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The quantization inherent in the finite precision arithmetic operations render the system linear.
Explanation: In the realization of a digital filter, either in digital hardware or in software on a digital computer, the quantization inherent in the finite precision arithmetic operations render the system linear.
In recursive systems, which of the following is caused because of the nonlinearities due to the finiteprecision arithmetic operations?
Explanation: In the recursive systems, the nonlinearities due to the finiteprecision arithmetic operations often cause periodic oscillations to occur in the output even when the input sequence is zero or some non zero constant value.
The oscillations in the output of the recursive system are called as ‘limit cycles’.
Explanation: In the recursive systems, the nonlinearities due to the finiteprecision arithmetic operations often cause periodic oscillations to occur in the output even when the input sequence is zero or some non zero constant value. The oscillations thus produced in the output are known as ‘limit cycles’.
Limit cycles in the recursive are directly attributable to which of the following?
Explanation: The oscillations in the output of the recursive system are called as limit cycles and are directly attributable to roundoff errors in multiplication and overflow errors in addition.
What is the range of values called as to which the amplitudes of the output during a limit cycle ae confined to?
Explanation: The amplitudes of the output during a limit circle are confined to a range of values that is called the ‘dead band’ of the filter.
Zero input limit cycles occur from nonzero initial conditions with the input x(n)=0.
Explanation: When the input sequence x(n) to the filter becomes zero, the output of the filter then, after a number of iterations, enters into the limit cycle. The output remains in the limit cycle until another input of sufficient size is applied that drives the system out of the limit cycle. Similarly, zero input limit cycles occur from nonzero initial conditions with the input x(n)=0.
Which of the following is true when the response of the single pole filter is in the limit cycle?
Explanation: We note that when the response of the single pole filter is in the limit cycle, the actual nonlinear system acts as an equivalent linear system with a pole at z=1 when the pole is positive and z=1 when the poles is negative.
What is the dead band of a single pole filter with a pole at 1/2 and represented by 4 bits?
Explanation: We know that
Given a=1/2 and b=4 => v(n1) ≤ 1/16=> The dead band is (1/16,1/16).
The limit cycle mode with zero input, which occurs as a result of rounding the multiplications, corresponds to an equivalent second order system with poles at z=±1.
Explanation: There is an possible limit cycle mode with zero input, which occurs as a result of rounding the multiplications, corresponds to an equivalent second order system with poles at z=±1. In this case the two pole filter exhibits oscillations with an amplitude that falls in the dead band bounded by 2b/(1a1a2).
What is the necessary and sufficient condition for a second order filter that no zeroinput overflow limit cycles occur?
Explanation: It can be easily shown that a necessary and sufficient condition for ensuring that no zeroinput overflow limit cycles occur is a1+a2<1
which is extremely restrictive and hence an unreasonable constraint to impose on any second order section.
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