What does the convolution operation in signal processing represent?
A Modulation
B Combination
C Filtering
D Amplification
Convolution represents the combination of an input signal with a system’s impulse response. It helps determine the output of linear time-invariant systems by integrating the product of the input and impulse response over time.
Which of the following describes the impulse response of a system?
A System stability
B Time-domain analysis
C Output for a unit impulse
D Frequency spectrum
The impulse response is the output of a system when the input is a unit impulse. It plays a key role in characterizing the behavior of linear time-invariant systems and is used to calculate the system’s response to any input.
What type of system is characterized by the output only depending on past and current inputs?
A Causal
B Non-causal
C Linear
D Time-invariant
A causal system’s output at any time depends only on the current and past inputs, not future inputs. This makes the system physically realizable, ensuring it can be implemented in real-time systems.
In a system analysis, what does the term “stability” refer to?
A Predictability
B Frequency response
C Unbounded output
D Bounded output for bounded input
Stability in a system means that for any bounded input, the output will also remain bounded. An unstable system produces unbounded or unpredictable outputs, which can lead to system failure or undesirable behavior.
What does the system’s step response characterize?
A Output for a sinusoidal input
B Output for a unit step input
C Behavior with a constant input
D Time-domain stability
The step response characterizes how a system reacts to a step input, which is a signal that switches from zero to a constant value at a specific time. It provides insight into the transient behavior and stability of the system.
What does the term “linear system” imply in system theory?
A Output depends on future inputs
B Output depends only on current inputs
C Output is a weighted sum of inputs
D Output is random
A linear system adheres to the principle of superposition, meaning that the output is directly proportional to the input. If the input changes, the output will change in proportion, making the system predictable and manageable.
What is the primary use of the impulse response in system analysis?
A Calculate signal bandwidth
B Predict the system’s future behavior
C Measure system stability
D Determine system response to arbitrary inputs
The impulse response helps determine a system’s output for any arbitrary input by convolution. It fully characterizes a linear time-invariant system and is essential for calculating the system’s output in response to various inputs.
What is the outcome of applying the convolution operation on a system?
A Output signal
B Impulse response
C Signal bandwidth
D Frequency spectrum
The convolution operation combines the input signal with the system’s impulse response to generate the output signal. It is a fundamental operation used in signal processing to predict how a system will react to any input signal.
What is the main purpose of using a linear system in signal processing?
A Remove noise
B Predict signal trends
C Simplify system analysis
D Analyze frequency content
Linear systems simplify analysis because they adhere to the principle of superposition, allowing for straightforward calculations and predictions of system behavior. They are foundational in many signal processing tasks, including filtering and system design.
What does the frequency response of a system describe?
A Behavior over time
B System’s output for a sinusoidal input
C Response to random noise
D Output for an impulse input
The frequency response of a system describes how the system responds to sinusoidal inputs at different frequencies. It is crucial for understanding how the system amplifies or attenuates various frequency components of an input signal.
What is the primary characteristic of a time-invariant system?
A Output depends on input delay
B Output varies over time
C System properties change with time
D System behavior remains unchanged over time
A time-invariant system’s behavior does not change with time. If the input signal is delayed, the output will also be delayed by the same amount, preserving the system’s properties over time.
What does the term “convolution integral” refer to?
A Signal sampling method
B Calculating system stability
C Mathematical expression for continuous-time convolution
D Determining system response to an impulse
The convolution integral is a mathematical operation used to find the output of a continuous-time linear system by integrating the product of the input signal and the system’s impulse response over time. It is essential for system analysis.
What type of system is described by having no memory?
A Linear
B Memoryless
C Causal
D Time-varying
A memoryless system’s output depends only on the current input and not on any past inputs. This type of system has no internal state or memory and is easier to analyze and implement.
What does the system’s “response” describe?
A Output to any input
B System’s stability
C System’s frequency spectrum
D Output for noise input
The system’s response describes how the system reacts to any given input. Whether the input is a sinusoidal, step, or arbitrary signal, the response helps understand how the system processes the signal and affects its output.
Which of the following describes a system with a bounded output for any bounded input?
A Memoryless
B Unstable
C Stable
D Non-linear
A stable system produces a bounded output for any bounded input. This ensures that the system’s behavior remains predictable, and it avoids runaway responses, which is a critical requirement for practical system design.