Resample by Distance Interval
Resample by Number of Pings
Resample by Time Interval

The Resample by Distance Interval operator resamples the input variable using a fixed distance interval in the distance domain, and a specified start range, stop range and number of data points in the depth domain.

The Resample by Number of Pings operator resamples the input variable using a fixed number of pings in the time/distance domain, and a specified upper range, lower range and number of data points in the range domain.

The Resample by Time Interval operator resamples the input variable using a fixed time interval in the time domain, and a specified start range, stop range and number of data points in the depth domain.

You may choose to sample all data points, or only those from the ping at the center of each interval. A mean weighted mean, median, maximum, minimum or percentile resampling operation can be performed.

You enter the processing settings for the operator on the Resample page of the Variable Properties dialog box.

Echoview accepts a single operand of the following data types as input:

In all cases, calculations are performed in the linear domain, not the decibel domain. See Resample operator algorithms for more information.

Settings

The Resample by Distance Interval/ Resample by Number of Pings/ Resample by Time Interval Variable Properties dialog box pages include (common) Variable Properties pages and these operator pages:

Operands page

Resample page

The Input section determines the pings that are to be sampled for each sample interval.

Settings

Description

Ping selection

Choose to apply statistical functions to all pings in interval, or to the middle ping in the sample interval.

Note: In the Select middle ping mode, if there is an original ping in the time interval corresponding to the resampled ping, the closest one to the ping center is selected. When there is no ping available, a no data ping is output on the echogram.

Distance mode

For resampling by distance there is a choice of resampling using GPS or Vessel logs (if available) in units of either nautical miles or meters.

Distance interval

Number of pings in interval

Time interval

Specify the distance (nautical miles) / number of pings / time (seconds) sample interval for resampling.

The Operation section determines the statistical operation to be used for resampling.

Settings

Description

Resampling operation

Choose the statistical operation to use for resampling your data.

See Resample operator algorithms for more information.

Percentile

For resampling using the percentile operation, enter the required Nth Percentile. For example a percentile of 90 will return a 90th Percentile score below which 90% of the sampled data points lie.

Weighting along-track

This setting is only accessible when resampling using the Mean resampling operation on the Resample by time interval and Resample by distance interval operators.

If selected, the resampled value is calculated using a weighted mean, otherwise an ordinary mean (unweighted) is used.

The Output section is used to set the display limits and data resolution to output for the resampled pings.

Settings

Description

Use ranges from operand 1

Click Use ranges from operand 1 to use the ranges specified by operand 1.

Note: This setting is unsuitable to use where Operand 1 contains pings with no samples in them. In this case, Echoview encounters problems with the Start range and Stop range of such empty pings.

Custom ranges

Click Custom ranges to enter and use your own ranges.

Custom ranges together with Start range and Stop range define the Start sample range and End sample range boundaries of the output ping. Number of data points defines the resolution of the samples within those bounds. In the range dimension the resampling can sometimes look like a zoom.

resample in range

Resample variable

Not resampled in the along-track direction.

Start range = 50 m

Stop range = 100 m

Data points = 20

Input variable

Start range = 0.096 m

Stop range = 249.9 m

Data points = 1301
 

Start range

Enter the start range in meters, i.e. the range of the first sample in the output echogram.

Stop range

Enter the stop range in meters, i.e. the range of the last sample in the output echogram.

Number of datapoints

Specify the desired data resolution to output for the depth range specified.

Note: Where data is available on the input echogram between the Start range and Stop range it will be used to create the pings in the output echogram. Where no data is available on the input echogram in this range, "no data" appears in the output echogram.

Algorithm

The Resample operators resample pings in both the range and the along-track directions using one of the available operations. Resampling works by creating cells, based on the settings specified on the Resample page of the Variable properties dialog box, identifying which samples fall within each cell and applying statistical operation to those samples - very typically a mean operation. Sample Sv, TS and unspecified dB are converted to the linear domain for intermediate calculations with output values reconverted to the dB domain.

The diagram below shows an original sample in a grid of such samples (black) and a resampled sample (red).

general diagram for resampling

Where:

i is the index for pings in the operand
I is the index for pings in the output variable
j is the index for samples in an operand ping := {0 ... n-1}
J is the index for resampled samples in an output ping := {0 ... m-1}
n is the number of samples in an operand ping
m is the number of samples in the output ping. Entered as Output Number of Datapoints on the Resample page of the Variable properties dialog box
' denotes a value associated with the output variable (as distinct from the operand variable)
ri, j is the range of sample j in ping i of the operand variable
r'I, J is the range of sample J in ping I of the output variable
Ri, j is the near range boundary of sample j in ping i of the operand variable.
    for j = 1 to n-1

Ri, 0 is the start range of ping i in the operand (m).

Ri, n is the stop range of ping i in the operand (m).

R'I, J is the near range boundary of sample J in ping I of the output variable

R'I, 0 is the start range of the output ping (m).
Specified in the Output section of the Resample page of the Variable properties dialog box
Entered as Output Start Range when Custom ranges is selected
Is the start range from operand 1 when Use ranges from operand 1 is selected

R'I, m is the stop range of the output ping (m).
Specified in the Output section of the Resample page of the Variable properties dialog box
Entered as Output Start Range when Custom ranges is selected
Is the stop range from operand 1 when Use ranges from operand 1 is selected

Custom ranges > Start range specifies the start range of the output ping.

Custom ranges > Stop range specifies the Stop range of the output ping.

Custom ranges > Number of Datapoints specifies the sample resolution of the output ping.

When Custom ranges are specified, the range resampling can look like a zoom.

di, j is the distance of ping i for sample j in the operand variable (from ping 0 in the same variable).

Note: This may be measured in meters (if the resample by distance interval operator is used) or seconds (if the resample by time interval operator is used) or in pings (if the resample by number of pings operator is used). When measured in pings, only integral values are used (whole ping numbers).
d'I, J is the distance of ping I for sample J in the output variable (from ping 0 in the same variable).
Di, j is the near boundary distance of ping i for sample j in the operand variable (from ping 0 in the same variable).
    for i = 1 to m-1

D0, j = 0

Dm, j = dm-1, j + (dm-1, jDm-1, j)

D'I, J is the near boundary distance of ping I for sample J in the output variable (from ping 0 in the same variable).

Notes:

Operations

The operations available can be divided into two groups, mean statistics and sampled statistics. They are described individually below:

Mean statistic

The weighted mean statistic is used when you choose Mean for the Resampling operation on the Resample page of the Variable properties dialog box.

Note: The Resample operator offers only the weighted mean operation for range resampling. Prior to Echoview 6, several other mean algorithms for range resampling were available. Pre-Echoview 6 EV files that specify unavailable mean algorithms will default to using the weighted mean algorithm.

Weighted mean

A weighted mean takes into account the area of overlap between operand samples and output samples and weights contributions accordingly.

The weighted mean is calculated as:

Equation 1

Where:

yI, J =

the value of sample J in the output ping I

xi, j =

the value of sample j in the operand ping i

wi, j = w1 x w2

where:

w1 is the sample weighting for the range direction, calculated as follows:
  w1 = m(Ri, j+1, R'I, J+1 )M(Ri, j, R'I, J ) for a Weighted mean calculation.
w2 is the sample weighting for the along-track direction, calculated as follows:
  w2 = 1 for an Unweighted mean calculation.
m(Di, j+1 , D'I, J+1 )M(Di, j , D'I, J ) for a Weighted mean calculation.
m(a,b) is the minimum of a and b
M(a,b) is the maximum of a and b
X = the set of all samples in the operand ping
Y = the set of all samples in the operand ping which contribute to the resulting sample J, defined as:

for weighted means,

Y := { i,j Î X: [R'I, J ≤ Ri, j ≤ R'I, J+1 Ú 
    R'I, J ≤ Ri, j+1 ≤ R'I, J+1 Ú 
 

 

(Ri, j ≥ R'I, J Ù Ri, j+1 ≤ R'I, J+1)]Ù
    [D' I, J < Di, j < D'I, J+1 Ú
    D'I, J ≤ Di, j+1 ≤ D'I, J+1 Ú
    (Di, j ≥ D'I, J  Ù  Di, j+1 ≤ D'I, J+1)]}

See the introductory diagram above for definitions of any remaining symbols.

Sampled statistics

Minimum

When you choose Minimum for the Resampling operation on the Resample page of the Variable properties dialog box, the minimum algorithm calculates yI, J (the value of sample J in the output ping I) as:

yI, J = W0

Where:

yI, J = the value of sample J in the output ping I
W0 = the value of sample 0 (the first sample) in the list W — (defined below)
X = the set of all samples in the operand
Y =

the set of all samples in the operand which contribute to the resulting sample I, J — defined as:

 

Y := {i,j Î X: R' I, J < ri, j R'I, J+1 Ù D' I, J < di, j D'I, J+1}

W =

the ordered list of sample values xi, j for all i,j in set Y, being (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

N = the number of samples in the list W

See the introductory diagram above for definitions of any remaining symbols.

Maximum

When you choose Maximum for the Resampling operation on the Resample page of the Variable properties dialog box, the maximum algorithm calculates yI, J (the value of sample J in the output ping I) as:

yI, J = W0

Where:

yI, J = the value of sample J in the output ping I
W0 = the value of sample 0 (the first sample) in the list W — (defined below)
X = the set of all samples in the operand ping
Y =

the set of all samples in the operand which contribute to the resulting sample I, J — defined as:

 

Y := {i,j Î X: R' I, J < ri, j R'I, J+1 Ù D' I, J < di, j D'I, J+1}

W =

the ordered list of sample values xi, j for all i,j in set Y, being (W0, W1, W2, .... WN-1) such that Wi ≥ Wi+1 

N = the number of samples in the list W

See the introductory diagram above for definitions of any remaining symbols.

Median

When you choose Median for the Resampling operation on the Resample page of the Variable properties dialog box, the median algorithm calculates yI, J (the value of sample J in the output ping I) as:

yI, J =   Wk       if N is odd
(W k+Wk+1)/2   if N is even

Where:

yI, J = the value of sample J in the output ping I
Wk = the value of sample k in the list W — (defined below)
k = ëN/2û *
N = the number of samples in the list W
X = the set of all samples in the operand
Y =

the set of all samples in the operand which contribute to the resulting sample I, J — defined as:

 

Y := {i,j Î X: R' I, J < ri, j R'I, J+1 Ù D' I, J < di, j D'I, J+1}

W =

the ordered list of sample values xi, j for all i,j in set Y, being (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

See the introductory diagram above for definitions of any remaining symbols.

Percentile

When you choose Percentile for the Resampling operation on the Resample page of the Variable properties dialog box, the Nth Percentile algorithm calculates yI, J (the Nth Percentile score for sample J in the output ping I) as:

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

Where:

yI, J = the Nth Percentile score for sample J in the output ping I
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 Resample page of the Variable Properties dialog box
X = the set of all samples in the operand
Y =

the set of all samples in the operand which contribute to the resulting sample I, J — defined as:

 

Y := {i,j Î X: R' I, J < ri, j R'I, J+1 Ù D' I, J < di, j D'I, J+1}

W = the ordered list of sample values xi, j for all i,j in set Y, being (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

See the introductory diagram above for definitions of any remaining symbols.

About virtual variables
Resample operators

Footnote:

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

See also

About virtual variables
Operator licensing in Echoview