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ssrs 2d barcode with the secondorder system function given by in Software
with the secondorder system function given by Recognizing Code 128 Code Set B In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code128 Generation In None Using Barcode creator for Software Control to generate, create Code 128 Code Set C image in Software applications. and the firstorder system function
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Generate Code 128A In None Using Barcode maker for Online Control to generate, create Code 128C image in Online applications. Creating Barcode In ObjectiveC Using Barcode printer for iPhone Control to generate, create barcode image in iPhone applications. In implementing a discretetime system in hardware or software, it is important to consider the finite wordlength o effects. For example, if a tilter is L be implemented on a tixedpoint processor, the filter coefficients must be quantized lo a finite number of bits. This will change the frequency response characteristics of the filter. In this section, we look at the finite precision effects in digital tilter implementations. USS Code 128 Maker In Java Using Barcode printer for Java Control to generate, create Code 128 image in Java applications. Print Code 128 Code Set A In Java Using Barcode creator for Java Control to generate, create USS Code 128 image in Java applications. 8.6.1 Binary Representation of Numbers
There are two basic systems for representing numbers in a digital system: fixed point and floating point. There is a tradeoff in which type of representation to use. The dynamic range that is available in a floatingpoint representation IS much larger than with fixedpoint numbers. However, fixedpoint processors are typically faster and less expensive. Below, we briefly describe these number representations. Fixed Point
In the binary representation of a real number, x, using B I bits, there are three commonly used formats: sign magnitude, one's complement. and two's complement, with two's complement being the most common. In these systems, the only difference is in the way that negative numbers are represented. S g magnitude: With a signmagni~ude in format, a number x is represented as
where X,, is an arbitrary scale factor and where each of the bits hi are either 0 or 1. Thus, ho is the sign bit, and the remaining bits represent the magnitude of the fractional number. Bit h l is called the most sign$canr bit (MSB). hB is called the leusr significant bit (LSB). For example, with X = 1, and ,  ,y = 0.8125 = 1.1 1010 CHAP. 81
IMPLEMENTATION OF DISCRETETIME SYSTEMS
One's complement: In one's complement form, a negative number is represented by complementing all of the bits in the binary representation of the positive number. For example, with X,, = I and x = 0.8125 = 0.1 1010, X = 0.8125 = 0.11010 = 1.00101 Two's conzplement: With a two's complement format, a real number x is represented as Thus, negatlve numbers are formed by complementing the bits of the positive number and adding I to the least significant bit. For example, with X , = I, the two's complement representation of .r = 0.8125 is x = 0.8125 =0.I1010+0.00001 = 1.00110 Note that with B + I bits, the smallest difference between two quantized numbers, the resolution, is
5 x < X,, and all quantized numbers lie on the range X,, Floating Point
For a word length of B I bits in a fixedpoint number system, the resolution is constant over the entire range of numbers, and the resolution decreases ( A increases) in direct proportion to the dynamic range, 2X,,. A floatingpoint number system covers a larger range of numbers at the expense of an overall decrease in resolution, with the resolution varying over the entire range of numbers. The representation used for floatingpoint numbers is typically of the form x = M ,2E where M, the mantissa, is a signed BMbit fractional binary number with 5 I M I < I . and E , the exponent, is a BEbit signed integer. Because M is a signed fraction, it may be represented using any of the representations described above for fixedpoint numbers. Quantization Errors in FixedPoint Number Systems
In performing computations within a fixed or floatingpoint digital processor, it is necessary to quantize numbers by either truncation or rounding from some level of precision to a lower level. For example, because multiplying two 16bit fixedpoint numbers will produce a product with up to 3 1 bits of precision, the product will generally need to be quantized back to 16 bits. Truncation and rounding introduce a quantization error where x is the number to be quantized and Q[.Y]is the quantized number. The characteristics of the error depend upon the number representation that is used. Truncating numbers that are represented in signmagnitude form result in a quantization error that is negative for positive numbers and positive for negative numbers. Thus, the quantization error is symmetric about zero and falls in the range

