Introduction

This note records some interesting points about acoustic.

Nature of Human hearing

An good explanation of human hearing nature in the paper:

Give a pure tone with a certain frequency and intensity, for a normal listener there is a masking threshold function associated with this tone such that if noise is added to the tone and the power spectrum of the noise is strictly below the masking threshold at all frequencies, that noise will be inaudible, i.e., it will be completely masked by the tone. In General the masking threshold has a peak at the frequency of the tone, and monotonically decreases on both sides of the peak. This means the noise components near the tone frequency are allowed to have higher intensities than other noise components that are farther away from that frequency while remaining inaudible.

A short segment of a speech signal can be considered as a superposition of many sine waves. If each of these sine waves were presented alone to a normal listener, there would be an associated masking threshold function with a peak at the frequency of that sine wave. When all such sine waves are superimposed, their associated threshold functions must also superimpose. Exactly how these functions interact with each other is unknown. However, no matter how complicated the interaction might be, there must exist an overall masking threshold function for the given segment of speech signal such that an added noise will be inaudible if its power spectrum is below the threshold at all frequencies. The overall masking threshold function follows to some extent the spectral peaks and valleys of the speech spectrum. (The supra threshold masking curves for limiting noise to a given level of subjective loudness will be similar in shape.) This characteristic behavior of the masking threshold function is more commonly associated with the spectral envelope of speech.