 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
ssrs 2d barcode where in Software
where Code 128C Decoder In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code 128 Printer In None Using Barcode creation for Software Control to generate, create Code128 image in Software applications. A =~ , , 2  ~
Decoding Code 128A In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. USS Code 128 Creation In C#.NET Using Barcode maker for Visual Studio .NET Control to generate, create Code 128 Code Set C image in VS .NET applications. On the other hand, for a two's complement representation, the truncation error is always negative and falls in the range A(e(O Paint Code 128 Code Set C In .NET Using Barcode drawer for ASP.NET Control to generate, create Code 128 image in ASP.NET applications. Code128 Maker In Visual Studio .NET Using Barcode creator for Visual Studio .NET Control to generate, create Code 128C image in Visual Studio .NET applications. IMPLEMENTATION OF DISCRETETIME SYSTEMS
Code 128 Code Set A Generator In VB.NET Using Barcode maker for .NET Control to generate, create Code 128 Code Set B image in .NET applications. Data Matrix 2d Barcode Drawer In None Using Barcode printer for Software Control to generate, create Data Matrix image in Software applications. [CHAP. 8
Make Barcode In None Using Barcode drawer for Software Control to generate, create bar code image in Software applications. Encoding GTIN  128 In None Using Barcode drawer for Software Control to generate, create UCC  12 image in Software applications. With rounding, the quantization error is independent of the type of fixedpoint representation and falls in the range Paint Code39 In None Using Barcode maker for Software Control to generate, create Code 39 Extended image in Software applications. Creating Code128 In None Using Barcode generation for Software Control to generate, create Code 128B image in Software applications. For floatingpoint numbers. the mantissa is either rounded or truncated, and the size of the error depends on the value of the exponent. Identcode Maker In None Using Barcode creation for Software Control to generate, create Identcode image in Software applications. Print 1D Barcode In .NET Using Barcode creation for .NET Control to generate, create 1D image in VS .NET applications. 8.6.2 Quantization of Filter Coefficients
Print Code 128 Code Set A In Java Using Barcode drawer for Android Control to generate, create Code128 image in Android applications. Bar Code Creator In Java Using Barcode maker for Java Control to generate, create barcode image in Java applications. In order to implement a filter on a digital processor. the filter coefficients must be converted into binary form. This conversion leads to movements in the pole and zero locations and a change in the frequency response of the filter. The accuracy with which the filter coefficients can be specified depends upon the word length of the processor, and the sensitivity of the filter to coefficient quantization depends on the structure of the filter, as well as on the locations of the poles and zeros. For a secondorder section with poles at z = r e f J e , Code39 Maker In Java Using Barcode encoder for Eclipse BIRT Control to generate, create Code39 image in BIRT reports applications. Draw Bar Code In Visual Basic .NET Using Barcode encoder for VS .NET Control to generate, create bar code image in .NET applications. the filter coefficients in a direct form realization are
Painting Code 39 Full ASCII In None Using Barcode generator for Font Control to generate, create Code 39 Extended image in Font applications. ANSI/AIM Code 128 Maker In Java Using Barcode generator for Java Control to generate, create Code128 image in Java applications. If a(1) and a(2) are quantized to B 1 bits, the real part of the pole location is restricted to 2B+' possible values, and the radius squared is restricted to 2 B values. The set of allowable pole locations for a bbit processor is shown in Fig. 8 16. Fig. 816. The set of allowable pole locations in the first quadrant 1 of the zplane for a secondorder 1 R filter implemented in direct form using a 4bit processor. A general sensitivity analysis of a pthorder polynomial
CHAP. 81
IMPLEMENTATION OF DISCRETETIME SYSTEMS
shows that the root locations are more sensitive to coefficient quantization errors when the roots are tightly clustered. For example, if the coefficients a(k) are quantized, then the sensitivity of the location of the ith pole to changes Aa(k) in the coefficients a(k) is approximately Aa(k) With
where
then
Thus, if the poles are tightly clustered, la;  njI is small, and small changes in a ( k )will result in large changes in the pole locations. The movement of the poles may be minimized by maximizing the distance between the poles, lai  a / 1 . This may be accomplished by implementing a highorder filter as a combination of first or secondorder &stems. For example, with a cascade of secondorder sections. each pair of complex conjugate poles and zeros may be realized separately, thereby localizing the coefficient quantization errors to each section. For an FIR filter, H (z) = h(n)zCn
when the coefficients are quantized, the system function becomes
Thus, the quantization errors may be modeled as H ( z ) in parallel with A H ( z ) as shown in Fig. 817. If we assume that the coefficients h(n)are less than I in magnitude, and that the coefficients are rounded to B 1 bits, Therefore, a loose bound on the error in the frequency response is
As with IIR filters, if the zeros are tightly clustered, the zero locations will be sensitive to coefficient quantization errors. However, FIR filters are commonly implemented in direct fonn for two reasons: 1. The zeros of FIR filters are not generally tightly clustered. 2. In direct form, linear phase is easily preserved. IMPLEMENTATION OF DISCRETETI ME SYSTEMS
[CHAP. 8
Fig. 817. filters.
Model for the coefticient quunliza~ion error in FIR
8.6.3 RoundOff Noise
Roundoff noise is introduced into a digital filter when products or sums of products are quantized. For example, if two ( B + I)bit numbers are multiplied, the producl is a ( 2 8 I)bit number. I f the product is to be saved in a ( B + I)bit register or used in a ( B + I)bit adder, it must be quantized to ( B I)bits, which results in the addition of roundqfnoiw. This roundoff noise propagates lhrough the filter and appears at the output of the of filter as roundoff noise. I n this section, we illustrate the analys~s roundoff noise effects by example. Consider the secondorder IIR filter ~mplementedin direct form I shown in Fig. 8lS(u). The difference equation For this network is If we assume that all numbers are represented by B I fixedpoint numbers and that the network uses ( B I)bit adders, each ( 2 R I)bit product must be quantized to B I bits by either truncation or rounding. Fig. 818(h) shows the quantizers explicitly. The difference equation corresponding to this system is the nonlinear equation If the quantizers are replaced with noise sources that are equal to the quantization error, we have an alternative representation shown in Fig. 818(c). This representation is particularly useful when it is assumed that the quantization noise has the following properties: Each quantization noise source is a w i d e  , ~ e nstationary white n o i s ~ s~ process. The probability distribution Function of each noise source is uniformly distributed over the quantization interval. 3. Each noise source is uncorrelated with the input to the quantizer. all other noise sources, and the input to the system. With B I bits, and a fractional representation for all numbers, the second property implies that the quantization noise for rounding has a zero mean and o variance equal to

