Amplitude modulation (AM) and the effect of nonlinearity. A waveform of an AM signal (A) and its corresponding spectral representation (B). Modulation depth is 100%. USB: upper sideband; LSB: lower sideband. When such an AM signal is submitted to a saturating nonlinear system, the output spectrum shows multiple sideband components around the carrier (D). The waveform of the carrier in the nonlinear output demonstrates a complex AM (C).
Ear canal acoustical signal and analysis. (A) The bias tone at pSPL and two tone signal at SPL. The tail portion (about ) of the signal is flat with no biasing. (B) The acoustical signal in (A) is high-pass filtered at to eliminate the bias tone. Note: there is no modulation in the amplitude of the high-passed signal.
Spectra of the ear-canal acoustic signals for different primary frequencies. (A) ; (B) . The original time waveforms were high-pass filtered at . Compositions of the harmonic and DPs are labeled. Note: the multiple sideband peaks and the elevated baseline around each DP component.
Temporal modulation patterns at the lower primary frequencies . Band-passed waveforms of the odd- and even-order DPs are displayed in the upper and lower panels, respectively. The bandwidth of the filters (zero-phase Butterworth) is centered at the DP frequencies. Envelopes of the waveforms are derived from the moving-window method. The DPs are labeled in each panel. Vertical grid lines indicate the peaks and troughs of the bias tone (see Fig. 2 for a reference) where magnitudes of the odd-order DPs are suppressed and even DPs are enhanced. Refer to the tail portions for DPOAE magnitudes without biasing. Note: the modulation pattern of is similar to even DPs.
Temporal modulation patterns at the higher primary frequencies . Band-passed waveforms and envelopes of the odd- and even-order DPs are displayed in the upper and lower panels, respectively. Vertical grid lines indicate the peaks and troughs of the bias tone. The temporal modulation patterns are fundamentally different for odd and even DPs. Signal conditions are indicated in the lower panel. Note: (1) the CDT waveform is from a lower primary level ( SPL) and the envelope of this DP at SPL primary level is outlined with a pair of solid lines; (2) the CDT at higher primary level is partially modulated.
Spectral fine-structures of low-frequency modulated DPOAEs . Left column: odd-order DPs; right column: even DPs. Labels of the DPs are indicated in the center of each panel. Enhanced components of the LSB (closed symbols) and USB (open symbols) are labeled with Roman numerals according to the spectral distance from the DP. There is a interval between adjacent sidebands with labels. Sideband I is from the even-DP components and from odd DPs. USBs and LSBs are generally symmetrical. Note: there are also smaller sideband components between the labeled ones, especially for . Time waveforms of the DPs are displayed in Fig. 4 .
Spectral fine-structures of low-frequency modulated DPOAEs . Left column: odd-order DPs; right column: even DPs. Sideband components present at multiples of from the DP (center of each panel). Enhanced sideband components (labeled) present at odd multiples of away from the even-order DPs and even multiples of for odd DPs. The spectral interval between adjacent labeled sidebands is . Time waveforms of the DPs and signal conditions are displayed in Fig. 5 . For CDT, spectra from two primary levels are shown. Note: the greater sideband magnitudes relative to CDT at the lower primary level ( SPL, thick line).
Modulation contours of CDT. Absolute sideband magnitudes and their relative amplitude with reference to the CDT are plotted as functions of bias tone and primary levels in the upper and lower portions of each panel, respectively. Data represent an average of the sideband I [(A) and (C)] and II [(B) and (D)] across USB and LSB. Elevations of the contours are indicated. The contour lines reflect the mean sideband amplitude . Effective signal conditions can be observed from the contours of the relative sideband amplitudes (lower portion of each panel). Data from the lower primary frequencies are displayed in the upper [(A) and (B)] panels and higher primary frequencies in the lower panels [(C) and (D)], respectively.
Modulation contours of QDT. Absolute sideband magnitudes and their amplitude relative to QDT are plotted in the upper and lower portions of each panel, respectively. Data represent the mean of the sideband I [(A) and (C)] and II [(B) and (D)] magnitudes across USB, LSB, and all animals . Sideband amplitude from different primary frequencies are displayed in the upper [(A) and (B)] and lower panels [(C) and (D)], respectively.
Growths of CDT sideband amplitudes. (A) and (B) Growth functions of the absolute sideband amplitudes of the CDT as a function of the primary level. (C) and (D) Growths of the sideband magnitudes relative to the CDT. Data of sideband I averaged across USB and LSB are displayed in (A) and (C), averaged sideband II magnitude in (B) and (D). Data reflect the error (SE) from all animals . Bias tone level is pSPL or .
Growths of QDT sideband amplitudes. Growth functions of the absolute amplitudes of the QDT sidebands are shown in (A) and (B), those of the relative sideband magnitudes in (C) and (D). Average amplitudes of sideband I and II across USB and LSB are displayed in the left and right panels, respectively. Data represent the . Bias tone level is .
Temporal modulation pattern in relation to the cochlear . (A) The modulation pattern of QDT during a period of the bias tone (dashed line). (B) Schematic representations of the OP change on the for the rise and fall of the bias pressure. The arrows indicate the compressive portions of the that correspond to the periodic generations of QDT in (A). (C) The modulation pattern of CDT within a biasing cycle (dashed line). (D) Illustration of the cochlear for the cycle of biasing. Arrows indicate the two centers of the with optimal gain where the peaks of CDT are produced (C). Note: the numbers of DP generation stages are different for the CDT and QDT.
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