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barcode lib ssrs 1J.6 Signal Manipulations in Software
1J.6 Signal Manipulations Decoding Code 128B In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Generating Code128 In None Using Barcode encoder for Software Control to generate, create Code 128 Code Set B image in Software applications. In our study of discretetime signals and systems we will be concerned with the manipulation of signals. These manipulations are generally compositions of a few basic signal transformations. These transformations may be classified either as those that are transformations of the independent variable n or those that are transformations of the amplitude of x ( n ) (i.e., the dependent variable). In the following two subsections we will look briefly at these two classes of transformations and list those that are most commonly found in applications. Code 128B Scanner In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Code 128B Generator In C# Using Barcode generation for .NET Control to generate, create Code128 image in Visual Studio .NET applications. sequence that is conjugate symmetric is sometimes said to be hermitian.
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Making Code 128B In VB.NET Using Barcode printer for VS .NET Control to generate, create USS Code 128 image in Visual Studio .NET applications. Code 128A Printer In None Using Barcode drawer for Software Control to generate, create Code 128A image in Software applications. SIGNALS AND SYSTEMS
Paint UPC A In None Using Barcode creator for Software Control to generate, create UCC  12 image in Software applications. Making Data Matrix ECC200 In None Using Barcode generator for Software Control to generate, create ECC200 image in Software applications. Transformations of the Independent Variable
Drawing European Article Number 13 In None Using Barcode generator for Software Control to generate, create EAN13 image in Software applications. Generate Barcode In None Using Barcode printer for Software Control to generate, create barcode image in Software applications. Sequences are often altered and manipulated by modifying the index n as follows: Generating USPS PLANET Barcode In None Using Barcode drawer for Software Control to generate, create USPS Confirm Service Barcode image in Software applications. GS1  12 Creation In None Using Barcode encoder for Microsoft Excel Control to generate, create UCC  12 image in Office Excel applications. where f (n) is some function of n. If, for some value of n, f (n) is not an integer, y(n) = x( f (n)) is undefined. Determining the effect of modifying the index n may always be accomplished using a simple tabular approach of listing, for each value of n, the value of f (n) and then setting y(n) = x( f (n)). However, for many index transformations this is not necessary, and the sequence may be determined or plotted directly. The most common transformations include shifting, reversal, and scaling, which are defined below. EAN / UCC  14 Creation In None Using Barcode drawer for Excel Control to generate, create UCC128 image in Office Excel applications. Painting UPC  13 In None Using Barcode printer for Microsoft Excel Control to generate, create EAN13 image in Office Excel applications. Shifting This is the transformation defined by f (n) = n  no. If y(n) = x(n  no), x(n) is shifted to the right by no samples if no is positive (this is referred to as a delay), and it is shifted to the left by no UPCA Printer In Visual Basic .NET Using Barcode drawer for .NET Control to generate, create GTIN  12 image in Visual Studio .NET applications. Make Barcode In Java Using Barcode maker for Java Control to generate, create barcode image in Java applications. samples if no is negative (referred to as an advance). Barcode Reader In C# Using Barcode scanner for .NET Control to read, scan read, scan image in Visual Studio .NET applications. EAN 128 Generation In None Using Barcode maker for Online Control to generate, create GS1 128 image in Online applications. Reversal This transformation is given by f (n) =  n and simply involves "flipping" the signal x(n) with respect to the index n.
Time Scaling This transformation is defined by f (n) = Mn or f (n) = n/ N where M and N are positive integers. In the case of f (n) = Mn, the sequence x(Mn) is formed by taking every Mth sample of x(n) (this operation is known as downsampling). With f (n) = n / N the sequence y(n) = x ( f (n)) is defined as follows: otherwise
(this operation is known as upsampling). Examples of shifting, reversing, and time scaling a signal are illustrated in Fig. 12. (a) A discretetime signal.
( h ) A delay by no = 2.
(c)Time reversal.
2 1 ;;;, 2 1 ;(;/2; 1 2 3 4 (d) Downsampling by a factor of 2.
(e) Upsampling by a factor of 2.
Fig. 12. Illustration of the operations of shifting, reversal, and scaling of the independent variable n. 5 6 7 8 9 SlGNALS AND SYSTEMS
[CHAP. 1
Shifting, reversal, and timescaling operations are orderdependent. Therefore, one needs to be careful in evaluating compositions of these operations. For example, Fig. 13 shows two systems, one that consists of a delay followed by a reversal and one that is a reversal followed by a delay. As indicated. the outputs of these two systems are not the same. x(n) Trio
x ( n  no) x (  n  no) ( a )A delay Tn,followed by a timereversal Tr .
x(n) x(n) x(n
+ no) (b)A timereversal Tr followed by a delay T",, Fig. 13. Example illustrating that the operations of delay and reversal do
not commute.
Addition, Multiplication, and Scaling
The most common types of amplitude transformations are addition, multiplication, and scaling. Performing these operations is straightforward and involves only pointwise operations on the signal. Addition The sum of two signals
is formed by the pointwise addition of the signal values.
Multiplication The multiplication of two signals
is formed by the pointwise product of the signal values.
Scaling Amplitude scaling of a signal x ( n ) by a constant c is accomplished by multiplying every signal value by c: y(n)=cx(n) oo<n<oo
This operation may also be considered to be the product of two signals, x ( n ) and f ( n ) = c.
1.2.7 Signal Decomposition
The unit sample may be used to decompose an arbitrary signal x ( n ) into a sum of weighted and shifted unit samples as follows: This decomposition may be written concisely as
where each term in the sum, x(k)S(n  k ) , is a signal that has an amplitude of x ( k ) at time n = k and a value of zero for all other values of n . This decomposition is the discrete version of the svting property for continuoustime signals and is used in the derivation of the convolution sum.

