By Benoit Boulet

ISBN-10: 1584503815

ISBN-13: 9781584503811

ISBN-10: 1584506601

ISBN-13: 9781584506607

This booklet is a self-contained creation to the speculation of signs and structures, which lies on the foundation of many components of electric and desktop engineering. within the seventy brief lectures formatted to facilitate self-learning and to supply effortless reference, the publication covers such themes as linear time-invariant (LTI) platforms, the Fourier remodel, the Laplace rework and its program to LTI differential platforms, state-space platforms, the z-transform, sign research utilizing MATLAB, and the appliance of rework options to verbal exchange structures. a wide range of applied sciences, together with suggestions keep an eye on, analog and discrete-time filters, modulation, and sampling structures are mentioned in reference to their foundation in signs and platforms idea. The accompanying CD-ROM comprises applets, resource code, pattern examinations, and routines with chosen strategies. good points: * presents 70 brief lectures to facilitate self-learning * Covers subject matters together with LTI structures, Fourier and Laplace transforms, sign research utilizing MATLAB, the z-transform, sampling platforms, suggestions regulate structures, IIR and FIR filters, and modulation for communique structures * contains a CD-ROM with applets, routines, code, figures, and chosen recommendations * info the speculation in the back of computing device and electric engineering; ideal for pros or scholars of indications and platforms

On the CD * LEARNWARE APPLETS (Discrete-time Convolution, Fourier sequence, Bode plot) * MATLAB SCRIPTS: MATLAB script records include sequences of MATLAB instructions that practice a wanted computation for an instance * bankruptcy FOLDERS: ideas to chose difficulties, MATLAB scripts, and all the figures from the ebook, prepared through bankruptcy * pattern checks: pattern midterm and fi nal examinations

SYSTEM necessities minimal: Pentium II notebook operating Microsoft home windows ninety eight; Microsoft web Explorer five or Netscape 7 browser with Java Plug-in 1.Recommended: Pentium four notebook working Microsoft home windows XP or home windows 2000; Microsoft web Explorer 6 or Netscape 7 browser with Java Plug-in 1.

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**Extra info for Fundamentals of signals and systems**

**Example text**

Linear? Yes. Let y1 (t ) := Sx1 (t ) = tx1 (t ), y2 (t ) := Sx2 (t ) = tx2 (t ) . Then, y (t ) = S [ ax1 (t ) + bx2 (t )] = t[ ax1 (t ) + bx2 (t )] = atx1 (t ) + btx2 (t ) = ay1 (t ) + by2 (t ) 4. Causal? Yes. The output at time t depends on the present value of the input only. 5. Stable? No. Consider the constant input x (t ) = B ¡ for any K , T such that y (T ) = TB > K , namely, T >> K ; that is, the output is unbounded. B (d) y[ n] = 0 ¨ x[ n k ] k =h Answer: 1. Memoryless? No. The output y[n] is computed using all future values of the input.

34. 34 Discrete-time unit impulse. 35. 35 step signal. 50) and conversely, the unit impulse is the first-difference of a unit step: I [ n] = u[ n] u[ n 1]. 51) Also, the unit step can be written as an infinite sum of time-delayed unit impulses: h u[ n] = ¨ I [ n k ]. 52) k =0 The sampling property of the unit impulse is an important property in the theory of sampling and in the calculation of convolutions, both of which are discussed in later chapters. The sampling property basically says that when a signal x[n] is multiplied by a unit impulse occurring at time n0, then the resulting signal is an impulse at that same time, but with an amplitude equal to the signal value at time n0: x[ n]I [ n n0 ] = x[ n0 ]I [ n n0 ].

No. The system has memory since at time t, it uses the past value of the input x (t 1) . 2. Time-invariant? Yes. y1 (t ) = Sx (t T ) = x (t T ) = y (t T ) . 1 + x (t 1 T ) Elementary Continuous-Time and Discrete-Time Signals and Systems 45 3. Linear? No. The system S is nonlinear since it does not have the superposition property: For x1 (t ), x2 (t ), let y1 (t ) = x1 (t ) x2 ( t ) , y2 ( t ) = 1 + x1 (t 1) 1 + x2 (t 1) Define x (t ) = ax1 (t ) + bx2 (t ). Then y (t ) = ax1 (t ) + bx2 (t ) ax1 (t ) bx2 (t ) | + = ay1 (t ) + by2 (t ) 1 + ax1 (t 1) + bx2 (t 1) 1 + x1 (t 1) 1 + x2 (t 1) 4.

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