By Michael J. Kroes, William Watkins, Frank Delp, Ronald Sterkenberg
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Extra resources for Aircraft Maintenance and Repair (7th Edition)
6 below, it is represented by a vertical line of height A at position x 0 . 11) [and h (0) = 1⁄ 2 ]. 12) −∞ and the ␦ -function is the derivative of the step function. 4(b)]. 4 rep and comb The rep operator produces a new function by repeating a function at regular intervals specified by its suffix. 13) The shifted waveforms p (t − nT ) may be overlapping. This will be the case if the duration of p is greater than the repetition interval T. 4 Step functions: (a) the unit step; (b) a scaled and shifted step.
18) where h is the step function. To investigate the form of the rounding this produces, we form the convolution of a (t ) with the rising edge, given by e (t ) = kt и h (t ). 19) For large t , the exponential term becomes small, and we see that the response approaches k (t − ), corresponding to a delay of applying to the pulse as whole (in addition to the rounding distortion), assuming is small compared with the pulse duration. 11 so that it starts, like the exponential impulse response, at time zero rather than at −T /2, then this rectangular ‘‘impulse response’’ causes a delay of T /2, so this pulse with length T = 2 will give the same delay and will be approximately equivalent.
These lower side lobes could be expected from the much smoother shape of this pulse, compared with the rectangular or triangular pulses, the highest side lobes of which are 13 dB and 27 dB below the peak, respectively. We note that the cost of lower side lobes is a broadening of the main lobe relative to the spectrum of the gating pulse of width 2T. 65 at the 4-dB points. 6 Rounded Pulses The step discontinuity of rectangular pulses is the cause of the poor spectrum, with high side lobes. This discontinuity in level is removed by generating rising and falling edges of finite slope.