Signals and Systems Practice Test

These questions are part of the practice quiz. Start practicing

• What is the Z-transform H(z), ROC, and the stability of the system for h[n] = (1/2)^n u[n]?
• Which statement best characterizes linear systems with respect to input-output relationships?
• For a single-input, single-output time-invariant linear system, the impulse response h(t) is the system's output when the input is which signal?
• Which expression represents the discrete-time convolution sum?
• Which of the following describes a stable discrete-time LTI system?
• Which statement correctly describes the discrete-time representation of a finite-duration, non-periodic signal using the DFT?
• In the Laplace domain, why is e^{s t} considered an eigenfunction of an LTI system with impulse response h(t)?
• A dynamic system is defined as which statement?
• What is the relationship between the width of a signal in time and the width of its Fourier transform?
• Which statement correctly describes the relationship between stability and the ROC of a Laplace transform for a causal LTI system with an absolutely integrable impulse response?
• Which statement correctly describes the Complex Exponential Fourier Series representation?
• In a system where two separate cosine signals of different frequencies are summed and transmitted, the receiver splits the signal into two branches and applies band-pass filters to each branch. What is the primary purpose of these band-pass filters?
• How do higher harmonics behave for smooth periodic signals in a Fourier series?
• Which operation transforms a circuit's time-domain differential equation into a frequency-domain representation by substituting s with jω?
• The impulse response h(t) is the system's output when the input is which signal?
• Which statement describes a non-linear system?
• An ideal low-pass filter is characterized by which of the following?
• Which statement correctly distinguishes continuous-time (CT) signals from discrete-time (DT) signals and provides valid examples?
• A discrete signal is defined as:
• Which of the following statements are highlighted as characteristics of linear, time-invariant systems?
• State the sampling theorem in terms of bandwidth B and sampling rate Fs, and the aliasing condition.
• What is the initial value theorem in Laplace domain?
• Which statement about energy signals is true?
• Which statement describes the signal immediately after the encoder in the ADC chain?
• Why are complex exponentials e^{j ω0 t} eigenfunctions of LTI systems, and what is the eigenvalue?
• What is the Z-transform relationship for a delayed sequence x[n-1]?
• Under BIBO stability, if the input is bounded, what can be said about the output?
• What is the final value theorem in Laplace domain and what condition must be satisfied?
• The instantaneous power in a passive resistor is:
• For a discrete-time system, a pole on the unit circle corresponds to which stability behavior?
• What is the circuit transfer function H(jω) defined as?
• What is the effect on the spectrum when a continuous-time signal is sampled?
• Define the Z-transform and explain the significance of its region of convergence (ROC).
• Which transform is most appropriate for analyzing the frequency content of a discrete-time sequence on the unit circle?
• In the context of reconstructing a continuous signal from samples, is the sampled signal assumed to be periodic?
• If a signal is bandlimited to B Hz, what is the minimum sampling rate Fs to avoid aliasing?
• State the BIBO stability criterion and the associated impulse response condition for CT and DT systems.
• In an ideal analog-to-digital conversion chain, which order of blocks yields a digital output?
• For a causal continuous-time LTI system, where is the ROC relative to its poles?
• Fourier series representation uses an infinite number of harmonics. Which statement best describes this idea?
• Multiplying a signal by e^{j ω0 t} results in what change to its spectrum?
• BIBO stability stands for which of the following?
• Quantization maps a sample value to a finite set of permissible values by rounding to the nearest; the maximum quantization error equals S/2, where S is the step size.
• Which statement about finite-energy signals is true?
• Provide the Fourier transform of a rectangular pulse of width T and height A centered at t=0.
• In a Fourier series context, when can the series be truncated without substantial loss of accuracy?
• Nyquist criterion states the minimum sampling frequency Fs must be at least twice the bandwidth of the signal. Which option reflects that requirement?
• After the quantization step, the signal is best described as which?
• In discrete time, how is the step response s[n] related to the impulse response h[k]?
• For a causal system, what is a typical property of the region of convergence (ROC) of its Z-transform in relation to stability?
• Explain causality in a system and what it implies about the impulse response.
• Which statement correctly defines energy and power signals and their standard formulas?
• Which expression describes how to obtain the output y(t) from the input x(t) and the impulse response h(t) in an LTI system?
• In discrete-time systems, the unit impulse sequence δ[n] has which fundamental property?
• In frequency domain, what does H(jω) represent?
• What operation on h[n] yields the discrete-time step response s[n]?
• For a continuous-time system described by y'' + 3 y' + 2 y = x, which is its transfer function H(s)?
• Which statement best defines a distortionless system?
• An energy signal is characterized by which property?
• Why do multiple copies appear in the spectrum of a sampled signal?
• Which statement best describes bandwidth-limited signals?
• What is the impulse response of an LTI system and how is the output computed for any input?
• What defines the fundamental period of a periodic signal?
• Which statement correctly describes FIR and IIR filters with respect to impulse response and stability?
• Singularity functions consist of:
• How is the cutoff frequency defined in terms of H(jω) magnitude?
• A continuous signal is defined for:
• For h(t) = e^{−2t} u(t), what is its Laplace transform H(s) and ROC, and is the system causal and BIBO stable?
• Which statement defines a causal system?
• What is the effect of a notch (zero) in the transfer function on the output for a sinusoidal input at the notch frequency?
• An instantaneous system is always which of the following?
• In the z-transform context, what does the final value theorem relate?
• If two cosine signals with different frequencies are summed and transmitted, what feature allows their separation at the receiver using band-pass filters?
• The cutoff frequency Fc of a real low-pass RC filter is given by which expression?
• Discrete-time convolution has the same fundamental relationship as continuous-time convolution. Which statement best describes this relationship?
• Which option correctly describes the distortionless system in terms of waveform preservation?
• Discrete-time convolution has the same fundamental relationship as continuous-time convolution. Which statement is true?
• Which statement best describes the use of energy spectral density and PSD?
• Which statement about deterministic signals is true?
• The convolution sum formula y[n] = sum_k x[k] h[n-k] is used to compute the output of a discrete-time system; which property must hold for this to be valid?
• In the frequency domain, which variable denotes angular frequency?
• A time delay t0 in the time domain corresponds to what operation in the frequency domain?
• An instantaneous system is characterized by which of the following?
• In a transfer function, what is the significance of poles and zeros?
• Explain the reconstruction formula for a bandlimited signal from its samples using sinc interpolation.
• What is the effect of the delay operator Z^{-1} on a discrete-time signal x[n]?
• A dynamic and causal system has output that depends on
• What is the Fourier transform of a unit step input u(t), and what is notable about it?
• In the z-transform context, what does the initial value theorem relate?
• Consider h(t)=e^{−a t} u(t) with a>0. What is its Laplace transform H(s) and the ROC?
• In a linear time-invariant system with a single input and output, the relation between input x(t) and output y(t) is given by which expression?
• For a causal LTI system described by the difference equation y[n] + a1 y[n−1] = b0 x[n], which of the following is its transfer function H(z)?
• What is the purpose of the inverse Z-transform?
• If a causal LTI system has impulse response h[n] = a^n u[n], what is the ROC and stability condition?
• If a signal is sampled below the Nyquist rate, which phenomenon occurs?
• If H(s) = 1/(s^2 + 3s + 2), where are the poles located?
• Define the frequency response H(jω) of an LTI system and describe its relationship to the impulse response.
• A time-invariant system has the property that:
• Which description best matches a digital signal?
• Given h[0] = 2, h[1] = 1, and h[k] = 0 for k > 1, what is s[1] = ∑_{k=0}^{1} h[k]?
• In the passband of an ideal filter, the amplitude is ...
• In the Laplace domain, what is the region of convergence (ROC) for a right-sided causal sequence and for a left-sided anti-causal sequence?
• In a discrete-time LTI system, which expression corresponds to the eigenvalue for input e^{jωn}?
• For a causal discrete-time LTI system, what condition on its poles ensures BIBO stability?
• If Fc equals Fs/2, what does this imply about the filter's passband with respect to the sampling rate?
• The term bandwidth in this context refers to which portion of the spectrum?
• Under what condition will the steady-state output have zero phase lag relative to the input?
• The total energy of a signal is defined as:
• Which statement best describes a discrete-time signal?
• Which statement best describes a power signal as given?
• Which statement about energy signals is true?
• Which statement about low-pass filtering in signal reconstruction is true?
• Parseval's theorem for continuous-time signals relates time-domain energy to frequency-domain energy via which relation?
• Why are ideal low-pass filters non-causal and not realizable with a causal, finite-delay system?
• Which of the following statements is presented as a typical relationship between Fc and Fs in sampling?
• Write the convolution relations for continuous-time and discrete-time LTI systems.
• Which statement about non-periodic signals is true?
• For a causal discrete-time LTI system, which pole condition guarantees BIBO stability?
• Which of the following are valid methods to determine a circuit's frequency response H(f)?
• The impulse response of a discrete-time LTI system completely characterizes the system.
• Why is it common to treat the discrete-time sequence obtained after sampling as if it were periodic for analysis?
• Define the Short-Time Fourier Transform (STFT) and its purpose in time-frequency analysis.
• The frequency response of a linear time-invariant system is obtained from which of the following?
• How is the number of harmonics typically estimated in a Fourier series representation?
• Similarly, what happens if a signal is very broad in the time domain regarding its Fourier transform?
• What is line spectra referring to in signal analysis?
• Which are the two defining properties of a linear time-invariant system?
• What is the function of a quantizer?
• Which statement describes a continuous signal?
• What condition must the original signal satisfy to avoid aliasing when sampling at rate Fs?
• Which of the following describes the impulse response of a stable, causal LTI system?
• A periodic signal is defined as:
• If a discrete-time LTI system has impulse response h[n] = δ[n−N], the output to x[n] is:
• After the sampling step, the resulting signal is best described as which?
• What is the discrete-time Fourier transform (DTFT) and what is its periodicity?
• The z-transform is a technique for design and analysis of discrete-time systems and signals.
• What is the impulse response of a pure delay system h[n] = δ[n−N]?
• Parseval's theorem relates a signal's energy in the time domain to what in the frequency domain?
• Which formula defines the signal-to-noise ratio (SNR) in decibels?
• Which statement about a discrete-time system is true?
• Which statement describes a causal impulse response?
• Parseval's theorem for discrete-time signals expresses energy equivalence between time and frequency domains as?
• Discrete Fourier Transform (DFT) is used to represent a finite-duration, non-periodic signal by sampling its spectrum. Which statement is accurate about this representation?
• The Sampling Theorem states that a bandlimited signal with maximum frequency Fh is completely specified by its samples taken at a rate of at least ...
• For an LTI system with transfer function H(s), the output for input e^{s t} is which?
• For a bounded-input bounded-output stable LTI system subjected to a sinusoidal input x(t) = cos(ω0 t), what is the steady-state output?
• What is the difference between a causal vs noncausal impulse response and how does it affect realizability?
• In a sinusoidal steady-state response, which quantity determines the output amplitude?
• In the inverse Z-transform, which method is commonly used to compute the time-domain sequence by evaluating residues at the poles of X(z)?
• Which behavior is characteristic of a marginally stable discrete-time system with a pole on the unit circle?
• In a continuous-time linear time-invariant system, the step response s(t) is related to the impulse response h(t) by which expression?
• Which statement correctly describes the unit impulse δ(t) and its discrete counterpart δ[n]?
• In continuous time, the step response is the convolution of the impulse response with which input?
• An ideal low-pass filter has a constant amplitude and linear phase in the passband. Why is linear phase desirable?
• In a discrete-time linear time-invariant system, the output y[n] equals the convolution of the input x[n] with the impulse response h[n].
• The convolution sum y[n] = sum_k x[k] h[n-k] is used to compute the output of a discrete-time system, provided the system is linear and time-invariant.
• Rise time is defined as the time it takes for the output to go from what fraction to what fraction of its maximum value?
• For a stable LTI system, where are its poles located in the complex plane?
• Encoding is the process of representing the permissible values by a word (for example, 16 bits).
• What is the effect of cascading two LTI systems on their transfer functions?
• Which statement correctly describes aliasing risk with sampling rate?
• What does a Fourier series representation of a periodic signal consist of?
• Which statement about energy signals and power signals is true?
• Which statement about energy spectral density and PSD is true?
• Which statement best describes the relationship between line spectra and Fourier representations?
• In an ADC chain, what does the encoder do?
• Which statement best describes a sampler?
• If h[n] has finite length (nonzero for 0 ≤ n ≤ N), what happens to s[n] for n ≥ N?
• Aliasing occurs when shifted versions of the spectrum of a sampled signal overlap, preventing perfect reconstruction.
• For a low-pass filter, the rise time and the bandwidth are ...
• Which statement best describes a discrete-time, discrete-amplitude signal?
• If a discrete-time system has a pole on the unit circle (|z|=1), what is its stability characterization?
• If the sampling frequency is greater than twice the signal bandwidth, what is the outcome?
• Which statement best defines a deterministic signal?
• Which statement describes a shift-invariant discrete-time system?
• If a signal is sampled at Fs, the sampling interval is T = 1/Fs. Which statement is correct?
• Which statement about the Z-transform's region of convergence is true for a causal, stable system?