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In this paper, a specific application of cepstral processing is considered to illustrate homomorphic signal processing. In particular, an analytic expression is derived for the frequency domain representation of a signal that has been recovered from a multi-path signal with cepstral processing. The multi-path signal is composed of time-delayed, scaled versions of the transmitted signal, and the transmitted signal is to be recovered. The recovered signal is expressed analytically in the frequency domain. By truncating an infinite series, the recovered signal can be expressed in the time domain. The analytic expressions can be used to predict the distortion that will result in the recovered signal when the cepstral processing is implemented with Discrete Fourier Transforms (DFTs). The analytic expression of a recovered signal is compared with the signal recovered with DFTs. The signal recovery from a multi-path signal that is composed of the transmitted signal and an amplified version of the transmitted signal is discussed and considered in two examples. The examples also demonstrate the scaling of nonminimum phase signals to minimum phase signals.

Students often complain that the rules of mathematics are being changed. A short conversation between a professor and a class of college algebra students dramatizes this in the realm of complex numbers and the legal realm of speed limits.

The article focuses on Rubik's Slide, a new electronic puzzle game. It informs that in the game player have to transform a given initial state of the cube into a given final state in limited moves. It discusses the solution of the game's different modes including Hard, Medium and easy, based on permutation and combinations.