Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If P≤ft( z ) = H≤ft( z )H≤ft( 1/z ) ha

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Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If P≤ft( z ) = H≤ft( z )H≤ft( 1/z ) has a zero at z = 1/2 + 1/2j , and P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly?

Accepted Answer

Given: P≤ft( z ) = H≤ft( z )H≤ft( 1/z ) P≤ft( 1/z ) = H≤ft( 1/z )H≤ft( z ) Thus, P(z) = P(z⁻¹) In such a condition, if z = z₀ is a zero then: z_0^*,z = 1/z_0 and z = 1/z_0^* are also zeroes. Given, z_0 = 1 + j2 is zero z = z_0^* = 1 - j2 is also zero z = 1/z_0 = {2≤ft( 1 - j )}{≤ft( 1 + j )≤ft( 1 - j )} = 2 - 2j2 = 1 - j is also a zero z = 1/z_0^* = 2/{≤ft( 1 - j )≤ft( 1 + j )} = {2≤ft( 1 + j )}2 = 1 + j is also a zero The corresponding pole-zero plot will be: ![image](https://cdn.prepp.in/uploa

Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If $P (z) = H (z) H (\frac{1}{z})$ has a zero at $z = \frac{1}{2} + \frac{1}{2} j$ , and P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly?

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Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If P(z)=H(z)H(z1​) has a zero at z=21​+21​j, and P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly?