FILTERS, SIGNALS, AND THEIR TRANSFORMS

The example x(t), x_t, X_k, X(Z), $X(\omega )$can be understood as follows. A lower-case letter with a function argument (t) denotes a continuous time function (rare). Lower case with a subscript denotes a signal or filter as a function of discrete time (common). Upper case with subscript denotes a discrete Fourier transform. Z-transforms are denoted by the function argument (Z). Where a function argument $\omega$ is occasionally seen, such as in $A(\omega )$,it is generally a shorthand for $A(Z=e^{i\omega})$.For a definition of the complex conjugate of filters, see page .

		 aA 		feedback filter (autoregression)
		 bB 		convolution filter
		 cC 		causal filter; reflected wave; cross-spectrum
		 dD 		downgoing wave
		 E 		escaping wave
		 fF 		component of layer matrix; force; generic function
		 gG 		component of layer matrix; analytic signal; causal garbage filter
		 hH 		admittance
		 I 		causal integration operator
		 JKLMO 		unused
		 N 		noise
		 pP 		phase shift; pressure; all-pass filter; generic input space
		 qQ 		quadrature filter; generic output space
		 rR 		impedance; reflection seismogram
		 sS 		S is spectrum; st is autocorrelation
		 T 		transmitted wave
		 uU 		upcoming wave; logarithm of S
		 vV 		velocity
		 W 		weighting function; vertical component of flow
		 xX 		generic input signal
		 yY 		generic output signal
		 $\phi \Phi$ 		phase