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In IIR Filter design by the Bilinear Transformation, the Bilinear Transformation is a mapping from
Explanation: From the equation,
it is clear that transformation occurs from s-plane to z-plane
In Bilinear Transformation, aliasing of frequency components is been avoided.
Explanation: The bilinear transformation is a conformal mapping that transforms the jΩ-axis into the unit circle in the z-plane only once, thus avoiding the aliasing.
Is IIR Filter design by Bilinear Transformation is the advanced technique when compared to other design techniques?
Explanation: Because in other techniques, only lowpass filters and limited class of bandpass filters are been supported. But this technique overcomes the limitations of other techniques and supports more.
The approximation of the integral in
Explanation: By integrating the equation,
We use y'(nT)=-ay(nT)+bx(nT) to substitute for the derivative in
and thus obtain a difference equation for the equivalent discrete-time system. With y(n) = y(nT ) and x(n) = x( nT), we obtain the result as _ of the following?
Explanation: When we substitute the given equation in the derivative of other we get the resultant required equation.
The z-transform of below difference equation is?
Explanation: By performing the z-transform of the given equation, we get the required output/equation.
What is the system function of the equivalent digital filter? H(z) = Y(z)/X(z ) = ?
Explanation: As we considered analog linear filter with system function H(s) = b/s+a
Hence, we got an equivalent system function
In the Bilinear Transformation mapping, which of the following are correct?
Explanation: The bilinear transformation is a conformal mapping that transforms the jΩ-axis into the unit circle in the z-plane and all the points are linked as mentioned above.
In Nth order differential equation, the characteristics of bilinear transformation, let z= rejw,s=o+jΩ Then for the values of Ω, ℴ are
In equation if r < 1 then ℴ < 0 and then mapping from s-plane to z-plane occurs in which of the following order?
Explanation: In the above equation, if we substitute the values of r, ℴ then we get mapping in the required way