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Unformatted text preview: 1 6.345HST.728 Automatic Speech Recognition Spring Term, 2010 Auditory Processing of Speech. Louis D. Braida Sensory Communication Group Research Laboratory of Electronics and Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science February 17, 2010 * c circlecopyrt L. D. Braida 1 Introduction In this section we discuss some terminology. 1.1 Sound Level A sound having a pressure waveform p ( t ) = 2 P cos (2 ft + ) has an rms pressure P (Newtons per square meter, or Pascals). The rms sound pressure is conveniently described in the of Sound Pressure Level (SPL) as the ratio of P to a reference pressure P of 2 10 5 newtons per square meter, 20 Pascals, or 0 . 0002 dynes per square centimeter. This is conveniently measured on a logarithmic scale in decibels ( dB ): dB SPL = 20 log 10 P P The intensity, I , of a sound is the rate of energy flow across a unit area and is measured in watts per square meter. The Sound Intensity Level (SIL) of a sound is the ratio of I to I , where I = 10 12 watts per square meter. This is conveniently measured on a logarithmic scale in decibels: dB SIL = 10 log 10 I I The reference for sound pressure, P is compatible with the reference for sound intensity I in air, thus 20 log 10 P P = 10 log 10 I I 1.2 Sensation Level The detection threshold of a sound is often a convenient reference for measuring sound pressures. Not only are many phenomena simpler when expressed relative to detection thresholds, but is is fairly straightforward to measure, unlike the absolute level. If the detection threshold of a sound has an rms pressure P * the Sensation Level (SL) of the sound is defined as the ratio of the pressure of the sound, P to P * . This is conveniently measured on a logarithmic scale in decibels: dB SL = 20 log 10 P P * . It is easy to show that dB SL = 20 log 10 P P 20 log 10 P * P . In other words, the Sensation Level of a sound (in dB) is the difference between the Sound Pressure Level (in dB) of the sound and the Sound Pressure Level (in dB) of the sound at threshold. 1 1.3 Spectra Periodic Signals A periodic pressure waveform p ( t ) = summationdisplay k =1 2 P k cos (2 kf t + k ) with fundamental frequency f and period T = 1 f is said to have a line power spectrum with components P k 2 at frequencies kf . The power in the signal between frequencies f A and f B is P ( f A ,f B ) = k B summationdisplay k = k A P k 2 where k A is the largest k for which kf f A and k B is the smallest k for which f B kf . Noise Noise is often modelled as a random process with a well defined continuous power spectrum, N ( f ) and a random phase spectrum. The power spectrum of the noise process n ( t ) is defined so that if n ( t ) is filtered by an ideal bandpass filter that passes frequencies f A f f B , the power in the process that emerges from the output of the filter is P out = f B integraldisplay f A N ( f ) df (1) Noise that has the property that...
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