What defines a linear system in signal processing?
A Time invariance
B Proportionality
C Time dependence
D Additivity
A linear system follows the principle of superposition, meaning the output of a system in response to multiple inputs is the sum of the outputs for each input individually. This property is essential in analyzing and predicting system behavior.
What does the time-invariance property of a system imply?
A System’s behavior is consistent over time
B Output depends on current input only
C System’s behavior changes over time
D Output depends on future inputs
A time-invariant system produces the same output for a given input regardless of when the input is applied. This consistency means that if the input is delayed, the output will also be delayed by the same amount.
Which of the following describes a causal system?
A Output depends on future inputs
B Output depends on past and current inputs
C Output depends on past inputs
D Output is random
A causal system’s output at any time depends only on the past and current inputs, not future inputs. This ensures that the system can operate in real-time, where future data is not available.
What does a memoryless system mean?
A Output depends on previous inputs
B Output is random
C Output depends on the current input
D Output depends on past and future inputs
A memoryless system’s output is solely determined by the current input, without any reliance on past or future values. This makes the system simple to analyze and implement, with no internal state.
Which of the following is a key property of a linear time-invariant (LTI) system?
A Output changes over time
B Output is proportional to input
C Output depends on future inputs
D Output is not predictable
LTI systems have the properties of linearity (output is proportional to input) and time invariance (output does not change over time). These systems are widely used due to their predictability and ease of analysis.
What is the response of a system called when the input is a unit impulse?
A Step response
B Frequency response
C Impulse response
D Time response
The impulse response is the output of a system when the input is a unit impulse. It is a fundamental property of linear time-invariant systems and is used to analyze and predict the system’s behavior to any input.
What does the superposition principle state for linear systems?
A Output is a weighted sum of inputs
B Output depends on current input
C Output is random
D Output is based on past and future inputs
The superposition principle states that for linear systems, the output produced by a sum of inputs is the sum of the outputs produced by each input individually. This property is vital for system analysis and design.
What is a defining characteristic of a time-varying system?
A Output is consistent over time
B Output depends on future inputs
C Output is only periodic
D System’s behavior changes with time
A time-varying system has properties that change over time. Unlike time-invariant systems, where the behavior remains constant, a time-varying system’s response to an input may vary depending on the time the input is applied.
What does the stability of a system mean?
A System has no feedback
B Output remains bounded for any bounded input
C Output grows without bound
D Output depends on future inputs
A stable system produces a bounded output for any bounded input. This ensures that the system will not exhibit runaway behavior or unpredictability, which is essential for reliable and safe operation in practical applications.
What does the term “causality” imply in a system?
A Output depends on future inputs
B Output depends only on present input
C Output depends only on past inputs
D Output depends on future and past inputs
Causal systems only depend on past and present inputs to determine the output, not future inputs. This makes causal systems physically realizable because future inputs are not available in real-time processing.
What does a linear system imply regarding its output for multiple inputs?
A Output is random
B Output is independent of input
C Output for multiple inputs is non-linear
D Output for a combined input equals the sum of outputs for individual inputs
In linear systems, the principle of superposition applies: the output for a combination of inputs is the sum of the individual outputs for each input. This property makes linear systems easier to analyze and understand.
What does time-invariance of a system mean regarding its response to a delayed input?
A The output is amplified
B The output is the same but delayed
C The system cannot process delayed inputs
D The output changes over time
A time-invariant system produces the same output when the input is delayed, but the output will be delayed by the same amount. This consistency in behavior is a hallmark of time-invariant systems.
What does a stable system imply in terms of input-output relationship?
A Output grows indefinitely
B Output depends on future input
C Output is bounded for bounded input
D Output is unpredictable
A stable system ensures that if the input is bounded (i.e., it does not grow without bound), the output will also remain bounded. This is crucial for ensuring the system operates within desired limits.
What is the primary function of a system’s impulse response?
A Measure frequency response
B Characterize system stability
C Predict system output for any input
D Amplify input signals
The impulse response of a system characterizes how the system will respond to any input. By convolving the impulse response with the input signal, we can predict the system’s output for arbitrary inputs.
What is the difference between a causal and non-causal system?
A Causal systems depend only on past and present inputs
B Non-causal systems depend only on past inputs
C Non-causal systems depend on present inputs only
D Causal systems depend on future inputs
Causal systems depend on past and present inputs to generate output, making them suitable for real-time applications. Non-causal systems, on the other hand, would require future inputs, which is not feasible in most practical systems.