One of the ZEROs of a third order Causal Linear Phase High Pass FIR filter lies atz = 0.5 Find the location of the other zeros and hence find the Transfer function andImpulse Response of the filter.

To find the location of the other zeros of the third order Causal Linear Phase High Pass FIR filter, we know that the zero at z = 0.5 is one of the zeros. Since the filter is causal, all the other zeros must lie outside the unit circle in the z-plane.

To determine the transfer function of the filter, we can use the zero-pole representation. Since we have one zero at z = 0.5, the transfer function can be written as:

H(z) = (z - 0.5) * H1(z)

where H1(z) represents the transfer function with the remaining zeros.

To find H1(z), we can divide the transfer function of the filter by (z - 0.5):

H1(z) = H(z) / (z - 0.5)

Now, we need to find the impulse response of the filter. The impulse response can be obtained by taking the inverse Z-transform of the transfer function.

Taking the inverse Z-transform of H(z), we get:

h[n] = Inverse Z-transform {H(z)}

By substituting the transfer function H(z) with (z - 0.5) * H1(z), we can rewrite the equation as:

h[n] = Inverse Z-transform {(z - 0.5) * H1(z)}

By applying the inverse Z-transform, we can find the impulse response of the filter.

Please note that the exact values of the other zeros and the transfer function cannot be determined without additional information.