I'm reading this paper https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4562283/ , but I cannot make sense of what MPS nor how should I read the pictures that make use of this method.

The authors say

The MPS, beyond classical representations such as the waveform and spectrogram (Figure 1A and B, upper and middle panels), displays the time-frequency power in modulation across both spectral and temporal dimensions (Figure 1A and B, lower panels). The MPS has become a particularly useful tool in auditory neuroscience because it provides a neurally and ecologically relevant parameterization of sounds

I'm clueless about what the meaning of time-frequency power in modulation across both spectral and temporal dimensions. Can someone provide a brief explanation about this and MPS?


A time-frequency graph also know as a TF distribution, is a spectrogram, a spectrograph, a sonogram, a waterfall display of sound. They are all different names for the same thing. They look like this:


Just as white light contains many wavelengths of colors, sound energy contains bass, mids and high all in the same moment in time, a bit like a water wave has multiple wave sizes, sound energy is the same with sound pressure levels.

Modulation refers to the variation of a simple signal, like tarzan modulates his voice using a kind of tremolo effect, so does a car alarm, and a bird has very varied squeak effects with tremolo effects and also changes from squeaks into clicks into hisses, spectral changes in the timbral quality of the sound. Modulation is a scientific word for the variations of the amplitudes and frequencies of a communications signal.

They write about temporal modulation and spectral(pitch) modulation, it's just hte changes on the time-frequency graphs.

Modulation power spectrum is a relatively obscure field of bioacoustics, it attempts to generalize the fluctuations and patterns of loudness and squeak spectrums into another graph, which is a bit like a secondary time and freqency graph derived from the first sound time and frequency graph, else a 2D graph as in the illustrations, which show sound fluctuation prevalence as an average of the TF graph(a averaged sound fluctuation prevalence of the spectrograph). so, if tarzan's voice oscillates every 1 second, he has a major modulation at 1Hz spectrally, and a minimal amplitude modulation, and they will graph that as a peak as 1Hz on the MPS graph.

enter image description here We can see on this image that The human speech spectrogram on the top left is mostly at 500HZ, with some S and CH sounds at 2000hz.

For the MPS of the human voice, they have correlated Spectral modulations against Temporal modulations. It is easy to see that the human voice mosly changes at arond 1HZ, same as tarzan's voice, because syllables and pauses take about .5 to 1 second (average words per minute of a human is about 50, average syllables per minute is about 120). So it is easy to see a temporal modulation peak at 1Hz. The less clear thing is that it is plotted against spectral modulation, which is 2-3 octaves of change, an octave being a doubling of wave speed and frequency. So we can say that the main spectral modulations of the human voice occur over 2-3 octaves at a speed of about 1Hz. There is a secondary peak, which suggest that there is a change of about 1 octave that occurs at about 200-300 HZ. That is the gruff buzz that you hear in your own man voice, it is about 150HZ and it has about .5-1octave, the base frequency of your voice being 150Hz and various 3rds adn 5ths of an octave, and another octave at 350Hz, seems to be visible from that graph. tarzan voice: https://www.researchgate.net/profile/Alexandre_Hyafil/publication/283260815/figure/fig2/AS:293940512215079@1447092287682/A-Phase-Frequency-coupling-can-be-mistaken-for-Phase-Amplitude-Coupling-Top-curves-An.png

MPS seems to have been used to study neuron responses in psycho-acoustics.

Neurons interpret sounds using some kinds of complex time and freqency variation(modulation) recognition(resolution) and the researchers use MPS as they say it fits well with the neuron psychoacoustics study.

I would suggest that there are many other ways of measuring psycho acoustic nerve responses and bioacoustics than only MPS, it is an over simplification of sound analysis, and the Digital-Signal-Processing forum on this website will inform you that there are also 100ds of other maths and analysis algorythms that you can run on sound to study Time-Frequency Graphs, and to define sound in many different ways than MPS.

very pure sounds like sine waves make tight lines on a time frequency graph, noise makes very scattered signals at all frequencies, and sounds with many harmonic modes make nice ordered lines of smaller subharmonics that reflect the base frequency of a signal, which resemble echoes of the original sound in parralel with it, and that are on a different frequency.

Time frequency graphs are quite interesting to study and there are probably some studies of bird calls on YT: https://www.youtube.com/watch?v=_FatxGN3vAM

  • $\begingroup$ Still not sure if I'm getting it. (1) What (I think) I understand is that MPS graph shows the variation of pitch (spectral modulation) vs variation of time (temporal modulation). So if Tarzan's voice jumps from a tree using his voice with a tremolo effect, and his voice oscillates from 10 to 20 hz every second, should I expect to see at the 1hz a distribution of red to blue from 10 to 20hz corresponding to the change in pitch? (2) Consider the "fall" in the MPS for human speech, nearer to 0, do I see more red because within invervals close to zero voice shows a greater change in pitch? $\endgroup$
    – Cure
    Sep 23 '18 at 11:54
  • $\begingroup$ that's about right. (2)The human voice spectrogram is illustrated as a correlation of spectral versus temporal modulations. We can see at .5Hz the giant peak at the start corresponds to the slow change in words and syllables, which varies by 2-3 octaves of pitch. There is also another peak at 150Hz which corresponds to the gruff tone of a male voice, which varies by 1 octave, and which has 3rd and 5th harmonics and at 300hz, an octave above 150hz. I'll add a bit just under the image with another image of tarzan's vice. given a moment to read the peacks, spectrograms are easy to read. $\endgroup$ Sep 23 '18 at 15:50

MPS is the two-dimensional Fourier transform of the spectrogram. Assuming that you know what a Fourier transform and a spectrogram is, the MPS method consists in treating the spectrogram as an image on which to apply the Fourier transform. Thus, one can extract an estimate of the joint modulation on the frequency and temporal domain of a signal. If I attempt to provide an intuitive explanation of how to interpret an MPS, I would say that it allows the researcher to quantify the irregularity of a signal across time and frequency bands.


Here a clear explanation, cheers!


  • 3
    $\begingroup$ Link-only answers are generally not acceptable on Stack Exchange sites. The link may change or become unreachable in the future, and without a summary of what the link contains this answer would be useless. Please summarize what is in the link (don't just copy and paste) and use the link solely for reference. If you remove the link and the answer cannot stand on its own, it is not a good answer. $\endgroup$
    – Bryan Krause
    Sep 19 '19 at 16:18

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