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barcode generator for ssrs CHAP. 31 in Software
CHAP. 31 Read ANSI/AIM Code 128 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Encode Code 128 In None Using Barcode creator for Software Control to generate, create Code128 image in Software applications. will be bounded by
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With rounding, the quantization noise is uniformly distributed over the interval [A/2, A/2], and the quantization noise power (the variance) is ,, .: 12 = With a step size
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[CHAP. 3
: , and a signal power the signaltoquantization noise ratio, in decibels (dB), is
Thus, the signaltoquantization noise ratio increases approximately 6 dB for each bit. The output of the quantizer is sent to an encoder,which assigns a unique binary number (codeword) to each quantization level. Any assignment of codewords to levels may be used, and many coding schemes exist. Most digital signal processing systems use the two'scomplement representation. In this system, with a (B 1) bit codeword, c = [bo, l ,. . . , b B ] h the leftmost or most significant bit, bo, is the sign bit, and the remaining bits are used to represent either binary integers or fractions. Assuming binary fractions, the codeword bobl . . . bs has the value b2 An example is given below for a 3bit codeword.
Binary Symbol
Numeric Value
3.3 DIGITALTOANALOG CONVERSION
As stated in the sampling theorem, if x,(t) is strictly bandlimited so that Xa(jSZ) = 0 for I 2 > no, if s1 and T, < T /QO,then x a ( t )may be uniquely reconstructed from its samples x(n) = x,(nT,). The reconstruction process involves two steps, as illustrated in Fig. 36. First, the samples x(n)are converted into a sequence of impulses, and then x,(t) is filtered with a reconstructionfilter, which is an ideal lowpass filter that has a frequency response given by This system is called an ideal discretetocontinuous (DIC) converter. Because the impulse response of the reconstruction filter is CHAP. 31
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Fig. 36. (a) A discretetocontinuous converter with an ideal lowpass reconstruction filter. (h) The frequency response of the ideal reconstruction filter. the output of the filter is
xa(t) = n=00 t nTs)/TT C x(n)hAr  nTs) = C x(n)sin n ( nT,$)/Ts
n=m
This interpolation formula shows how x,(t) is reconstructed from its samples x(n) = x,(nTs). In the frequency domain, the interpolation formula becomes which is equivalent to
XAjW
T ~ X ( ~ J * ~ S ) I1 < n n
otherwise TS
Thus, x ( e i w )is frequency scaled (o= QTS), and then the lowpass filter removes all frequencies in the periodic above the cutoff frequency Q. = TIT,. , spectrum x(eiQTr) Because it is not possible to implement an ideal lowpass filter, many D/A converters use a zeroorder hold for the reconstruction filter. The impulse response of a zeroorder hold is OitlT, otherwise
ho(0 = and the frequency response is
After a sequence of samples xa(nT,)has been converted to impulses, the zeroorder hold produces the staircase approximation to xu(!)shown in Fig.37. With a zeroorder hold, it is common to postprocess the output with a reconstruction compensation filter that approximates the frequency response SAMPLING
[CHAP. 3
2T. T.
2. T 3. T 4. T 2T. T.
2. T 3. T 4. T Fig. 37. The use of a zeroorder hold to interpolate between the samples in x , ( t ) . so that the cascade of Ho(ejo) with H C ( e j w )approximates a lowpass filter with a gain of T, over the passband. Figure 38 shows the magnitude of the frequency response of the zeroorder hold and the magnitude of the frequency response of the ideal reconstruction compensation filter. Note that the cascade of H , ( j n ) with the zeroorder hold is an ideal lowpass filter.

