Determine the natural response of the system: Difference equation is

y(n)-y(n-1)-2y(n-2)=x(n) and y(-1) = 1; y(-2) = 0

yh (n) = \(\frac{4}{3}\) (1)n – \(\frac{1}{3}\) (-1)n

yh (n) = \(\frac{4}{3}\) (-1)n – \(\frac{1}{3}\) (-1)n

yh (n) = \(\frac{4}{3}\) (2)n – \(\frac{1}{3}\) (-1)n

yh (n) = \(\frac{4}{3}\) (2)n – \(\frac{1}{3}\) (2)n

The difference equation for an Nth order discrete-time system is ___________

\(∑_{k=-∞}^∞\) ak y(n-k) = \(∑_{k=-∞}^∞\) bk x(n-k)

\(∑_{k=0}^∞\) ak y(n-k) = \(∑_{k=0}^∞\) bk x(n-k)

\(∑_{k=0}^N\) ak y(n-k) = \(∑_{k=0}^N\) bk x(n-k)

\(∑_{k=-∞}^0\) ak y(n-k) = \(∑_{k=-∞}^0\) bk x(n-k)

Explore topic-wise MCQs in Signals & Systems Questions and Answers.

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

1.	Determine the natural response of the system: Difference equation is
A.	y(n)-y(n-1)-2y(n-2)=x(n) and y(-1) = 1; y(-2) = 0
B.	yh (n) = \(\frac{4}{3}\) (1)n – \(\frac{1}{3}\) (-1)n
C.	yh (n) = \(\frac{4}{3}\) (-1)n – \(\frac{1}{3}\) (-1)n
D.	yh (n) = \(\frac{4}{3}\) (2)n – \(\frac{1}{3}\) (-1)n
E.	yh (n) = \(\frac{4}{3}\) (2)n – \(\frac{1}{3}\) (2)n
Answer» D. yh (n) = \(\frac{4}{3}\) (2)n – \(\frac{1}{3}\) (-1)n

Discussion

2.	The difference equation for an Nth order discrete-time system is ___________
A.	\(∑_{k=-∞}^∞\) ak y(n-k) = \(∑_{k=-∞}^∞\) bk x(n-k)
B.	\(∑_{k=0}^∞\) ak y(n-k) = \(∑_{k=0}^∞\) bk x(n-k)
C.	\(∑_{k=0}^N\) ak y(n-k) = \(∑_{k=0}^N\) bk x(n-k)
D.	\(∑_{k=-∞}^0\) ak y(n-k) = \(∑_{k=-∞}^0\) bk x(n-k)
Answer» D. \(∑_{k=-∞}^0\) ak y(n-k) = \(∑_{k=-∞}^0\) bk x(n-k)

Discussion