Noise Power Spectrum from Log Video Amplifier

I know that if I use a square law detector on band limited noise - let's assume it's rectangular - the noise power spectrum becomes the convolution of the input power spectrum. After lowpass-filtering all of the higher frequency products, the video output spectrum is triangular (from convolving the rectangular input spectrum with itself).

I am using a log video amplifier for detection on band limited noise, but I'm not sure what the theoretical video spectrum should be in that case. I could go through the math using a power series expansion, but I'm not sure what the transfer function is, given that the input signal is RF and goes through zero (where log(0) is undefined). Is there an intuitive way to understand this case? I have to explain this to others, and a simple explanation of what to expect would be very helpful.

• Do you mean a detector log video amplifier? Or are you just trying to analyze what happens after the detector? Commented Sep 2, 2021 at 14:29