qr code vb.net library * Non-recursive lters are called nite impulse response lters, abbreviated FIR. in Visual Studio .NET

Creating Code-128 in Visual Studio .NET * Non-recursive lters are called nite impulse response lters, abbreviated FIR.

* Non-recursive lters are called nite impulse response lters, abbreviated FIR.
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CHAPTER 13 The Digital Processor
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which means that, FOR A GIVEN SAMPLING FREQUENCY !s and variable analog frequency !, the ratio r !=!s should not exceed the value of r 0:5 1=2. Thus the FREQUENCY RESPONSE of a digital lter generally needs to be calculated only over the range of r 0 to r 0:5. Example
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Show that the DT processor in Fig. 358 will serve as a low-pass lter.
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Fig. 358
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Solution Note that this is a non-recursive lter in which b0 1:0 and b1 1:0 (see lefthand side of Fig. 354 in section 13.8). Thus, upon substituting these values into eq. (608) we FIRST have that H z 1:0 z 1 Next, since we wish to nd the steady-state sinusoidal frequency response of the given processor, we now make the substitution z  j2r into the above H z . If we do this, changing the notation H z to H r and making use of Euler s formula, the above equation for H z becomes H r 1:0  j2r 1:0 cos 2r j sin 2r Thus H r is now in the rectangular form H r a jb jH r j=, where p jH r j a2 b2 and  arctan b=a 612 where, in this particular case, we have a 1:0 cos 2r and b sin 2r. Hence we have, here, by eq. (611), q p jH r j 1 cos 2r 2 sin2 2r 2 1 cos 2r in which we made use of the identity sin2 x cos2 x 1 (from problem 64), and also, by eq. (612),  arctan sin 2r= 1 cos 2r because arctan x arctan x. Note: Euler s formula, in the form  jx cos x j sin x, is valid for x in radians, where degrees (radians)(180/). Thus, if we wish to work in degrees, we would write sin 360r and cos 360r. It will be informative, now, to show graphically how jH r j and  change with changing values of r, for the case of Fig. 358. 610
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To do this we begin with the following table of values which, as you can verify, was found by making use of the above formulas for jH r j and .
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r 0.0 0.1 0.2 0.3 0.4 0.5 jH r j 2.00 1.90 1.62 1.18 0.62 0.00  0.00 18.00 36.00 54.00 72.00 90.00*
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The above results are shown graphically in Figs. 359 and 360.
Fig. 359
Fig. 360
First, Fig. 359 shows that, while the circuit of Fig. 358 is a basic form of low-pass lter, it is very broad in its action, not possessing the sharp cuto characteristic we generally would want such a lter to have. This is understandable, because Fig. 358 is the most basic type of low-pass digital lter. Next, Fig. 360 shows that the ratio of phase shift to frequency is constant, which means that the non-recursive (FIR) lter of Fig. 358 has constant time delay and thus produces no time-delay distortion (note 20 in Appendix). The fact that FIR lters have constant time delay is an advantage in certain applications. Another advantage of FIR lters is that they are always stable (because of the absence of feedback). Thus our ALGEBRA has let us to the fact that the OUTPUT of Fig. 358 depends upon the FREQUENCY ! of the ORIGINAL ANALOG SIGNAL; the details of WHY this happens can be explained as follows. Let us begin by recalling, with the aid of Fig. 361, the action of the UNIT DELAY circuit in Fig. 358. In Fig. 361, A represents the sampled value of an analog signal at a time t, while B is the same value as A but delayed T seconds from A, as shown. Thus timewise, at t T, the output of the time delay unit is the past value of the analog signal at time t.
* Direct substitution of r 1=2 into the equation for  gives  arctan 0=0 , where 0/0 has, itself, an indeterminate value. If, however, using your calculator, you successively nd the values of  for, say, r 0:496; 0:497; 0:498, and so on, it will be apparent that  approaches the limiting value of 90 for r 1=2.
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