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Discrete systems in series and parallel

2017-12-23 12:46  
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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:

image003.gif

image002.gif

image005.gif

Where:

image007.gif

As you noticed there were changing made:

image009.gif

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

image011.gif

Discrete systems in parallel

If we have two discrete systems connected in parallel:

image012.gif

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:

image014.gif


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