Which of the following is the rational system function of an LTI system characterized by the difference equation y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)?

\(\frac{\sum_{k=0}^N b_k x(n-k)}{1+\sum_{k=0}^N a_k y(n-k)}\)

\(\frac{1+\sum_{k=1}^N a_k y(n-k)}{\sum_{k=0}^N b_k x(n-k)}\)

\(\frac{\sum_{k=0}^N b_k x(n-k)}{1+\sum_{k=1}^N a_k y(n-k)}\)

\(\frac{1+\sum_{k=0}^N a_k y(n-k)}{\sum_{k=0}^N b_k x(n-k)}\)

Explore topic-wise MCQs in Digital Signal Processing Questions and Answers.

This section includes 2 Mcqs, each offering curated multiple-choice questions to sharpen your Digital Signal Processing Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.

1.	We can view y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\) as the computational procedure (an algorithm) for determining the output sequence y(n) of the system from the input sequence x(n).
A.	True
B.	False
Answer» B. False

Discussion

2.	Which of the following is the rational system function of an LTI system characterized by the difference equation y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)?
A.	\(\frac{\sum_{k=0}^N b_k x(n-k)}{1+\sum_{k=0}^N a_k y(n-k)}\)
B.	\(\frac{1+\sum_{k=1}^N a_k y(n-k)}{\sum_{k=0}^N b_k x(n-k)}\)
C.	\(\frac{\sum_{k=0}^N b_k x(n-k)}{1+\sum_{k=1}^N a_k y(n-k)}\)
D.	\(\frac{1+\sum_{k=0}^N a_k y(n-k)}{\sum_{k=0}^N b_k x(n-k)}\)
Answer» D. \(\frac{1+\sum_{k=0}^N a_k y(n-k)}{\sum_{k=0}^N b_k x(n-k)}\)

Discussion

Explore topic-wise MCQs in Digital Signal Processing Questions and Answers.

We can view y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\) as the computational procedure (an algorithm) for determining the output sequence y(n) of the system from the input sequence x(n).

Which of the following is the rational system function of an LTI system characterized by the difference equation y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)?