Download Static And Dynamic Electricity by William R. Smythe PDF

By William R. Smythe

This booklet has hardback covers.Ex-library,With ordinary stamps and markings,In reasonable , compatible as a examine reproduction.

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3 21) + a) Figure 3-5 shows the phase of this differentiator for several values of a. Notice that a = 0 implies Euler's differentiation and a = 1 implies the impractical inverse trapezoidal differentiation. When a is larger, the phase is closer to the ideal 90°; unfortunately, the function is also more noisesensitive. Since the selection of a is noise dependent, it normally must be done on the working system. If you need to improve the response of Euler's differentiation, this is a simple and practical alternative.

For the filter of Equation 3 . 1 , if R(z) is the input and C(z) is the output, then TL) ( Z > - C { Z ) 2 3 9 1 ( Ζ + 1 } ... 5219 R(z) (34) [ ' 2. 5) 3. Divide both sides by the largest power of ζ that occurs on either side. 2391( 1 + or C ( z ) _ ° ^ C M . 6) 4. Transform to the time domain. This is done while recognizing that a factor of 1/z in the ζ domain implies that the time-domain signal is delayed by one sample. The expression 1/z indicates a delay of two cycles. For ex2 From Transfer Function to Algorithm 27 ample, C(z) transforms back to C„ and C(z)/z transforms to C - .

If an input is constructed of many frequencies, then those components below half the sample rate are unaffected and those above half the sample rate alias to lower frequencies. Figure 3-9 shows a second experiment to demonstrate aliasing. It re­ quires an oscilloscope, a signal generator, and a few common components. The resistors and capacitors set the 555 timer so that the digital switch Input frequency (T= sample period) Figure 3-8 Aliasing. Figure 3-9 Aliasing experiment. 3. The ζ Domain 42 samples the input approximately at 1 kHz for about 10 /is.

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