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Time and Frequency Domain Representation

Notation and basic equations Following the representation in [75], the notation and the basic equations are as follows. [Pg.39]

Continuous functions and signals in the time domain are denoted by lower case letters with the argument in parentheses, e.g. x(t). Sampling at constant intervals A t produces a discrete approximation x[n] to the continuous signal, defined at times f = n A t, n = 0,1,2. Square brackets are used for the arguments of discrete functions. The Fourier transform establishes the connection between the time and frequency domains [76]  [Pg.39]

Frequency domain functions are denoted by upper case letters. Of importance for the TDFRS experiment is the discrete Fourier transform of an array of N data points within a period of N At  [Pg.39]

The response y(t) of a linear system to an excitation x(t) is a convolution of x(t) with the response function h(t). The TDFRS experiments are performed with periodic boundary conditions and discrete sampling, asking for the discrete periodic convolution [Pg.39]

The convolution theorem reduces Eq. (57) to a simple product in frequency space Y = XH (58) [Pg.39]


To understand the basic concepts of modulation, we first review time- and frequency-domain representations of signals. The information present in m(t) can be completely specified by a complex function of speech amplitude vs. frequency, M f), obtained using the Fourier transform. Since M f) contains aU of the information in m t), it is possible to go back and forth between m t) and M f) using the forward and inverse Fourier transforms. [Pg.1369]


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