Why does a series of pulses generate a pitch?

[Daniel Petka]

TL;DR Summary

A single (very short) pulse has all the frequencies, so it should excite all the little hair sensors in the cochlea and I don't understand why sending this pulse repeatedly creates a pitch.

Here's the thing: the ear detects a pitch by splitting a sound wave into it's frequency components in the cochlea, which is in a way a spatial Fourier transform (ish...) But I never liked this analogy because it doesn't explain why I hear a pitch when a series of pulses entern my ear.

A single (very short) pulse has all the frequencies, so it should excite all the little hair sensors in the cochlea and I don't understand why sending this pulse repeatedly creates a pitch. A soundwave can be decomposed into sine waves, but if we go in that direction, it's kinda tricky to talk about the duration of the transform interval.. because I can still hear the individual pulses. T

here is this thing called wavelet transform, which decompises the signal into wave packets instead. But I found one example that I don't think can be explained by wavelets: chirped pulse trains. Imaging sending a pulse, then another pulse 0.1s later, another one 0.25s later etc. The immediate "frequency" (the time between the pulses) changes constantly and yet I can still hear a changing pitch. The effect can be replicated by playing two sawtooth waves, one at 10Hz and the other one at 10.1 Hz.

 

[berkeman]

I'm not sure I understand what your question is, but with respect to multiple pulses and the frequency components, do you think that lining up the pulses in the time domain to try to align the phases of the harmonic sinusoidal components might be important?

 

[BillTre]

The sensory cells within the inner ear structure respond to different frequencies.

Its my understanding that:
Some cells at low frequencies can respond with a spike (action potential) per wave.
Others can't respond as fast as the frequency they are set-up to sense. They use a frequency coding.
In both cases the sensory cells respond in a signal path that defines the frequency that would be perceived.

Here's a Wikipedia article: https://en.wikipedia.org/wiki/Neural_encoding_of_sound

 

[DaveE]

The Fourier Transform of a pulse train is dominated at low frequencies by the fundamental frequency (pulse repetition frequency) and its harmonics. That is why you hear "tones".

https://sceweb.sce.uhcl.edu/harman/CENG3315_DSP_Spring2020/00_3315_2021/3315_web_2021/Fourier Series References_2_28_2021.pdf

BTW: It's not a spatial FT, it's temporal.

 

[Daniel Petka]

The Fourier Transform of a pulse train is dominated at low frequencies by the fundamental frequency (pulse repetition frequency) and its harmonics. That is why you hear "tones".

https://sceweb.sce.uhcl.edu/harman/CENG3315_DSP_Spring2020/00_3315_2021/3315_web_2021/Fourier Series References_2_28_2021.pdf

BTW: It's not a spatial FT, it's temporal.

Well first of all, the ear doesn't perform a Fourier transform as you would need to listen from minus infinity to infinity. There is short time FT and wavelet but then.. what is the window length? And yes, it's essentially temporal, but your ear doesn't view it that way. The cochlea only knows which hair cells get excited. The ones closer to the edge of the ear correspond to high frequencies and the ones further down to lower ones. Hope that clears thing up a bit

 

[Daniel Petka]

The sensory cells within the inner ear structure respond to different frequencies.

Its my understanding that:
Some cells at low frequencies can respond with a spike (action potential) per wave.
Others can't respond as fast as the frequency they are set-up to sense. They use a frequency coding.
In both cases the sensory cells respond in a signal path that defines the frequency that would be perceived.

Here's a Wikipedia article: https://en.wikipedia.org/wiki/Neural_encoding_of_sound

Thank you, I'll look into it.

 

[Daniel Petka]

I'm not sure I understand what your question is, but with respect to multiple pulses and the frequency components, do you think that lining up the pulses in the time domain to try to align the phases of the harmonic sinusoidal components might be important?

Phase doesn't matter in most cases, but sometimes it matters a lot. You'll see what I mean if you open any online tone generator and play a 10Hz sawtooth wave and another 10.1Hz sawtooth wave in another tab at the same time. If pitch was related to frequency, you would only hear the same pitch all the time. But as you hear, the pitch changes constantly. And the question is why. I don't think you can ignore the time domain in this case. The higher pitches correspond to pulses being closer together (which is kind of intuitive but I haven't heard anyone mention this before)