Consider an LSI system with the following input-output relationship: (a)Sketch t
ID: 3639157 • Letter: C
Question
Consider an LSI system with the following input-output relationship:
(a)Sketch the signal-flow diagram of the system and indicate the number of needed storage elements.
(b)Determine the impulse response of the system and represent it in a 2's complement Q3 format.
(c)Consider the following input:
Compute the output of the system at n=7, y(7), if the input x(n) and the impulse h(n) are represented in a 2's complement Q3 format. SHOW your work and computations to receive credit.
(d)If only 4 bits can be stored for the computed output sample y(7), determine the resulting error.
Explanation / Answer
Linear time-invariant system theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas. It investigates the response of a linear and time-invariant system to an arbitrary input signal. Trajectories of these systems are commonly measured and tracked as they move through time (e.g., an acoustic waveform), but in applications like image processing and field theory, the LTI systems also have trajectories in spatial dimensions. Thus these systems are also called linear translation-invariant to give the theory the most general reach. In the case of generic discrete-time (i.e., sampled) systems, linear shift-invariant is the corresponding term. A good example of LTI systems are electrical circuits that can be made up of resistors, capacitors and inductors