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Introduction to DSP - filtering: digital filter equation

Output from a digital filter is made up from previous inputs and previous outputs, using the operation of convolution: filter equation

Two convolutions are involved: one with the previous inputs, and one with the previous outputs. In each case the convolving function is called the filter coefficients.

The filter can be drawn as a block diagram:

Two convolutions are involved: one with the previous inputs, and one with the previous outputs. In each case the convolving function is called the filter coefficients.

The filter can be drawn as a block diagram:

The filter diagram can show what hardware elements will be required when implementing the filter:

Hardware elements required for implementing a filter

The left hand side of the diagram shows the direct path, involving previous inputs: the right hand side shows the feedback path, operating upon previous outputs.

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