# Can steady-state noise contain a fundamental frequency?

I am doing speech-in-noise testing. We use the so-called matrix test. The Flemish/Dutch version of this test features a female speaker. I ran some sentences through 'Praat' and it provided me with a fundamental frequency (F0) of about 220 Hz, which makes sense.

Now the noise that comes alongside it (Fig. 1) was basically made by overlaying white noise with the frequency spectrum of the speech, if I understand correctly (I'm a biologist) and I quote (Luts et al, 2014):

To generate the stationary speech-weighted noise the long-term average speech spectrum (LTASS) of the 500 sentences was determined. For each sentence, silence parts were removed (frames of 20 ms with RMS < 0.001) and the spectrum was calculated with a 4096-points fast Fourier transform using a rectangular window and without overlap. These spectra were then averaged, applying a weight according to the length of each sentence. For this LTASS, a 2048-taps finite impulse response filter was generated and applied on an 11 seconds long white noise. This noise is shown in Fig.1:

At our lab we call this stationary, speech-shaped noise (I'm in Audiology), but an anonymous referee kept shooting at this term and (s)he suggested steady-state noise. So let's go for that.

Now my question is whether this type of steady-state noise contains F0 components just like the original speech material it was produced from? F0 in speech is generated by the way air moves past the vocal folds, so it has a physiological correlate. One of my colleagues started laughing and said that steady state noise, being derived from white noise in this case, does not contain any harmonics. Since white noise is artificially generated to be random, and since it's not produced by he vocal folds I guess I understand their reaction.

Anyway, I ran the noise through 'Praat' and lo and behold, it produced an F0 of ~240 Hz, close to the original speech material. However, 'Praat' reportedly first identifies voiced components in the speech through recognizing formants (if I am not mistaken) before determining F0 components. However, there are seemingly no such components in the steady-state noise. Fig. 2 shows the output of Praat. The blue blobs are, afaik, the identified formants (there shouldn't be any) and the estimated F0. There's no output, but if I concatenate multiple instances of this noise it determines an F0 of around 240 Hz, close to the original female speaker.

Is the F0 information correctly identified by 'Praat' and could this F0 cue be available (useful) to human listeners to understand speech in noise?

• Of course it can. But not white noise nor pink noise. Commented Nov 23, 2019 at 20:59
• Thanks for your answer - can you add some explanation, or even better some references that explain the why behind your statement? I'm editing a paper on it and it's quite a crucial point that changes the premise of my experiments. Thanks! Commented Nov 23, 2019 at 21:42
• White noise and pink noise have even distribution of frequencies although the amplitude varies. But you could add them to a sin wave and have a fundamental with noise. Over all they are not technically colored noise any longer. In your case you would have white noise , if that is actually what you added, along with F0, F1, F2, F3 and possibly other formants. Commented Nov 23, 2019 at 22:28

First impressions are that there are some contributors to your project - possibly one of the 'referees' and the other laughing colleague that you mention - that don't understand the difference between 'pure noise' and 'speech-shaped noise'.

Seeing as all noise is basically made up of random frequency components at an equal level (this does depend on the type of noise we are talking about...), it is reasonable to suggest that in speech-shaped noise the distribution of relative frequency component levels is shaped by the impulse response, and therefore the spectrum of the speech you are using as the 'template'.

I therefore think that it is entirely reasonable to state that speech-shaped noise will contain F0 components at a level that is relatively higher than surrounding frequency components.

One has to bear in mind that in unshaped noise, there will still be f0 components (and everything else in-band) but the difference between this and shaped noise is the relative levels of these particular components and not their potential presence or absence.

• Thanks for your answer +1. Could you perhaps elaborate a little on ...it is reasonable to suggest that in speech-shaped noise the distribution of relative frequency component levels is shaped by the impulse response as this seems to be the core of your argument; unfortunately it's a bit over the top of my head. Specifically, I guess, the impulse component I don't understand. It's also mentioned in the quote. Commented Nov 6, 2019 at 13:18
• sure. There's a fair amount of DSP Theory quoted in your original post, but suffice to say that what is happening here is that the "LTASS" can be considered to be an "EQ Curve" which follows the shape of the averaged speech. Once you have this "EQ Curve" you can then apply this to pure white noise to obtain 'speech shaped' white noise. I think it is fairly certain that this "EQ Curve" (a.k.a. 2048-taps finite impulse response filter) will have a fundamental peak at your F0 frequency (amongst others) which is then applied as 'gain' to that region of the flat noise sample.
– Mark
Commented Nov 6, 2019 at 13:27
• Further to this, I think it would be interesting for you to research "Impulse responses" and "Convolution". Convolution is a digital signal processing function that allows an 'impulse response' to be applied to a signal in order to generate a new 'convololved' signal. It is a technique typically used in digital filtering and reverb processing. For instance, you can generate an impulse response for a building or a structure, and then apply this impulse response to a dry signal in order to allow the reverb characteristic of a known structure to be used in a post-production context.
– Mark
Commented Nov 6, 2019 at 13:33