# How are the amplitude [dB] and correlation [%] calculated?

Follow**Amplitude:**

Essentially, the signal is read in and a digital down-conversion technique is implemented to produce quadrature (I/Q) data for each bin of each profile. These values are ultimately tied to the input voltage, but no scaling to voltage is done internally (since it’s not needed) and the digital values are used as is. The I/Q values are used to calculate a signal amplitude and intermediate cross-correlation products, which are accumulated over the number of pings in the ensemble.

To reduce processing speed, the firmware uses an approximation for the magnitude calculation using something called the “alpha max plus beta min” algorithm (http://en.wikipedia.org/wiki/Alpha_max_plus_beta_min_algorithm). This does produce a small error in the amplitude (of up to ~4% depending on the I/Q values). The correlation uses the magnitude values for normalization, so you will also see a small approximation error there as well. The velocity measurements are not affected by this approximation in any way.

When the data for an ensemble has been collected, the amplitude signal is normalized (divided by the number of pings accumulated) to produce a linear intensity signal that is sent to the acquisition computer.

Inside the acquisition computer, this signal is converted to dB using the formula Amplitude dB = (20 * log10((amplitude + 1) / MAX_AMPLITUDE)

The +1 is used to prevent a log10(0) error and the MAX_AMPLITUDE value is 8000.

(Note that the acquisition software allows you to collect the linear amplitude from the instrument instead of the log amplitude if desired.)

**Correlation**:

The correlation is the normalized amplitude of the auto-correlation function; i.e. if Z1 = I1 + iQ1 for ping 1 and Z2 = I2 + iQ2 for ping 2, the intermediate product P = Z2 * Z1* (Z2 times the complex conjugate of Z1) and the correlation is:

Correlation = Magnitude (P) / (magnitude (Z1) * magnitude (Z2))

The instrument outputs this as an integer value normalized to fit into one byte (i.e. 255 = 100%). The collection software automatically takes care of the scaling when the display and export are carried out.

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