This article presents an original algorithm operating in the frequency domain for estimating the affine transformation between a pair of images. The affine matrix is estimated by the relationships between companion stretched slices of the Fourier transforms magnitudes of the two images. The translational vector is estimated by phase-correlation after compensating for the contribution of the affine matrix. This approach is "global" in the sense that it uses the whole images information and it does not rest upon features extraction and matching. It can be efficiently implemented via FFT and it is suited to unsupervised estimation of affine transformations. Experimental evidence of the effectiveness and robustness of the proposed method is reported.

A method for designing a finite automaton whose output exhibits a given rational power spectral density R(z) belonging to a particular class, is presented. If the automaton input is composed of independent and identically distributed symbols, its state process is a homogeneous Markov chain whose transition probability matrix pi may by obtained from the input probability mass function and the state transition function. Since the poles of R(z) only depend on pi whereas its zeros depend on the matrix A specifying the output function, a matrix pi with the desired eigenvalues (and perhaps additional ones) is first derived and, the matrix A is determined so as to ensure the realization of the desired zeros (as well as the cancellation of the additional poles possibly introduced in the first step). The method exploits the properties of circulant matrices; in particular, a sufficient condition is provided under which a circular matrix with given eigenvalues (ordered in a Hermitian sequence) is stochastic.>

Codes whose spectral density and its lower order derivatives vanish at zero frequency are investigated, and necessary and sufficient conditions for the spectral properties are given. In particular, for the most common balanced alphabets, a complete characterization is furnished for the class of symbol-by-symbol codes with vanishing spectrum and second derivative. The fundamental results are extended to block codes, and suitable criteria for their design are given. Specific examples of binary and ternary block codes are presented; their performance in terms of low power content at low frequencies compares advantageously with that of some conventional codes.>

A method is proposed for launching and extracting the timing wave in a PAM digital transmission system, which combines the simplicity of linear self-timing, the economy in bandwidth of nonlinear self-timing, and the high performance of the added timing wave approach. The method requires that the digital signal is cyclostationary with a period which is an even multiple of the symbol periodT; the simplest solution for deriving such a signal from a stationary message is to apply it to a periodically time-varying system, as a memoryless block coder. With reference to such a scheme we derive the spectrum of the timing jitter. Very simple conditions are found on block encoding in order that the encoded message exhibits the desired characteristics. Finally, ternary codes are discussed and the performance of a specific code is evaluated and compared to that of conventional extraction schemes.