DSP Robotics Support

Test scenario. Generated pink noise. Fixed (or periodic pulsation) frequency, let say at 3kHz. I'm setting the amplitude of the signal, so that in FFT software (windowed FFT, possibility to get average display over time, FFT up to 128kpts) - frequency peak is on the level (or a bit below) of surrounding background noise. In other words - neither spectrum nor spectrogram is showing anything visible or barely visible at 3kHz, where the signal was generated.

Question. How to approach visualization of such signals? How to uncover them? How deep (dB) they can be burried below the surrounding noise, so that they can be uncovered?

Statistically they can be buried infinitely low. The noise serves as a dither, allowing the signal to be set with amplitudes non-quantized to the bit-death/resolution. The only problem is, lower the signal-to-noise ratio, bigger window is required, because you need bigger sample-size for the noise to average out to flat spectrum. It's an very interesting mathematical phenomenon with great relevance to statistical analysis and AD/DA conversion as well as data-storage and possibly even cryptography.

So this is an example of mine.

Audio file contains pink noise mixtures with 3kHz continuous tone. Decibel levels were at -40, -48. -50, -53 and -60dB in relation to max=zero. The -50 and -53dB are border values for surrounding noise. Last sample is few dB below spectrogram and long-term average spectrum detection. Analyzer is set to provide generally good visibility.

How to approach such signals? At least I need some methods-specific keywords that would relate to the topic; otherwise google isn't helpful.