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Total energy E and average power P on a perohm basis are in VS .NET
Total energy E and average power P on a perohm basis are Decode QR Code In VS .NET Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in VS .NET applications. Drawing QRCode In VS .NET Using Barcode encoder for Visual Studio .NET Control to generate, create QR Code 2d barcode image in .NET framework applications. i 2 ( t ) d t joules i 2 ( t ) dt watts
QRCode Scanner In Visual Studio .NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in VS .NET applications. Printing Bar Code In Visual Studio .NET Using Barcode encoder for .NET framework Control to generate, create barcode image in VS .NET applications. For an arbitrary continuoustime signal x(t), the normalized energy content E of x ( t ) is defined as Reading Barcode In .NET Framework Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications. QR Code 2d Barcode Creation In Visual C# Using Barcode generator for .NET framework Control to generate, create QR Code image in Visual Studio .NET applications. The normalized average power P of x ( t ) is defined as
Generate QR Code 2d Barcode In Visual Studio .NET Using Barcode generation for ASP.NET Control to generate, create QR Code image in ASP.NET applications. QR Code Creation In VB.NET Using Barcode creation for .NET framework Control to generate, create QR image in .NET applications. Similarly, for a discretetime signal x[n], the normalized energy content E of x[n] is defined as
Linear Printer In VS .NET Using Barcode maker for Visual Studio .NET Control to generate, create 1D image in Visual Studio .NET applications. Bar Code Encoder In Visual Studio .NET Using Barcode generation for .NET Control to generate, create barcode image in Visual Studio .NET applications. SIGNALS AND SYSTEMS
GS1128 Generator In .NET Framework Using Barcode drawer for .NET framework Control to generate, create UCC128 image in .NET framework applications. Code 93 Full ASCII Generation In .NET Framework Using Barcode printer for VS .NET Control to generate, create USD3 image in .NET applications. [CHAP. 1
EAN13 Creation In .NET Using Barcode drawer for ASP.NET Control to generate, create UPC  13 image in ASP.NET applications. Print Data Matrix 2d Barcode In Java Using Barcode creator for Android Control to generate, create Data Matrix ECC200 image in Android applications. The normalized average power P of x[n] is defined as 1 P = lim N +  2 N + 1 ,,= N Based on definitions (1.14) to (1.17), the following classes of signals are defined: 1. x(t) (or x[n]) is said to be an energy signal (or sequence) if and only if 0 < E < m, and so P = 0. 2. x(t) (or x[n]) is said to be a power signal (or sequence) if and only if 0 < P < m, thus implying that E = m. 3. Signals that satisfy neither property are referred to as neither energy signals nor power signals. Note that a periodic signal is a power signal if its energy content per period is finite, and then the average power of this signal need only be calculated over a period (Prob. 1.18). EAN / UCC  13 Drawer In Java Using Barcode generation for BIRT reports Control to generate, create European Article Number 13 image in BIRT reports applications. Recognizing Bar Code In .NET Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. 1.3 BASIC CONTINUOUSTIME SIGNALS
Make Code128 In Visual Basic .NET Using Barcode generator for Visual Studio .NET Control to generate, create Code128 image in .NET framework applications. Barcode Generator In Visual C#.NET Using Barcode creator for .NET framework Control to generate, create barcode image in Visual Studio .NET applications. A. The Unit Step Function: The unit step function u(t), also known as the Heaciside unit function, is defined as GS1  12 Recognizer In .NET Using Barcode recognizer for .NET Control to read, scan read, scan image in Visual Studio .NET applications. Generating UCC  12 In ObjectiveC Using Barcode printer for iPhone Control to generate, create UPCA Supplement 2 image in iPhone applications. which is shown in Fig. 14(a). Note that it is discontinuous at t = 0 and that the value at t = 0 is undefined. Similarly, the shifted unit step function u(t  to) is defined as which is shown in Fig. 14(b). Fig. 14 ( a ) Unit step function; ( b )shifted unit step function.
B. The Unit Impulse Function: The unit impulse function 6(t), also known as the Dirac delta function, plays a central role in system analysis. Traditionally, 6(t) is often defined as the limit of a suitably chosen conventional function having unity area over an infinitesimal time interval as shown in CHAP. 11
SIGNALS AND SYSTEMS
Fig. 15 Fig. 15 and possesses the following properties: But an ordinary function which is everywhere 0 except at a single point must have the integral 0 (in the Riemann integral sense). Thus, S(t) cannot be an ordinary function and mathematically it is defined by where 4 ( t ) is any regular function continuous at t An alternative definition of S(t) is given by
= 0. Note that Eq. (1.20) or (1.21) is a symbolic expression and should not be considered an ordinary Riemann integral. In this sense, S(t) is often called a generalized function and 4 ( t ) is known as a testing function. A different class of testing functions will define a different generalized function (Prob. 1.24). Similarly, the delayed delta function 6(t  I,) is defined by 4 ( t ) W  to) dt
=4Po) (1.22) where 4 ( t ) is any regular function continuous at t = to. For convenience, S(t) and 6 ( t  to) are depicted graphically as shown in Fig. 16. SIGNALS AND SYSTEMS
[CHAP. 1
Fig. 16 ( a ) Unit impulse function; ( b )shifted unit impulse function.
Some additional properties of S ( t ) are
S( t ) =S(t) x ( t ) S ( t ) = x(O)S(t) if x ( t ) is continuous at
t = 0. x ( t ) S ( t  t o ) = x ( t o ) 6 ( t t , ) if x ( t ) is continuous at t = to. Using Eqs. (1.22) and ( 1.241, any continuoustime signal x(t can be expressec Generalized Derivatives: If g( t ) is a generalized function, its nth generalized derivative g("Y t ) = dng(t )/dt " is defined by the following relation: where 4 ( t ) is a testing function which can be differentiated an arbitrary number of times and vanishes outside some fixed interval and @ " ' ( t ) is the nth derivative of 4(t).Thus, by Eqs. ( 1.28) and (1.20) the derivative of S( t ) can be defined as where 4 ( t ) is a testing function which is continuous at t = 0 and vanishes outside some fixed interval and $ ( 0 ) = d 4 ( t ) / d t l , = o . Using Eq. (1.28), the derivative of u ( t ) can be shown to be S ( t ) (Prob. 1.28); that is,

