To 10 Hz. Superimposed on this signal is 60-Hz noise with an amplitude of 0.1 V. It is desired to attenuate the 60-Hz signal to less than 10% of its value using a Butterworth filter. Select a filter order to perform this task if the corner frequency is 10 Hz.

If we square both sides we got:

We divide both sides by and we got:

Now we can apply log on both sides and we got:

And solving for n we got:

And replacing we got:

And since n needs to be an integer the correct answer would be n=2 for the filter order.

Explanation:

For this case we can use the formula for the Butterworth filter gain given by:

[tec] G = \frac{1}{\sqrt{1 +(\frac{f}{f_c})^{2n}}}[/tex]

Where:

G represent the transfer function and we want that G =0.1 since the desired signal is less than 10% of it's value

represent the corner frequency

represent the original frequency

n represent the filter order and that's the variable that we need to find

If we square both sides we got:

We divide both sides by and we got:

Now we can apply log on both sides and we got:

And solving for n we got:

And replacing we got:

And since n needs to be an integer the correct answer would be n=2 for the filter order.

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