To determine which option is not suitable as either a low pass or a high pass filter, we need to understand the characteristics of each type of filter and the properties of the given options.


A low pass filter allows low-frequency signals to pass through while attenuating high-frequency signals. It is designed to pass signals below a certain cutoff frequency and attenuate signals above that frequency.


A high pass filter allows high-frequency signals to pass through while attenuating low-frequency signals. It is designed to pass signals above a certain cutoff frequency and attenuate signals below that frequency.


Let's analyze each option to determine its suitability as a low pass or high pass filter.

Option A - h(n) symmetric and M odd:
In this option, the filter coefficient sequence h(n) is symmetric, and the length M is odd. A symmetric filter has a frequency response that is even, meaning it allows both low and high-frequency signals to pass through. Therefore, this option can be suitable as both a low pass or a high pass filter.

Option B - h(n) symmetric and M even:
In this option, the filter coefficient sequence h(n) is symmetric, but the length M is even. A symmetric filter has a frequency response that is even, meaning it allows both low and high-frequency signals to pass through. However, the length M being even can introduce a nonzero response at the Nyquist frequency, which may not be desirable in some applications. Nevertheless, this option can still be suitable as both a low pass or a high pass filter.

Option C - h(n) anti-symmetric and M odd:
In this option, the filter coefficient sequence h(n) is anti-symmetric, and the length M is odd. An anti-symmetric filter has a frequency response that is odd, meaning it allows only high-frequency signals to pass through. It completely attenuates low-frequency signals. Therefore, this option is not suitable as either a low pass or a high pass filter.

Option D - h(n) anti-symmetric and M even:
In this option, the filter coefficient sequence h(n) is anti-symmetric, and the length M is even. An anti-symmetric filter has a frequency response that is odd, meaning it allows only high-frequency signals to pass through. It completely attenuates low-frequency signals. Therefore, this option can be suitable as a high pass filter.


Option C (h(n) anti-symmetric and M odd) is not suitable as either a low pass or a high pass filter because it completely attenuates both low and high-frequency signals.