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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?
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The Equi-loudness contours, chart provided at your link, is for hearing thresholds for isolated tones. Assuming speech is a sum of tones is a wrong assumption. But even if we go ahead with this assumption, it does not help to compute SNR for speech understanding under noise because of the following reasons.

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. Bottom: A wideband spectrogram of speech signal shown on Top.

Now, coming to your question on minimal SNR for people to understand speech, the notion of SNR is not well defined for speech as the power spectral density of speech is varying with time. Although you have provided a definition for SNR you can see that it just a ratio of full signal energy. Instead, we perceive speech as a function of time.

b. Speech perception in noise can be analysed from at least two aspects - intelligibility and quality. I assume by understanding speech you mean intelligibility, that is you can make out the phonemes uttered. Intelligibility in noise is dependent on the power spectral density of noise. Different acoustic noise have different spectrum, and affect the intelligibility to different extent. Like a tone interference may not effect speech intelligibility, but something like babble noise (example, in a party where many people are talking in the background) can easily impact the intelligibility.

c. Having recognized above nuances with respect to speech perception, the Equi-loudness contours specify the threshold of hearing for tone stimuli. The threshold of hearing is obtained in a quite environment (or absence of any other sound). The 0 dB is with respect to threshold of 1 kHz tone. Hence, the curves are of not much help to compute threshold in noise. However, these have been used in designing equilizers in sound playback systems.

d. In case you play two tones and ask the question of when is one sound masked by the other then this is termed as "masking threshold". Masking thresholds are used in MP3 codec to improve coding gains.

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