|
| \(a,b,c\) |
Constants in polynomial (§F) |
|
| \(a,b,c,d,i\) |
Coefficients of power law of ABR or OAE (§11.7.3, §17.3.1) |
|
| \(a,b,d\) |
Linear canonical transform (LCT) coefficients (§C) |
|
| \(a\) |
Complex temporal envelope |
|
| \(a\) |
Arbitrary signal (§14) |
|
| \(A\) |
Complex envelope spectrum |
|
| \(a_g \) |
Ideal geometrical image of envelope (§13.2.1) |
|
| \(a_n\) |
Complex temporal envelope in neural domain (§12.2) |
|
| \(a_s\) |
Sampled signal (§14) |
|
| \(A_s\) |
Sampled spectrum (§14) |
|
| \(b_n\) |
Random eigenfunction coefficient (§8.2.6) |
|
| \(B\) |
Bandwidth |
|
| \(B_n\) |
Noise-equivalent bandwidth (§9.4) |
|
| \(c\) |
Wave speed; Speed of light; Speed of sound |
|
| \(C\) |
Circle of confusion (§4) |
|
| \(C\) |
Channel capacity (§5.2.1) |
|
| \(C\) |
Schroeder phase curvature (§12.4.1, §17.3.1) |
|
| \(C\) |
Real part of Fresnel integral (§D) |
|
| \(C_T\) |
Linear canonical transform (LCT) kernel for operator \(T\) (§C) |
|
| \(d\) |
Temporal acuity; Detectable gap (§13.4.4, §15.6, §F) |
|
| \(d\) |
Group-delay dispersion impulse response (§12, §13.2) |
|
| \(D\) |
Aperture size (§4) |
|
| \(D\) |
Group-delay dispersion transfer function (§12, §13.2) |
|
| \(D\) |
Pulse sequence duration (§E) |
|
| \(D'\) |
Pulse sequence duration minus the last pulse duration (§E) |
|
| \(D_a\) |
Acoustic dipole strength (Table §3.1) |
|
| \(D_e\) |
Electromagnetic dipole strength (Table §3.1) |
|
| \(\boldsymbol{\mathbf{E}}\) |
Electric field (vector) (Table §3.1) |
|
| \(E\) |
Electric field (scalar) (§4) |
|
| \(ERB\) |
Equivalent rectangular bandwidth of auditory filter |
|
| \(f\) |
Frequency |
|
| \(f\) |
Focal length (§4) |
|
| \(f\) |
Arbitrary function (§3.2.1) |
|
| \(F\) |
Fourier transform of arbitrary function \(f\) (§3.2.1) |
|
| \(\boldsymbol{\mathbf{F}}\) |
Arbitrary wave field (Table §3.1) |
|
| \(f'\) |
Doppler-shifted frequency (§3.3.3) |
|
| \(f'\) |
Remapped imaged frequency under binaural diplacusis (§17.3.3) |
|
| \(f^\#\) |
F-number (§4.2.1) |
|
| \(f_0\) |
Fundamental frequency |
|
| \(f_c\) |
Carrier frequency |
|
| \(f_m\) |
Modulation frequency |
|
| \(f_n\) |
Cutoff frequency (Figure §9.3) |
|
| \(f_T\) |
Focal time |
|
| \(f_{T,gg}\) |
Focal time estimate of the gerbil and guinea pig time lens |
|
| \(f_{T,h}\) |
Focal time estimate of the human time lens |
|
| \(f_s\) |
Sampling rate |
|
| \(f_T^\#\) |
Temporal imaging f-number (§15.11.1) |
|
| \({\cal F}\) |
Fourier transform |
|
| \({\cal F}^{-1}\) |
Inverse Fourier transform |
|
| \(g\) |
Arbitrary function (§3.2.1) |
|
| \(g\) |
Complex envelope / Mapping function (§5.3.1) |
|
| \(g_1,g_2\) |
Fresnel integral variables (§D) |
|
| \(g_T\) |
Linear canonical transformed (LCT) function (§C) |
|
| \(h\) |
Impulse response function |
|
| \(\tilde h \) |
Impulse response function with reduced coordinate; Point spread function (§13.2.1) |
|
| \(\tilde h_d\) |
Defocused impulse response function for Gaussian pupil (§13.2.2) |
|
| \(h_{dr}\) |
Defocused impulse response function for rectangular pupil (§D) |
|
| \(h_L\) |
Time-lens impulse response function (§10.3, §13.2) |
|
| \(\boldsymbol{\mathbf{H}}\) |
Magnetic field (vector) (Table §3.1) |
|
| \(H\) |
(Shannon's) entropy (§5.2.1) |
|
| \(H\) |
Transfer function |
|
| \(H_d\) |
Amplitude transfer function (ATF) of generalized Gaussian pupil (§13) |
|
| \(H_{dr}\) |
Amplitude transfer function (ATF) of generalized rectangular pupil (§13) |
|
| \(H_L\) |
Time lens transfer function (§10.3) |
|
| \({\cal H}\) |
Hilbert transform (§6) |
|
| \({\cal H}^{-1}\) |
Inverse Hilbert transform (§6) |
|
| \({\cal H}\) |
Optical transfer function (§13) |
|
| \({\cal H}_d\) |
Defocused optical transfer function with Gaussian pupil (§13) |
|
| \({\cal H}_{dr}\) |
Defocused optical transfer function with rectangular pupil (§13) |
|
| \(i\) |
\(\sqrt{-1}\) |
|
| \(I\) |
Intensity |
|
| \(I\) |
Frequency interval (§15.10.1) |
|
| \(I_{coh}\) |
Coherent part of intensity (§8.2.1) |
|
| \(I_{inc}\) |
Incoherent part of intensity (§8.2.1) |
|
| \(I_{max}\) |
Maximum intensity (interference) |
|
| \(I_{min}\) |
Maximum intensity (interference) |
|
| \(I_{tot}\) |
Total intensity (§8.2.1) |
|
| \(I_0\) |
Object intensity (§4) |
|
| \(I_1\) |
Image intensity (§4) |
|
| \(I_r\) |
Intensity (radial) (Table §3.1) |
|
| \(I_\theta\) |
Intensity (azimuth) (Table §3.1) |
|
| \(I_\phi\) |
Intensity (elevation) (Table §3.1) |
|
| \(J_n\) |
Bessel function of the first kind of order \(n\) |
|
| \(k\) |
Wavenumber; Spatial frequency |
|
| \(k_x\) |
Horizontal component of spatial frequency (Table §1.2) |
|
| \(k_y\) |
Vertical component of spatial frequency (Table §1.2) |
|
| \(\boldsymbol{\mathbf{k}}\) |
Wavenumber vector |
|
| \(k_c\) |
Wavenumber at carrier frequency |
|
| \(k_i\) |
Imaginary-part of wavenumber function (absorption) (§3.4.2) |
|
| \(k_r\) |
Real-part of wavenumber function (dispersion) (§3.4.2) |
|
| \(K\) |
Gain (§5.3.1) |
|
| \(K\) |
Stiffness (§11.6.1) |
|
| \(K\) |
Loop gain (§9.3) |
|
| \(K_{BM}\) |
Passive basilar membrane stiffness (§11.6.1) |
|
| \(K_f\) |
Filter DC gain (§9.3) |
|
| \(K_m\) |
Phase detector sensitivity (§9.3) |
|
| \(K_v\) |
Voltage controller oscillator gain (§9.3) |
|
| \(l\) |
Integer |
|
| \({\mathscr L}(T) \) |
Linear canonical transform (LCT) for kernel operator \(T\) (§C) |
|
| \(m\) |
Integer |
|
| \(m\) |
Message (baseband) function (§5.3.1) |
|
| \(m\) |
Modulation depth (audibility, contrast) |
|
| \(m\) |
Frequency slope (chirpiness) (§B.3) |
|
| \(M\) |
Magnification |
|
| \(M'\) |
Complex magnification (defocused system) (§12.2.2) |
|
| \(M^*, M_f, M_{f'}, M_{f'}^*\) |
Distorted magnification under binaural diplacusis (§17.3.3) |
|
| \(m_0\) |
Chirp slope of object (§12.4.1) |
|
| \(M_0\) |
Magnification \(-v/u\) |
|
| \(m_1\) |
Chirp slope of image (§12.4.1) |
|
| \(m_r\) |
Rectangular pulse chirp slope (§B.3) |
|
| \(n\) |
Index of refraction |
|
| \(n\) |
Noise time-signal (§5.3.1) |
|
| \(n\) |
Harmonic number |
|
| \(n\) |
Integer |
|
| \(n_k\) |
Neural group velocity dispersion coefficient (§11.7.3) |
|
| \(N\) |
Noise power (§5.2.1) |
|
| \(N\) |
Number of samples |
|
| \(N\) |
Schroeder phase number of harmonics (§12.4.1) |
|
| \(N\) |
Number of pulses in sequence (§E) |
|
| \(NS\) |
Nonstationarity index (§A.4) |
|
| \(p\) |
Pressure |
|
| \(p\) |
Probability (§5.2.1) |
|
| \(P\) |
Pressure (frequency domain) |
|
| \(P\) |
Pupil function |
|
| \({\cal P}\) |
Cauchy principal value (§6) |
|
| \({\cal P}\) |
Generalized pupil function (§13.2.2) |
|
| \(P_e\) |
Entrance pupil (§14.4.2) |
|
| \(P_g\) |
Gaussian pupil function (§13.2.2) |
|
| \(P_r\) |
Rectangular pupil function (§13.3.2, §D) |
|
| \(q,q'\) |
Linear canonical transform (LCT) variables (§C) |
|
| \(Q\) |
Q-factor of bandpass filter |
|
| \(Q_{10}\) |
Q-factor of bandpass filter at -10 dB points (§11.6.4) |
|
| \(Q_{ERB}\) |
Q-factor of bandpass filter at the ERB bandwidth (§11.6.4) |
|
| \(r\) |
Displacement |
|
| \(r\) |
Received signal time-signal (§5.3.1) |
|
| \(r\) |
Correlation coefficient (Pearson's r) |
|
| \(\boldsymbol{\mathbf{r}}\) |
Position vector |
|
| \(r_c\) |
Critical distance (§8.4.2) |
|
| \(R\) |
Fixed distance (§8.5) |
|
| \(R\) |
Synchronization strength/index (§85) |
|
| \(R_{pp}\) |
Autocorrelation function of \(p\) (§8.2.2) |
|
| \(s\) |
Time lens curvature |
|
| \(s\) |
Time signal |
|
| \(s\) |
Laplace-transform complex frequency (§9.4) |
|
| \(s\) |
Sampler delta function array (comb function) (§14) |
|
| \(\hat{s}\) |
Estimate of time signal (§3.3.3) |
|
| \(s_{T,gg}\) |
Curvature estimate of the gerbil and guinea pig time lens |
|
| \(\boldsymbol{\mathbf{S}}\) |
Poynting vector (Table §3.1) |
|
| \(S, S_I\) |
Intensity/power spectrum |
|
| \(S\) |
Signal power (§5.2.1) |
|
| \(S\) |
Power spectral density / Spectrum (§8) |
|
| \(\mathit{S}\) |
Surface area of room (§8.4.2) |
|
| \(S\) |
Imaginary part of Fresnel integral (§D) |
|
| \(S_a\) |
Amplitude spectrum (§13.3.3) |
|
| \(s_h\) |
Time-lens curvature in humans (§11.6.4) |
|
| \(S_\omega\) |
Acoustic point source strength (Table §3.1) |
|
| \(t\) |
Time |
|
| \(t_0\) |
Gaussian pulse width parameter of the object; Entrance pupil |
|
| \(t_1\) |
Gaussian pulse width parameter of the image; Exit pupil |
|
| \(t'\) |
Complex Gaussian pulse width parameter |
|
| \(T\) |
Period |
|
| \(T\) |
Integration time constant |
|
| \(T\) |
Complex tone standard (§15.11.1) |
|
| \(T\) |
Linear canonical transform (LCT) matrix operator (§C) |
|
| \(\tilde T\) |
Integration variable (§13.2.1) |
|
| \(T_{60}\) |
Reverberation time |
|
| \(T_a\) |
Aperture time |
|
| \(T_c\) |
Carrier period |
|
| \(T_s\) |
Sampling rate period |
|
| \(v\) |
Velocity (§3.3.3) |
|
| \(v\) |
Distance between lens and screen (§4) |
|
| \(v\) |
Neural group-delay dispersion |
|
| \(V\) |
Visibility (§7.2.1, §8) |
|
| \(V\) |
Volume (§8.4.2) |
|
| \(V\) |
Voltage (§11.6.1) |
|
| \(v_g\) |
Group velocity |
|
| \(V_c\) |
Output voltage from loop filter (§9.4) |
|
| \(V_d\) |
Output voltage from phase detector (§9.4) |
|
| \(V_i\) |
Input voltage to phase detector (§9.4) |
|
| \(V_o\) |
Output voltage from voltage controller oscillator (§9.4) |
|
| \(v_p\) |
Phase velocity |
|
| \(v_{V-I}\) |
Neural group-delay dispersion for the segment between wave I and wave V (§11.7.3) |
|
| \(u\) |
Acoustic velocity (Table §3.1) |
|
| \(u\) |
Distance between object and lens (§4) |
|
| \(u\) |
Auditory input (cochlear) group-delay dispersion |
|
| \(\boldsymbol{\mathbf{u}}\) |
Sound velocity (Table §3.1) |
|
| \(u_e\) |
External environment group-delay dispersion (§11) |
|
| \(u_o\) |
Outer-ear group-delay dispersion (§11) |
|
| \(u_m\) |
Middle-ear group-delay dispersion (§11) |
|
| \(u_c\) |
Cochlear group-delay dispersion (§11) |
|
| \(w\) |
Wave energy density (Table §3.1) |
|
| \(W\) |
Cross-spectral density (§8) |
|
| \(W_d\) |
Reciprocal defocus parameter \(=1/u + 1/v + 1/s\) (§13, §F) |
|
| \(W_p\) |
Single pulse duration (§E) |
|
| \(x\) |
x-axis coordinate |
|
| \(x\) |
In-phase modulation (§5.3.1) |
|
| \(x\) |
Real part of analytic signal; arbitrary time signal (§6) |
|
| \(x\) |
Defocus parameter \(=u+sv/(s+v)\) (§12.4.1, §17.3.1) |
|
| \(X\) |
Fourier transform of real part of analytic signal \(X\) (§6) |
|
| \(x_0\) |
Arbitrary spatial position (§3.2.2) |
|
| \(y\) |
y-axis coordinate |
|
| \(y\) |
Quadrature modulation (§5.3.1) |
|
| \(x\) |
Imaginary part of analytic signal (§6) |
|
| \(z\) |
Distance along the z-axis (the optical axis) |
|
| \(z\) |
Analytic signal (§6) |
|
| \(X\) |
Fourier transform of analytic signal \(Z\) (§6) |
|
| \(Z_0\) |
Characteristic impedance (Table §3.1) |
|
| \(\alpha,\beta,\gamma\) |
Direction cosines of wavenumber vector (§4.2.2) |
|
| \(\alpha\) |
Instantaneous phase of complex degree of coherence \(\gamma\) (§8) |
|
| \(\alpha\) |
Total absorption (\(=k_i\)) (§10, §B) |
|
| \(\alpha\) |
Gaussian shape factor (§12.5.3) |
|
| \(\alpha'\) |
Phase-velocity absorption (§B) |
|
| \(\alpha”\) |
Group-velocity absorption (§10, §B) |
|
| \(\mathit{\alpha}\) |
Absorption coefficient (§8.4.2) |
|
| \(\beta\) |
Total dispersion (\(=k_r\)) (§10, §B) |
|
| \(\beta'\) |
Phase-velocity absorption (§10, §B) |
|
| \(\beta”\) |
Group-velocity dispersion (§10, §11, §12, §B) |
|
| \(\gamma\) |
Frequency deviation (§6.5.3) |
|
| \(\gamma\) |
Mutual coherence function (§8) |
|
| \(\gamma_{ii} \) |
Self-coherence function of input signal (§9.5) |
|
| \(\gamma_{oo} \) |
Self-coherence function of output signal (§9.5) |
|
| \(\gamma_{io} \) |
Coherence function between input and output signals (§9.5) |
|
| \(\Gamma\) |
Complex degree of coherence (§8, §9.5) |
|
| \(\delta\) |
Dirac delta function |
|
| \(\delta\) |
Linear phase of coherence function (§8) |
|
| \(\delta_{nm}\) |
Kronecker delta |
|
| \(\Delta f\) |
Spectral bandwidth of narrowband signal |
|
| \(\Delta f, \Delta f_{beat}\) |
Frequency spacing between beating tones (§F) |
|
| \(\Delta f, \Delta f_{oct}\) |
Octave stretch in cents (§15.10.1, §F) |
|
| \(\Delta f'\) |
Iterated octave stretch in cents (§15.10.1) |
|
| \(\Delta f_h\) |
Bandwidth of the time-lens phase modulation in humans (§11.6.4) |
|
| \(\Delta k\) |
Wavenumber difference between beating components (§3.2.1) |
|
| \(\Delta l\) |
Coherence length (§8.2.4) |
|
| \(\Delta n\) |
Path change in index of refraction (§11.6.1) |
|
| \(\Delta t\) |
Deviation from complex tone standard (§15.11.1) |
|
| \(\Delta t_{opt}\) |
Optimal ratio between geometrical and dispersive blurs (Table §12.2, §13.2.2) |
|
| \(\Delta \tau\) |
Coherence time |
|
| \(\Delta \omega\) |
Frequency difference between beating components (§3.2.1) |
|
| \(\Delta \omega\) |
Bandwidth of narrowband signal |
|
| \(\Delta \omega\) |
Phase ramp (§6.3) |
|
| \(\Delta \omega\) |
Phase ramp (§6.3) |
|
| \(\dot{\omega}\) |
Frequency velocity (§6.3) |
|
| \(\ddot{\omega}\) |
Frequency acceleration (§6.3) |
|
| \(\epsilon\) |
Dielectric constant (permittivity) (Table §3.1) |
|
| \(\epsilon_0\) |
Dielectric constant in vacuum (permittivity) (Table §3.1) |
|
| \(\zeta\) |
z-axis coordinate in the traveling pulse coordinate system (§10,§11, §12.2) |
|
| \(\zeta\) |
Damping factor (Figure §9.3) |
|
| \(\eta\) |
Displacement function (§3.3.1) |
|
| \(\eta\) |
Mask coordinate (§4.2.2) |
|
| \(\theta\) |
Azimuth (Table §3.1) |
|
| \(\theta\) |
Angle from optical axis (§4) |
|
| \(\theta_{min}\) |
Angular resolution (§4.2.2) |
|
| \(\kappa\) |
Adiabatic compressibility (Table §3.1) |
|
| \(\lambda\) |
Wavelength |
|
| \(\Lambda\) |
Triangle function |
|
| \(\lambda_n\) |
Eigenvalue (§8.2.6) |
|
| \(\mu\) |
Magnetic permeability (Table §3.1) |
|
| \(\mu\) |
Spectral degree of coherence (§8) |
|
| \(\mu_0\) |
Magnetic permeability in vacuum (Table §3.1) |
|
| \(\xi\) |
Mask coordinate (§4.2.2) |
|
| \(\rho\) |
Fluid density (Table §3.1) |
|
| \(\rho_{BM}\) |
Basilar membrane density per unit length (§11.6.1) |
|
| \(\sigma\) |
Multiplicative factor (§12.4.2, §F) |
|
| \(\tau\) |
Time lag |
|
| \(\tau\) |
Time coordinate in the traveling pulse coordinate system, group delay |
|
| \(\tilde\tau_0 \) |
Reduced coordinate of the object time (§13.2.1) |
|
| \(\tau_0\) |
Initial time of pulse in the traveling pulse coordinate system |
|
| \(\tau_1,\tau_2\) |
Time constants (Figure §9.3) |
|
| \(\tau_e\) |
Effective duration (§8.3.2, §A) |
|
| \(\tau_g\) |
Group delay |
|
| \(\tau_p\) |
Phase delay |
|
| \(\varphi\) |
Phase function (time domain) |
|
| \(\phi\) |
Phase function (frequency domain) |
|
| \(\phi\) |
Elevation (Table §3.1) |
|
| \(\phi_e\) |
Phase error (§9.3) |
|
| \(\phi_n\) |
Schroeder phase for component \(n\) (§12.4.1) |
|
| \(\phi_{\Delta f/2}\) |
Time-lens phase at the cutoff frequencies of \(Q_{10}\) (§11.6.4) |
|
| \(\psi\) |
Field function (§3.2.1) |
|
| \(\Psi\) |
Eigenfunction (§3.3.1, §8.2.6) |
|
| \(\omega\) |
Angular frequency; Modulation frequency |
|
| \(\bar{\omega}\) |
First moment of frequency (§8) |
|
| \(\Omega\) |
Integration domain including radiating source and receivers (§8.2.6) |
|
| \(\omega_c\) |
Carrier angular frequency |
|
| \(\omega_{coh}\) |
Coherent amplitude transfer function cutoff frequency (Gaussian pupil) (§13) |
|
| \(\omega_{coh,r}\) |
Coherent amplitude transfer function cutoff frequency (rectangular pupil) (§13) |
|
| \(\omega_H\) |
Hold-in range (§9.3) |
|
| \(\omega_{inc}\) |
Incoherent modulation transfer function cutoff frequency (Gaussian pupil) (§13) |
|
| \(\omega_L\) |
Lock range (§9.3) |
|
| \(\omega_m\) |
Modulation angular frequency |
|
| \(\omega_O\) |
Pull-out range (§9.3) |
|
| \(\omega_P\) |
Pull-in range (§9.3) |
)