Question

A Butterworth low pass filter is to be designed that has a maximum amount of attenuation in the passband of 3dB extending up to 9019Hz. The stopband should have a minimum amount of attenuation of 88.5dB from 45095Hz. Calculate the filter order needed to achieve this specification to 4 decimal places.

Answer 1

To calculate the filter order of a Butterworth low pass filter, use the formula Order = (log10(1 / (sqrt(power_ratio) - 1)) / (2 * log10(cutoff_frequency / stopband_frequency)). The filter order needed to achieve the specified attenuation is approximately 6.8918.

Step-by-step explanation:

To calculate the filter order needed to achieve the specified attenuation, we can use the formula:

Order = (log10(1 / (sqrt(power_ratio) - 1)) / (2 * log10(cutoff_frequency / stopband_frequency))

where power_ratio is the ratio of the maximum amount of attenuation in the passband to the minimum amount of attenuation in the stopband. In this case, power_ratio = 10(3/10) / 10-88.5/10) = 10283/10).

Using the given values, the filter order can be calculated to be approximately 6.8918 when rounded to 4 decimal