Test on Statistics for Digital Signal Processing

Question 1: Does the error in mean calculation typically cause the standard deviation (σ) of an acquired signal to appear higher than its actual value?

A. Ano

B. Ne

Explanation: The study materials state that the error in mean reduces the value of σ, meaning it causes the standard deviation of an acquired signal to appear lower than its actual value, not higher.

Question 2: According to the study materials, what are the limitations when calculating mean (μ) and standard deviation (σ) using the basic formulas?

A. If the mean (μ) is much greater than the standard deviation (σ), it can lead to excessive round-off error due to subtracting very close numbers.

B. Calculating running statistics requires all samples to be involved in each new calculation.

C. The formulas are inaccurate for nonstationary signals, which are generated from changing underlying processes.

D. The calculation of standard deviation only measures the DC portion of a signal, neglecting the AC portion.

Explanation: The study materials state two limitations for calculating mean and standard deviation: 'If μ >> σ → subtracting two numbers that are very close in value → excessive round off error' and that 'Running statistics → requires all samples be involved in each new calculation'. Option 2 refers to nonstationary signals, which is a problem addressed by a solution, but not a direct limitation of the basic calculation method itself, rather a characteristic of the signal. Option 3 is incorrect; the materials state that standard deviation 'Only measures AC portion of a signal'.

Question 3: Adding twelve random numbers together can create a signal with a Gaussian distribution.

A. Ano

B. Ne

Explanation: The study materials state that X = RND + … + RND (12 times) results in a Gaussian distribution, which can be used to create a normally distributed noise signal.

Question 4: In the second method for digital noise generation, to obtain a normally distributed random signal, the generated number is multiplied by the desired standard deviation and then the desired mean is added.

A. Ano

B. Ne

Explanation: The study materials state, 'Take each number generated by equation above Multiply it by desired standard deviation Add desired mean' as the final steps to generate normally distributed random signals using the second method.

Question 5: According to the second method for digital noise generation, why is a random number generator invoked twice to obtain R1 and R2?

A. To apply the central limit theorem by summing them.

B. To directly multiply them by the desired standard deviation.

C. To be used in a specific formula to calculate a normally distributed random number, X.

D. To ensure the mean of the generated signal is zero.

Explanation: The study materials state: 'Random number generator invoked twice to obtain R1 and R2 A normally distributed random number, X, is found ) 2 cos( ) log 2 ( 2 2 / 1 1 R R X e'. This clearly indicates R1 and R2 are used as inputs for the given formula to generate the normally distributed random number X.