By Moe R.E.
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14) to a timeinvariant discrete-time system [Bam92]. This is called lifting. If we introduce the processes uk (t) = u(t + kT ) for t ∈ [0, T ], then we ﬁnd ˆ k+ xk+1 = Ax T 0 Φ(t, τ)b(τ)uk (τ)dτ . 18). The properties of Here, xk = x(kT ) and A continuous-time LPTV systems can now be analyzed using time-invariant discrete-time techniques. 22). This requires the magnitude of all eigenvalues of A than one. This in turn is equivalent with the Floquet exponents —the eigenvalues of ˆ — having negative real parts.
As illustrated in Fig. 6, frequency translations are linear operations1 . They satisfy the principle of superposition, the basic requirement for linearity. Taking the sum of two frequency-shifted signals is equivalent with frequency shifting the sum of 1 This linearity is seldom stressed. g. a cosine, they are often thought of as nonlinear. This is a misconception that complicates the way we reason on these type of circuits. The key issue to observe is that one of the signals involved in the multiplication, the carrier, is known at the time when the circuit is implemented.
Therefore, we need techniques to create and manipulate models. This is where modeling and analysis come into play. Deﬁnition (Modeling and Analysis): Modeling and analysis concern the acts of creating, manipulating and interpreting models. e. models are considered a result of the operation. 1 MODELS, MODELING AND ANALYSIS models are just a means to gain the information necessary to make design decisions. Analysis involves interpreting models. The main difference between both concepts comes down to whether models are considered a result of the act or a means to obtain results.
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