"The spacing of the filters in a filter bank used to make an ordinary spectrogram is linear, whereas an auditory filter bank has a spacing that corresponds to the way in which sinusoidal frequency maps onto place on the basilar membrane, a so-called tonotopic map. For frequencies of about 1kHz and above, this mapping is logarithmic."

I read this in an article about how the ear works in processing sound. Can someone explain mathematically how the mapping for frequencies of about 1 kHz and above is logarithmic? Also it would be appreciated if anyone can suggest some literature regarding this topic.

  • $\begingroup$ I don't think mathematical proof for logarithmic scaling will be there. it should be experimental observation that human ears sensitivity is logarithmic. $\endgroup$ – arpit jain May 2 '17 at 16:37
  • $\begingroup$ What is the meaning of logarithmic scaling? How to scale something logarithmically? $\endgroup$ – Viswanath Hariharan May 2 '17 at 16:38
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    $\begingroup$ have you heard about Mel scale/Mel filter bank ? the frequency bins are scaled logarithmically to extract features/ representaion.. $\endgroup$ – arpit jain May 2 '17 at 16:40
  • $\begingroup$ Nope. I will check it out $\endgroup$ – Viswanath Hariharan May 2 '17 at 16:42

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