Perhaps one of the more important application areas of digital signal processing (DSP) is the power spectral estimation of periodic and random signals. Speech recognition problems use spectrum analysis as a preliminary measurement to perform speech bandwidth reduction and further acoustic processing. Sonar systems use sophisticated spectrum analysis to locate submarines and surface vessels. Spe...

The spectral problem where the field satisfies Dirichlet conditions on one part of the boundary of the relevant domain and Neumann on the remainder is discussed. It is shown that there does not exist a classical asymptotic expansion for short time in terms of fractional powers of t with locally computable coefficients. MSC Classification: 58G25

S U M M A R Y Combining CHAMP satellite magnetic measurements with aeromagnetic and marine magnetic data, the global geomagnetic field has now been modelled to spherical harmonic degree 720. An important tool in field modelling is the geomagnetic power spectrum. It allows the comparison of field models estimated from different data sets and can be used to identify noise levels and systematic er...

We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost O(N logN), compared to the standard brute force approach which costs O(N). The procedure retains this speed on the full sky and for ill-conditioned matrices. It is applicable to galaxy power spectra, CMB, polarization and w...

The most commonly applied technique to obtain an estimated power spectrum ) ( ˆ f S of a sampled time series ) (t x of finite length N, is to compute the Fourier transform ) 2 ( f j X  , followed by multiplication by its complex conjugate and scaling by the length of the finite observation, i.e. N f j X f j X f S / ) 2 ( ) 2 ( ) ( ˆ *     (see Chapter 7 in van Drongelen, 2007). The reliabi...

The power spectrum of a zero-mean stationary Gaussian random process is assumed to be known except for one or more parameters which are to be estimated from an observation of the process during a finite time interval. The approximation is introduced that the coefficients of the Fourier series expansion of a realization of long-time duration are uncorrelated. Based on this approximation maximum ...