qr code vb.net source sin 360r  arctan 1 cos 360r in Visual Studio .NET

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sin 360r  arctan 1 cos 360r
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Now, using the last two equations, you can verify that the following table of values of magnitudes and phase angles versus r is correct. r 0.0 0.1 0.2 0.3 0.4 0.5 jH r j 0.00 0.62 1.18 1.62 1.90 2.00 8 90* 72 54 36 18 0
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* Arctan 1 908
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In graphical form these values appear as follows:
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Note that merely CHANGING THE SIGN of the multiplier b1 converted the LOW-PASS lter of Fig. 358 into the HIGH-PASS lter of Fig. 365. Also note that phase shift  is exactly proportional to analog frequency ! (r !=!s ), which is characteristic of non-recursive digital lters. 320. Note that the processor is of the non-recursive type, corresponding to the left-hand side of Fig. 354 in section 13.8. Hence the sinusoidal frequency response of the processor is found by setting z  j2pr in eq. (608), along with the given values of the b multiplier coe cients. Doing this, and setting 2pr 360r if you prefer to work in degrees instead of radians, eq. (608) becomes, after applying Euler s formula, H r 0:40 0:55 cos 360r 0:13 cos 2 360r 0:05 cos 3 360r 0:03 cos 4 360r j 0:55 sin 360r 0:13 sin 2 360r 0:05 sin 3 360r 0:03 sin 4 360r The rst step now is to substitute, into the above equation for H r , the value r 0; doing this, you should nd that H 0 1 j 0 1. Next substitute, into the above equation for H r , the value r 0:1; doing this, you should nd that, approximately, H 0:1 0:93 j 0:38. Continuing on in this way, for r 0:2, 0.3, 0.4, and 0.5, should give you the following table of values: jH r j 1.00 1.05 0.83 0.46 0.17 0.00
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r 0.0 0.1 0.2 0.3 0.4 0.5
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H r 1:00 j 0:00 0:93 j 0:38 0:50 j 0:66 0:08 j 0:45 0:00 j 0:17 0:00 j 0:00
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The nal step, now, is to plot the above values of jH r j, using either linear or semi-log graph paper (section 9.5). The result, for both types of paper, is shown as follows.
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321. Fig. 366 is a recursive lter in which a1 0, a2 0:25, b0 1:0, b1 0, b2 1, and upon substituting these values into eq. (606) we have that 1 z 2 z2 1 2 1 0:25z 2 z 0:25 p Setting z2 0:25 0 gives the poles, z 0:25 j 0:50, both of which lie inside the unit circle; hence the lter is stable, answer. H z Setting z  j360r in the above equation for H z , then applying Euler s formula, gives H r  j720r 1 1 cos 720r j sin 720r j720r 0:25 0:25 cos 720r j sin 720r 
(a) (b)
One way to proceed now is to rst rationalize the equation (section 6.3); doing this, then making use of the trigonometrical identity sin2 x cos2 x 1, you ll nd the above equation becomes H r 0:75 1 cos 720r j1:25 sin 720r 1:0625 0:5 cos 720r
Now substituting, into the above equation, the required values of r, you can verify the following table of values (rounded o , here, to two decimal places):
r 0.00 0.05 0.10 0.20 0.25 0.30 0.40 0.45 0.50
H r 0:00 j 0:00 0:10 j 0:50 0:43 j 1:00 2:06 j 1:12 2:67 j 0:00 2:06 j 1:12 0:43 j 1:00 0:10 j 0:50 0:00 j 0:00
jH r j 0:00 0.51 1.09 2.35 2.67 2.35 1.09 0.51 0.00
Figure 366 is thus a BAND-PASS type of digital lter
Absolute value, 402 Active device, 28 Adder, full, 353 Admittance, 167 Algebra, review, 401 404 Algebraic long division, 437 Alternating current (ac), 76 Ammeter, 30 Ampere, 15 Ampli er, de nition, 432 transistor, 432 Analog signal, 324 Arctan, notation, 101 Associative, 401
Commutative, 401 Comparators, 362 Conductance, 66 Conductor, 2 Constant-current generator, 70 Constant-k lter, 219 223 Constant-voltage generator, 69 Conventional current, 18 Conversion factors, 404 Conversions, pi to T, T to pi, 196 Coulomb, 8 Coulomb s law, 8 Cramer s rule, 54 Critical coupling, 247 Current, 15
Battery, 20, 21 Bilateral, 72 Binary arithmetic, 325 328 Binary signal, 324 bandwidth needs, 357 Boolean algebra, 338 347
Capacitive reactance, 161 Capacitors, capacitance, 144 148 series and parallel, 148 Characteristic impedance, 216 Coe cient of coupling, 229
Decibel, 203 De Moivre s theorem, 131 Determinants, 38 57 Dielectric constant, 145 Digital lters, 393 400 Direct current (dc), 31 Discrete-time (DT) processors, 377 383 introduction, 377 recursive, non-recursive, 379 stability, 383 structure, 378, 389 transfer function H z , 377, 382
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