Extract transmission statistic equations

Transmission characteristic variables contain complex electrical impedance data for an active transducer that was recorded to a data file. The Extract transmission characteristic virtual variable outputs an impedance statistic for a specified transducer component.

Echoview reports the magnitude of the complex impedance statistic. An impedance value is calculated for each transmission characteristic sample that occurs during a transmitted pulse. For Simrad EK80 transmission characteristics, the number of samples recorded per ping is determined by the product of the pulse duration and sampling frequency, rounded down. The number of samples is recorded for each transducer sector, with the sum of the samples from each sector representing the transducer. Generally, the set of samples is small and as a result, the Inclusive method for interquartile range is more suitable than the Exclusive method.

Electrical impedance

Ohm's law may be expressed with complex voltage (V) and complex current (I) which then defines electric complex impedance (Z). The complex impedance has a real and imaginary part, where the imaginary part is expressed as an imaginary value multiplied by j (the square root of -1). The magnitude of the complex impedance is |Z|, and statistic calculations use the set of |Z| samples for the specified transducer component (which may be a sector or the aggregate of all sectors).

V = I Z

where:

j = √ -1 and a, b, c, d are real numbers recorded for each sample.

V = complex voltage in Volts

V = a + bj

I = complex current in Amperes

I = c + dj

Z = complex impedance in Ohms

Z = V / I

Statistical impedance

Median

The median of the |Z| for the specified transducer component = Wk if N is odd

where:

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

k
= *

N
=
the number of |Z| samples for the specified transducer component in the list W

W
=
the ordered list of |Z| samples for the specified transducer component:

(W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

Maximum

The maximum of the |Z| for the specified transducer component = WN-1 in the set W.

Interquartile range

For the set W, WIQR is the interquartiile range (IQR). WIQR is a measure of the spread of |Z| for the specified transducer component.

The IQR Inclusive method includes the median value during IQR calculations. When N is odd, the median value is included in both subsets for the first and third quartile. When N is even, the median is the mean of center values.

where:

WIQR = WQ3 -WQ1

WQ3
= the median of the subset for the half of W used for third quartile calculations

WQ1
=
the median of the subset for the half of W used for first quartile calculations

W
=
the ordered list of |Z| samples for the specified transducer component:

(W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

Footnote:

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

Wk	=	the value of sample k in the list W (defined below)
k	=	*
N	=	the number of \|Z\| samples for the specified transducer component in the list W
W	=	the ordered list of \|Z\| samples for the specified transducer component: (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

WIQR	=	WQ3 -WQ1
WQ3	=	the median of the subset for the half of W used for third quartile calculations
WQ1	=	the median of the subset for the half of W used for first quartile calculations
W	=	the ordered list of \|Z\| samples for the specified transducer component: (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1