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[AUDITORY] Question about level conversions

Dear list, hello!

I have a technical question about presentation levels and signal-to-noise ratios (SNRs), as expressed in the current literature and in more classical studies (some of the papers I have recently investigated: Richards (1992, JASA - doi:10.1121/1.402831) and Ahumada et al (1975, JASA - doi:10.1121/1.380453)).

I have some thoughts, which I will share next, please feel free to comment on any of these aspects in terms of maths or concepts, or in terms of conceptual accuracy....

In classical papers (think also of the work by David Green and colleagues), SNRs are often expressed as energy with respect to N0, often reported as E/N0. In this _expression_ E is typically the energy of a target signal (e.g., a tone) which is embedded in a noise, whose spectrum level is N0. I am interested to know the mathematical expressions needed to convert between noise levels to the appropriate target sound level. I will now give an example about how I am currently doing such a conversion.

The example: Let's say I have a Gaussian noise (duration=0.5 s) with frequencies between 0 and 5 kHz, with a total RMS level of 70 dB SPL. On the other hand, my target sounds have a centre frequency of 500 Hz, a duration of 0.1 s, temporally centred in the noise. I want to know the level of the tone, if E_tone/N0 needs to be 11.8 dB (this is actually from Ahumada et al (1975)).

My calculations are as follows:
So, my tone will have a level of 34.8 dB SPL for this example.

Am I correct with my calculation method or am I missing any important concept?

Thank you for the feedback,

Alejandro Osses