This record provides estimates of the impact of a shock Soviet assault at the strive against strength of the Strategic Air Command. It discusses the effectiveness and value of numerous protecting measures and recommends implementation of a couple of quite reasonably cheap measures.
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Note how the output response sequences is longer than the input. In this example the input sequence extends over a period of time equal to 3 sample intervals, and the unit sample response sequence over 2 sample intervals. As a result, the output sequence extends over 3 + 2 = 5 sample intervals. A mathematical expression for this process, known as convolution, follows immediately from the figure. Denoting the system's unit sample response by h{n) = h O 9 h l 9 h 2 9 . . Signals and systems 52 output input 1 •I • .
The other parts of thefigureillustrate what happens as the width of the pulse is decreased, keeping its area or strength constant at x units. In the limit of a very short input pulse, the system response is independent of the precise pulse shape or duration and is characteristic of the system alone: only the strength of the impulse affects the output, scaling it linearly. Such an indefinitely short pulse was introduced earlier as one of our standard models - it is the delta function or impulse d(t).
The message signal can therefore be recovered simply by passing the impulse waveform through a lowpass filter which passes all components up to / B unchanged, and completely removes the highfrequency replicas. Suppose now that the sampling frequency is (a) increased and (b) decreased. The effect on the sampled spectrum is shown in Fig. 35. Increasing the sampling frequency as in part (a) simply increases the spacing between the replicas of the message signal; lowpass filtering will still recover the original.