What does the Fourier series represent in signal processing?
A Signal frequency
B Signal transformation
C Signal compression
D Signal decomposition
The Fourier series is used to decompose a periodic signal into a sum of sine and cosine functions. This allows for the analysis of the frequency components of the signal, essential for signal processing, particularly in communication and filtering.
Which of the following is a feature of a discrete-time system?
A Continuous input
B Continuous output
C Defined at discrete intervals
D Infinite memory
A discrete-time system operates with signals that are defined only at specific discrete time intervals. These systems process sequences of data, typically represented as digital signals, and are fundamental in digital signal processing.
What is the primary use of the Laplace transform?
A Solving differential equations
B Filtering signals
C Signal reconstruction
D Sampling signals
The Laplace transform is primarily used to solve linear differential equations by converting them into algebraic equations in the s-domain. It simplifies the analysis of systems, particularly in control systems and circuit analysis.
What is the primary purpose of an impulse response in system analysis?
A To analyze system behavior to a unit impulse
B To evaluate system stability
C To determine system bandwidth
D To measure system noise
The impulse response describes how a system responds to a unit impulse input. It is crucial for understanding the system’s behavior and characteristics, particularly in linear time-invariant systems, and helps determine system stability and frequency response.
What does the Nyquist theorem ensure?
A Frequency filtering
B Signal amplification
C No loss of information during sampling
D Signal clarity
The Nyquist theorem states that to avoid aliasing and loss of information, the sampling rate must be at least twice the highest frequency present in the signal. This ensures accurate signal representation in the digital domain.
Which of the following describes a stable system?
A Unpredictable behavior
B Unbounded response
C Random behavior
D Limited output
A stable system produces a bounded output for any bounded input. This means that the system’s response remains finite, and the output does not grow uncontrollably, which is essential for reliable system operation in engineering applications.
What does Z-transform help analyze?
A Impulse responses
B Discrete-time signals
C Frequency spectra
D Continuous signals
The Z-transform is a mathematical tool used for analyzing discrete-time signals by converting them from the time domain into the z-domain. It facilitates easier analysis of difference equations and system behavior.
What type of system is defined by its output being solely dependent on the current input?
A Time-invariant
B Memoryless
C Causal
D Linear
A memoryless system’s output depends only on the current input and not on past or future inputs. This type of system is simple to model and analyze, as it has no internal state or memory of past inputs.
What does the frequency spectrum of a signal represent?
A Range of frequencies present in the signal
B Amplitude variation
C Signal modulation
D Time duration
The frequency spectrum of a signal shows how the signal’s energy is distributed across various frequencies. Analyzing the spectrum helps understand the signal’s composition and is crucial in communication systems and signal processing.
What is the significance of the convolution operation in signal processing?
A Changing signal amplitude
B Combining two signals to find system output
C Amplifying the signal
D Filtering signal noise
Convolution is a mathematical operation used to determine the output of a linear time-invariant (LTI) system when the input and the system’s impulse response are known. It combines the two signals in a specific way to generate the system’s output.
What does a causal system imply about its response?
A Response depends only on past inputs
B Response depends on present and future inputs
C Response is random
D Response depends on future inputs
A causal system’s output at any given time depends only on the current and past inputs, but not on future inputs. This property is essential for physical realizability in real-time systems.
In which domain does the Fourier transform operate?
A Time domain
B Z-domain
C Frequency domain
D Laplace domain
The Fourier transform converts a signal from the time domain to the frequency domain. It decomposes the signal into its constituent frequencies, allowing for analysis and processing in terms of frequency rather than time.
What is signal reconstruction in signal processing?
A Removing noise from signals
B Rebuilding a signal from sampled data
C Amplifying signal strength
D Modifying signal parameters
Signal reconstruction involves recreating the original continuous-time signal from its sampled version, often using interpolation techniques. It is crucial for maintaining the integrity of the signal during digital-to-analog conversion.
Which of the following defines a time-invariant system?
A Output depends on the time the input is applied
B System’s behavior changes with time
C System’s response is unpredictable
D Output remains unchanged if input is delayed
A time-invariant system’s response to an input will be the same regardless of when the input is applied. If the input is delayed, the output will simply be delayed by the same amount, maintaining the system’s characteristics.
What does a digital signal represent?
A Discrete values at specific time intervals
B Continuous time
C Continuous amplitude
D Sinusoidal waveform
A digital signal consists of discrete values that are sampled at specific time intervals. Unlike analog signals, which are continuous, digital signals are represented by binary values and are used in computers and digital systems for processing.