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Digital Signal Processing Using Matlab by André Quinquis

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2.1. Theoretical background

A signal is a physical support for information, depending on one or several independent variables, such as: time, range, temperature, pressure, etc. The signal concept generally refers to its mathematical or physical model, chosen in the most appropriate manner for describing the complexity of real signals.

According to whether a signal depends on only one variable or two variables, it is called one-dimensional (1D) or two-dimensional (2D). As a general rule, a multidimensional signal is defined as a function of several variables.

A discrete-time signal is represented by a digital series, uniformly or non-uniformly sampled. The first case is considered in the following and corresponds to a constant time delay between each two successive samples.

Usually, s(k) stands for the kth sample of the discrete-time signal {s(k)}k = 1, 2, .... However, the two notations usually overlap in order to simplify the theoretical presentation.

The signal theory is mainly related to the signal mathematical representation in the original or a transformed space, and to its algorithmic processing in order to extract the useful information.

2.1.1. Mathematical model of 1D and 2D discrete-time signals

The mathematical model of a discrete-time signal can be defined in terms of the function indicated below:

images

so that:

while, for 2D discrete-time signals n = (n1, n2) → x(n1, n2

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