Discrete systems in series and parallel

Discrete systems in series

Let as say that we have two discrete systems and their impulse responses are h1(n) and h2(n). Then when these discrete systems are connected in series, then overall impulse response:

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Where:

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As you noticed there were changing made:

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This is nothing more than convolution of impulse responses of both discrete systems:

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Discrete systems in parallel

If we have two discrete systems connected in parallel:

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As we see there is simple sum of output queues of each discrete system. So we can assume, that overall impulse response is as sum of systems connected in parallel:

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