Answer:

The statement "The cutoff frequency of the low pass Butterworth filter is the arithmetic mean of the two cutoff frequencies" is true. In order to understand why this statement is true, let's break it down and explain it in detail.

What is a low pass Butterworth filter?
A Butterworth filter is a type of electronic filter that is designed to have a frequency response as flat as possible in the passband and a roll-off rate that is as gradual as possible in the stopband. A low pass Butterworth filter allows low-frequency signals to pass through while attenuating high-frequency signals.

Cutoff frequency of a low pass filter:
The cutoff frequency of a low pass filter is the frequency at which the filter starts to attenuate the input signal. It is commonly defined as the frequency at which the filter's gain is reduced to -3 dB (half power) compared to the passband gain.

Two cutoff frequencies:
In the context of the question, it is mentioned that there are two cutoff frequencies. It is not explicitly mentioned why there are two cutoff frequencies, but these could be the -3 dB frequencies for a specific passband gain or the -3 dB frequencies for the upper and lower stopbands.

Arithmetic mean:
The arithmetic mean is the average of two values. It is calculated by adding up the values and dividing the sum by 2. In the case of the cutoff frequencies, taking the arithmetic mean would involve adding up the two cutoff frequencies and dividing the sum by 2.

Explanation:
In a low pass Butterworth filter, the cutoff frequency is typically defined as the -3 dB frequency. The -3 dB frequency is the frequency at which the filter attenuates the input signal by half its power. In a Butterworth filter, the cutoff frequency is determined by the order of the filter and the desired roll-off rate.

For a low pass Butterworth filter, the cutoff frequency is the frequency at which the gain of the filter is reduced to -3 dB. This means that at the cutoff frequency, the power of the output signal is half the power of the input signal.

If there are two cutoff frequencies mentioned in the question, it is likely that these are the -3 dB frequencies for the upper and lower stopbands. In this case, the arithmetic mean of these two cutoff frequencies would give the overall cutoff frequency of the filter.

Taking the arithmetic mean of the two cutoff frequencies ensures that the overall cutoff frequency is somewhere between the upper and lower cutoff frequencies, providing a balanced cut-off point for the filter.

Therefore, the statement "The cutoff frequency of the low pass Butterworth filter is the arithmetic mean of the two cutoff frequencies" is true.