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Test: Digital Filters Round Off Effects


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10 Questions MCQ Test Signals and Systems | Test: Digital Filters Round Off Effects

Test: Digital Filters Round Off Effects for Electrical Engineering (EE) 2022 is part of Signals and Systems preparation. The Test: Digital Filters Round Off Effects questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Digital Filters Round Off Effects MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Digital Filters Round Off Effects below.
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Test: Digital Filters Round Off Effects - Question 1

The quantization inherent in the finite precision arithmetic operations render the system linear. 

Detailed Solution for Test: Digital Filters Round Off Effects - Question 1

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.

Test: Digital Filters Round Off Effects - Question 2

In recursive systems, which of the following is caused because of the nonlinearities due to the finite-precision arithmetic operations?

Detailed Solution for Test: Digital Filters Round Off Effects - Question 2

Explanation: In the recursive systems, the nonlinearities due to the finite-precision arithmetic operations often cause periodic oscillations to occur in the output even when the input sequence is zero or some non zero constant value.

Test: Digital Filters Round Off Effects - Question 3

 The oscillations in the output of the recursive system are called as ‘limit cycles’. 

Detailed Solution for Test: Digital Filters Round Off Effects - Question 3

Explanation: In the recursive systems, the nonlinearities due to the finite-precision 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’.

Test: Digital Filters Round Off Effects - Question 4

 Limit cycles in the recursive are directly attributable to which of the following?

Detailed Solution for Test: Digital Filters Round Off Effects - Question 4

Explanation: The oscillations in the output of the recursive system are called as limit cycles and are directly attributable to round-off errors in multiplication and overflow errors in addition.

Test: Digital Filters Round Off Effects - Question 5

What is the range of values called as to which the amplitudes of the output during a limit cycle ae confined to?

Detailed Solution for Test: Digital Filters Round Off Effects - Question 5

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.

Test: Digital Filters Round Off Effects - Question 6

 Zero input limit cycles occur from non-zero initial conditions with the input x(n)=0. 

Detailed Solution for Test: Digital Filters Round Off Effects - Question 6

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 non-zero initial conditions with the input x(n)=0.

Test: Digital Filters Round Off Effects - Question 7

 Which of the following is true when the response of the single pole filter is in the limit cycle?

Detailed Solution for Test: Digital Filters Round Off Effects - Question 7

Explanation: We note that when the response of the single pole filter is in the limit cycle, the actual non-linear 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.

Test: Digital Filters Round Off Effects - Question 8

 What is the dead band of a single pole filter with a pole at 1/2 and represented by 4 bits?

Detailed Solution for Test: Digital Filters Round Off Effects - Question 8

Explanation: We know that

Given |a|=1/2 and b=4 => |v(n-1)| ≤ 1/16=> The dead band is (-1/16,1/16).

Test: Digital Filters Round Off Effects - Question 9

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.

Detailed Solution for Test: Digital Filters Round Off Effects - Question 9

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 2-b/(1-|a1|-a2).

Test: Digital Filters Round Off Effects - Question 10

 What is the necessary and sufficient condition for a second order filter that no zero-input overflow limit cycles occur?

Detailed Solution for Test: Digital Filters Round Off Effects - Question 10

Explanation: It can be easily shown that a necessary and sufficient condition for ensuring that no zero-input 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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