Symmetric h[n] with N even and Anti-symmetric h[n] with N odd, can notbe used for HPF design. Justify.

Symmetric h[n] with N even and Anti-symmetric h[n] with N odd cannot be used for HPF (High Pass Filter) design. This can be justified by considering the properties of these types of filters.

1. Symmetric h[n] with N even:

   • A symmetric filter has a symmetric impulse response, meaning that h[n] = h[N-n-1].
   • In a high pass filter, the impulse response should have alternating positive and negative values to attenuate the low-frequency components.
   • However, in a symmetric filter, the impulse response is symmetric around its midpoint, resulting in equal positive and negative values.
   • This symmetry prevents the filter from effectively attenuating the low-frequency components, making it unsuitable for HPF design.

2. Anti-symmetric h[n] with N odd:

   • An anti-symmetric filter has an anti-symmetric impulse response, meaning that h[n] = -h[N-n-1].
   • In a high pass filter, the impulse response should have alternating positive and negative values to attenuate the low-frequency components.
   • However, in an anti-symmetric filter, the impulse response is anti-symmetric around its midpoint, resulting in equal positive and negative values but with opposite signs.
   • This anti-symmetry also prevents the filter from effectively attenuating the low-frequency components, making it unsuitable for HPF design.

In summary, both symmetric h[n] with N even and anti-symmetric h[n] with N odd fail to meet the requirements of a high pass filter due to their inherent symmetrical or anti-symmetrical properties.