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What are the values of z for which the value of X(z)=0?
Explanation: For a rational ztransform X(z) to be zero, the numerator of X(z) is zero and the solutions of the numerator are called as ‘zeros’ of X(z).
What are the values of z for which the value of X(z)=∞?
Explanation: For a rational ztransform X(z) to be infinity, the denominator of X(z) is zero and the solutions of the denominator are called as ‘poles’ of X(z).
If X(z) has M finite zeros and N finite poles, then which of the following condition is true?
Explanation: If X(z) has M finite zeros and N finite poles, then X(z) can be rewritten as X(z)=z M+N.X'(z).
So, if N>M then z has a positive power. So, it has NM zeros at origin.
If X(z) has M finite zeros and N finite poles, then which of the following condition is true?
Explanation: If X(z) has M finite zeros and N finite poles, then X(z) can be rewritten as X(z)=z^{M+N}.X'(z).
So, if N < M then z has a negative power. So, it has NM poles at origin.
Which of the following signals have a polezero plot as shown below?
Explanation: From the given polezero plot, the ztransform of the signal has one zero at z=0 and one pole at z=a.
So, we obtain X(z)=z/(za)
By applying inverse ztransform for X(z), we get
x(n)= a^{n}u(n).
Which of the following signals have a polezero plot as shown below?(Let M=8 in the figure)
Explanation: From the figure given, the ztransform of the signal has 8 zeros on circle of radius ‘a’ and 7 poles at origin.
Explanation: The ztransform of the given signal is X(z)= z/(za)
So, it has one pole at z=a and one zero at z=0.
What is the nature of the signal whose polezero plot is as shown?
Explanation: From the polezero plot, it is shown that r < 1, so the signal is a decaying signal.
What are the values of z for which the value of X(z)=0?
Explanation: For a rational ztransform X(z) to be zero, the numerator of X(z) is zero and the solutions of the numerator are called as ‘zeros’ of X(z).
If Y(z) is the ztransform of the output function, X(z) is the ztransform of the input function and H(z) is the ztransform of system function of the LTI system, then H(z)=?
Explanation: We know that for an LTI system, y(n)=h(n)*x(n)
On applying ztransform on both sides we get, Y(z)=H(z).X(z)=>H(z)= ( Y(z))/(X(z) ).
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