Bilinear Transform - Example

Example

As an example take a simple low-pass RC filter. This continuous-time filter has a transfer function

\begin{align} H_a(s) &= \frac{1/sC}{R+1/sC} \\ &= \frac{1}{1 + RC s}. \end{align}

If we wish to implement this filter as a digital filter, we can apply the bilinear transform by substituting for the formula above; after some reworking, we get the following filter representation:

The coefficients of the denominator are the 'feed-backward' coefficients and the coefficients of the numerator are the 'feed-forward' coefficients used to implement a real-time digital filter.

Read more about this topic:  Bilinear Transform

Famous quotes containing the word example:

    “Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
    —Marcel Proust (1871–1922)