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aliasing anomalies application approximation array assume attenuation autocorrelation function average band band-pass filters becomes component computation convolution theorem convolved corresponding cosine cross-correlation cut-off frequency cyclic convolution defined definition denotes determined deviation digital filters Dirac comb discrete distribution downward continuation energy signal equal equations error Example expected value factor finite formula Fourier coefficients Fourier series frequency domain function g(t Gaussian geophysical ghost given gives Hankel transform harmonic Hilbert transform ideal illustrated by Fig imaginary impulse response input integral interpolation inverse Fourier transform Let us consider linear low-pass filter magnetic mean square Mesko minimum-phase multiples normalized number of points Nyquist interval obtained original output pair parameters pass-band periodic functions properties pulse random variables rectangle recursive filter retrocorrelation sampling interval second derivative Section seismic sequence shift shown in Fig sine spectra taper transfer function transition band vertical wavelet weight function window z-transform zero