By Yuriy Shmaliy

This booklet bargains a longer description of continuous-time signs regarding indications and structures. As a time-varying means of any actual nation of any item, which serves for illustration, detection, and transmission of messages, a contemporary electric sign possesses, in purposes, many particular houses. The textual content covers precept foundations of signs idea. providing bandlimited and analytic signs, the booklet studies the equipment in their description, transformation (by Hilbert transform), and sampling.

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34) 0 1 1 [δ(t + θ) + δ(t − θ)] = 2 2π = 1 π ∞ cos ωθejωt dω −∞ ∞ cos ωθ cos ωtdω . 36) −∞ where an auxiliary variable is z = t/2π, f0 is a regular shift frequency in Hz, and ω0 is an angular shift frequency in rad/s, ω0 = 2πf0 . , δ(f − f0 ) = 2πδ(ω − ω0 ). 3 Exponential Signal The following exponential models are used in signals descriptions. 38) is basic in the complex (symbolic) harmonic presentation of signals. It is usually associated with Euler’s7 formula x(t) = ejω0 t = cos ω0 t + j sin ω0 t .

2. In communications, two modulated (by voice) signals are sent in the same direction at the same time. Can you impose some restrictions for these signals to avoid their interaction in time and space? 3. Why precise signals are needed for accurate positioning systems? Explain the necessity of using the coded signals in Fig. 5. 4 (Signals classification). Given the following signals: 1. x(t) = A0 cos(ω0 t + ϕ0 ) 2. x(t) = A(t) cos[ω0 t + ϕ(t)] 3. y(t) = Bz(t) ⎧ ⎪ ⎨ t, 4. 5, ⎪ ⎩ 0, t>0 t=0 t<0 44 1 Introduction 5.

Before continuing, it seems worth to outline the major features of signals and their transforms: • A deterministic signal is precisely described by analytical functions; a random signal is described in probabilistic terms. • All real physical signals are causal and the mathematical signals may be noncausal. • A periodic signal reiterates its values periodically through some time nT ; a nonperiodic signal exists uniquely over all the time range. • A scalar signal is 1-D being represented in the time domain by the only function; a vector signal is multidimensional being combined with an assemblage of scalar signals.

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