Computing filter loss

RxLoss is a measure of how much information (or energy) is discarded by the filter. This allows you to correct the radar calibration for the difference between what a broad-band power sensor measures as the overall transmit energy, and what the RVP10 narrow-band receiver detects within its passband. The filter loss is a subtle quantity that depends on the combined characteristics of both the transmit waveform and the receiver FIR filter.

RVP10 computes these losses in two different ways. The loss displayed in Ps is based on sampling and filtering the actual burst pulse while the loss displayed in Pa is computed using the waveform and filter vector data of the signal processor.

Let b be the transmitted burst pulse vector. This means the voltage samples of the entire burst pulse at the actual sampling rate of the IFDR’s burst channel. Filter loss is computed by square of b over square of filtered b (convolution of b and f):

L o s s = \frac{{| b |}^{2}}{{| b ⨂ f |}^{2}}

Because burst pulse has real values, it has two frequency peaks. Only one of them matches the filter frequency. To compensate the double loss, the computed Loss above is divided by 2:

{R x L o s s}_{d B} = 10 {l o g}_{10} (\frac{L o s s}{2})