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Bilinear Transformation is used for transforming an analog filter to a digital filter.
Explanation: The bilinear transformation can be regarded as a correction of the backward difference method. The bilinear transformation is used for transforming an analog filter to a digital filter.
Which of the following rule is used in the bilinear transformation?
Explanation: Bilinear transformation uses trapezoidal rule for integrating a continuous time function.
Which of the following substitution is done in Bilinear transformations?
Explanation: In bilinear transformation of an analog filter to digital filter, using the trapezoidal rule, the substitution for ‘s’ is given as
What is the value of according to trapezoidal rule?
Explanation: The given integral is approximated by the trapezoidal rule. This rule states that if T is small, the area (integral) can be approximated by the mean height of x(t) between the two limits and then multiplying by the width. That is
What is the value of y(n)y(n1) in terms of input x(n)?
Explanation: We know that the derivate equation is
dy(t)/dt=x(t)
What is the expression for system function in zdomain?
Explanation: We know that
y(n)y(n1)= [(x(n)+x(n1))/2]T
Taking ztransform of the above equation gives
=>Y(z)[1z^{1}]=([1+z^{1}]/2).TX(z)
=>H(z)=Y(z)/X(z)= T/2[(1+z^{1})/(1z^{1} )].
In bilinear transformation, the lefthalf splane is mapped to which of the following in the zdomain?
Explanation: In bilinear transformation, the z to s transformation is given by the expression
z=[1+(T/2)s]/[1(T/2)s].
Thus unlike the backward difference method, the lefthalf splane is now mapped entirely inside the unit circle, z=1, rather than to a part of it.
The equationis a true frequencytofrequency transformation.
Explanation: Unlike the backward difference method, the lefthalf splane is now mapped entirely inside the unit circle, z=1, rather than to a part of it. Also, the imaginary axis is mapped to the unit circle. Therefore, equation is a true frequencytofrequency transformation.
If s=σ+jΩ and z=re^{jω}, then what is the condition on σ if r<1?
Explanation: We know that if =σ+jΩ and z=re^{jω}, then by substituting the values in the below expression
When r<1 => σ < 0.
If s=σ+jΩ and z=re^{jω} and r=1, then which of the following inference is correct?
Explanation: We know that if =σ+jΩ and z=re^{jω}, then by substituting the values in the below expression
=>σ = 2/T[(r^{2}1)/(r^{2}+1+2rcosω)] When r=1 => σ = 0.
This shows that the imaginary axis in the sdomain is mapped to the circle of unit radius centered at z=0 in the zdomain.
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