The Application of Discrete Time Convolution

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The Application of Discrete Time Convolution

Discrete time convolution can be used to determine the output of a
sampled data system from its input and pulse response. A
commonly used discrete system is a finite impulse response (FIR)
filter.

This tool presents you with a schematic of a FIR Filter. The boxes
marked

represent delay elements whose output is the previous value of
their input. Using the single step button you can observe the
input signal,

as its samples work their way through the delay elements.

There are a number of multiplication symbols in the filter with
weights, which are the system response, associated with them.The
product of these weights and the input signal samples are summed
together to give the output of the filter,

You can view the values at various points in the filter as
either a bar denoting the size of the value, by a number, or by
both means. The colours of the values or bars correspond to the
colours of the graphs. Observing both windows simultaneously,
the mechanism by which the convolution is performed can be seen.
The system response is coded in the multiplication weights, the
product of the input signal and the system response is
calculated at the output of the multipliers, and the final sum
is calculated by the summation unit driving the filter output.

Experiment with setting various system responses and signals
such as setting a single value of the input to 1 to convince
yourself that the system response values of the filter define
the unit pulse response of the filter.

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