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A low pass filter with a cut-off frequency of 30 Hz is cascaded with a high pass filter with a cut off frequency of 20 Hz. The resultant system of filters function as

Question

A low pass filter with a cut-off frequency of 30 Hz is cascaded with a high pass filter with a cut off frequency of 20 Hz. The resultant system of filters function as

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Solution

The resultant system of filters functions as a bandpass filter.

Here's why:

  1. A low-pass filter allows signals with a frequency lower than a certain cutoff frequency to pass through and attenuates frequencies higher than the cutoff frequency. In this case, the cutoff frequency is 30 Hz, so all frequencies above 30 Hz are attenuated.

  2. A high-pass filter does the opposite. It allows signals with a frequency higher than a certain cutoff frequency to pass through and attenuates frequencies lower than the cutoff frequency. In this case, the cutoff frequency is 20 Hz, so all frequencies below 20 Hz are attenuated.

  3. When these two filters are cascaded, or connected in series, the output of the system is the intersection of the outputs of the two filters. This means that the system will allow signals with frequencies between 20 Hz and 30 Hz to pass through, while attenuating all other frequencies.

  4. This type of filter, which allows a certain range of frequencies to pass through while attenuating frequencies outside of this range, is known as a bandpass filter. Therefore, the resultant system of filters functions as a bandpass filter.

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