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Explanation: The analog filter in the time domain is governed by the following difference equation,
Explanation: A simple approximation to the first order derivative is given by the first backward difference. The first backward difference is defined by
[y(n)y(n1)]/T.
Which of the following is the correct relation between ‘s’ and ‘z’?
Explanation: We know that s=(1z^{1})/T=> z=1/(1sT).
What is the center of the circle represented by the image of jΩ axis of the sdomain?
Explanation: Letting s=σ+jΩ in the equation z=1/(1sT) and by letting σ=0, we get
z0.5=0.5
Thus the image of the jΩ axis of the sdomain is a circle with centre at z=0.5 in zdomain
What is the radius of the circle represented by the image of jΩ axis of the sdomain?
Explanation: Letting s=σ+jΩ in the equation z=1/(1sT) and by letting σ=0, we get
z0.5=0.5
Thus the image of the jΩ axis of the sdomain is a circle of radius 0.5 centered at z=0.5 in zdomain.
The frequency response H(ω) will be considerably distorted with respect to H(jΩ).
Explanation: Since jΩ axis is not mapped to the circle z=1, we can expect that the frequency response H(ω) will be considerably distorted with respect to H(jΩ).
The left half of the splane is mapped to which of the following in the zdomain?
Explanation: The left half of the splane is mapped inside the circle of z0.5=0.5 in the zplane, which completely lies in the right half zplane.
An analog high pass filter can be mapped to a digital high pass filter.
Explanation: An analog high pass filter cannot be mapped to a digital high pass filter because the poles of the digital filter cannot lie in the correct region, which is the lefthalf of the zplane(z < 0) in this case.
Which of the following is the correct relation between ‘s’ and ‘z’?
Explanation: We know that z=1/(1sT)=> s=(1z^{1})/T.
What is the ztransform of the first backward difference equation of y(n)?
Explanation: The first backward difference of y(n) is given by the equation
[y(n)y(n1)]/T
Thus the ztransform of the first backward difference of y(n) is given as
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