Back to Subject
View Notes

Unit 5 - Practice Quiz

ECE180

1 A stochastic process is best described as:

A. A single random variable defined at a specific time.
B. A family of random variables indexed by a parameter (usually time).
C. A deterministic function of time.
D. A sequence of constant values.

2 If the time index is a countable set and the random variable takes continuous values, the process is classified as:

A. Continuous Random Sequence
B. Discrete Random Sequence
C. Continuous Random Process
D. Discrete Random Process

3 A stochastic process is called deterministic if:

A. Its future values can be predicted exactly from its past values.
B. It has a constant mean.
C. Its values are purely random and unpredictable.
D. Its power spectral density is flat.

4 A specific waveform or function of time observed from a stochastic process is called a:

A. Random variable
B. Sample function or realization
C. Probability density function
D. Correlation coefficient

5 Which function fully characterizes the statistical properties of a stochastic process at a single time instant ?

A. The autocorrelation function
B. The first-order probability density function
C. The power spectral density
D. The second-order probability density function

6 Two stochastic processes and are said to be statistically independent if their joint density function satisfies:

A.
B.
C. for all
D.

7 A stochastic process is Strict-Sense Stationary (SSS) if:

A. Its mean is constant.
B. Its statistical properties are invariant to a shift in the time origin.
C. Its autocorrelation depends only on the time difference.
D. Its power spectral density is constant.

8 For a first-order stationary process, which of the following must be true?

A.
B.
C.
D. All of the above

9 A process is Wide-Sense Stationary (WSS) if:

A. The mean is constant and the autocorrelation depends only on time difference .
B. All higher-order moments are constant.
C. The process is strictly stationary.
D. The variance is zero.

10 Which of the following statements is true regarding SSS and WSS?

A. All WSS processes are SSS.
B. All SSS processes are WSS (assuming moments exist).
C. There is no relationship between SSS and WSS.
D. WSS is a stricter condition than SSS.

11 For a Gaussian random process, Wide-Sense Stationarity (WSS) implies:

A. Strict-Sense Stationarity (SSS).
B. The process is white noise.
C. The process is non-deterministic.
D. Nothing about SSS.

12 The autocorrelation function of a WSS process is defined as:

A.
B.
C.
D.

13 Which of the following is a property of the autocorrelation function of a real WSS process?

A. is an odd function.
B.
C. (Even symmetry)
D. is always 0 for .

14 The maximum value of the autocorrelation function occurs at:

A.
B.
C.
D. It has no maximum.

15 The value represents the:

A. Mean value of the process.
B. Variance of the process.
C. Total average power (mean square value) of the process.
D. DC power of the process.

16 A stochastic process is said to be ergodic if:

A. All time averages are zero.
B. Its ensemble averages are equal to its corresponding time averages.
C. It is strictly stationary.
D. Its power spectral density is infinite.

17 For a process to be mean ergodic, which condition must hold as ?

A.
B.
C.
D. The process must be Gaussian.

18 The autocovariance function is related to the autocorrelation and mean by:

A.
B.
C.
D.

19 The cross-correlation function is defined as:

A.
B.
C.
D.

20 For jointly WSS processes and , the property indicates:

A. Even symmetry.
B. Odd symmetry.
C. Symmetry with respect to the process indices and time reversal.
D. Orthogonality.

21 Two processes and are said to be orthogonal if:

A. for all
B. for all
C.
D.

22 Two processes and are uncorrelated if:

A.
B. (or )
C. and are orthogonal.
D. They have different power spectral densities.

23 The Power Spectral Density (PSD), , of a WSS process is the Fourier Transform of:

A. The probability density function.
B. The autocorrelation function .
C. The mean function.
D. The cross-correlation function.

24 Which of the following is a fundamental property of the Power Spectral Density ?

A. can be negative.
B. is always real and non-negative ().
C. is purely imaginary.
D. decreases exponentially.

25 The total average power of a process can be obtained from the PSD by:

A.
B.
C.
D.

26 If is the PSD of a real random process, it is an:

A. Odd function of frequency.
B. Even function of frequency.
C. Exponential function.
D. Undefined function.

27 White noise is defined as a process having:

A. A constant Power Spectral Density for all frequencies.
B. A constant Autocorrelation function.
C. Zero variance.
D. A Gaussian PDF only.

28 The autocorrelation function of ideal white noise is:

A. A constant.
B. A Dirac delta function .
C. A sinc function.
D. A triangular function.

29 The Cross-Power Spectral Density is the Fourier Transform of:

A. Autocorrelation
B. Cross-correlation
C. Covariance
D. Joint PDF

30 Which relationship holds for the Cross-Power Spectral Density?

A.
B.
C.
D.

31 If two processes and are orthogonal, their Cross-PSD is:

A. Infinite.
B. Zero.
C. A constant.
D. Equal to .

32 If is the input to a linear time-invariant (LTI) system with transfer function , and is the output, the output PSD is given by:

A.
B.
C.
D.

33 For the same LTI system where is the output and is the input, the Cross-PSD is:

A.
B.
C.
D.

34 The DC component of a random process contributes to the PSD as:

A. A constant value across all frequencies.
B. An impulse (delta function) at .
C. Zero value.
D. A Gaussian pulse.

35 Real, wide-sense stationary noise with PSD is passed through an ideal low-pass filter with cutoff frequency . The output noise power is:

A.
B. (or if is in Hz)
C. $0$
D.

36 If , the process is:

A. Periodic.
B. White noise.
C. Not periodic (aperiodic).
D. Unbounded.

37 The inequality is a form of:

A. Cauchy-Schwarz inequality.
B. Markov inequality.
C. Chebyshev inequality.
D. Wiener-Khinchin theorem.

38 For a periodic WSS process with period , the autocorrelation function is:

A. Zero everywhere.
B. Periodic with period .
C. Decaying exponentially.
D. A delta function.

39 The spectral components of two different uncorrelated random processes are:

A. Identical.
B. Uncorrelated.
C. Orthogonal.
D. Summed.

40 What is the physical unit of Power Spectral Density if is a voltage signal?

A. Volts
B. Watts
C. Volts/Hz (or Watts/Hz into 1 Ohm)
D. Volts/Hz

41 If , where is a random variable with , the process is:

A. Ergodic.
B. Stationary but not Ergodic.
C. Neither Stationary nor Ergodic.
D. Time-varying.

42 The cross-correlation of input and output of a system can be used to determine:

A. The probability density of the input.
B. The impulse response of the system (if input is white noise).
C. The mean of the output only.
D. The total power.

43 If , the mean square value is:

A. 25
B. 1
C. Infinite (theoretically, for delta function) or undefined without bandwidth limits.
D. 26

44 If the PSD is a constant , the process is called:

A. Band-limited white noise.
B. Ideal white noise.
C. Pink noise.
D. Colored noise.

45 Which of the following functions cannot be a valid autocorrelation function?

A.
B.
C.
D. $1$

46 For a WSS process, if , the autocorrelation is:

A.
B.
C.
D.

47 If and are independent WSS processes, the autocorrelation of their sum is:

A.
B.
C.
D.

48 A random process where is uniformly distributed in is:

A. WSS but not SSS.
B. Not stationary.
C. WSS.
D. Non-ergodic.

49 The Power Spectral Density of the derivative of a process, , is related to by:

A.
B.
C.
D.

50 Which of the following is true for the Real part of the Cross-PSD, ?

A. It is an odd function of .
B. It is an even function of .
C. It is always zero.
D. It is always negative.