of variation

See Standard deviation above for the definition of s and, Mean above for the definition of .

Echoview computes the Cv of the values in the window in the linear domain.

Kurtosis

Where n, xj, s and are defined as above. For the Kurtosis calculation n > 3 is required to avoid an undefined division.

Echoview computes the kurtosis of the values in window in the linear domain. The output is also a linear value.

Notes:

For details on how convolutions are applied in Echoview see Convolution algorithms: Convolution filter operators.
The window shrinks as it approaches the edge of the data.
Calculations for samples with dB values are carried out in the linear domain. Results that are unitless ratios are linear. Results that have units are generally converted back into the dB domain.

XxYxZ Statistic

Settings

Operands page

XxYxZ Statistic page

Algorithm

See also