# The minimal signal to noise ratio (SNR) for people to understand a speech in the noisy background

This question seems easy to find an answer but I got lost in the end. I am trying to find the threshold for people to understand speech in a noisy environment. For example, assume the background noise is $\mathbf n$ and the speech signal is $\mathbf s$. I wanna know the threshold thr for the speech being recognizable by a human when: $$10\log\left(\frac{\lVert \mathbf s\rVert}{\lVert \mathbf n\rVert}\right) > \text{threshold}\implies\quad\text{so the speech \mathbf s is recognizable by human}$$

The most relevant scientific fact I found is the absolute hearing threshold, such as the ISO 226.

However, I got confused to interpret this ISO 226 figure because the $y$-axis is in SPL (dB). Based on my understanding, the SPL is also defined based on the minimal hearing threshold, which is kind of weird to understand how much signal strength (of a speech) is actually necessary for people to recognize.

• Can I say the signal strength of a $10\textrm{ kHz}$ signal needs to be $\approx 5\textrm{ dB}$ higher than the noise floor for being recognized by the human based on the red lines shown in this ISO 226 figure?
• If it is true, how can I know the threshold for a speech signal covering multiple frequencies?

a. Speech is a non-stationary signal implying that the spectral content evolves over time. In other words, the energy of the different frequencies in the spectrum from 0-8 kHz will change depending on the uttered phonemes (making up the speech). An example is shown in Fig.1 below. 