Time domain analysis

Question 1

signal in time domain main characteristics

Answer 1

-peak to peak amplitude
-max positive value
-max negative amplitude

Question 2

mean value formula

Answer 2

lim(T–>inf) 1/T *int(0,T)(x(t)dt)

Question 3

mean value formula in discrete domain

Answer 3

sum(x(ti)/n)

Question 4

mean square value formula

Answer 4

lim(T–>inf) 1/T *int(0,T)(x(t)^2 dt)

Question 5

root mean square (RMS) formula

Answer 5

sqrt(lim(T–>inf) 1/T *int(0,T)(x(t)^2 dt)) = sqrt(mean square value)

Question 6

what does the mean square value rapresents

Answer 6

the power of a signal

Question 7

why sometimes the RMS is preferred wrt the mean square value

Answer 7

because it has the advantage of having the same units of the signal to which is referred

Question 8

variance formula

Answer 8

lim(T–>inf) 1/T *int(0,T)((x(t)-mu(x))^2 dt)

Question 9

standard deviation formula

Answer 9

sqrt(variance)

Question 10

mean, variance and rms relationship

Answer 10

sigma^2 = rms^2 - mu^2 = psi^2 - mu^2

(sigma^2=variance
sigma=standard deviation=STD
mu=mean
psi=root mean square value
psi^2=mean square value)

Question 11

what does mu (mean) represents

Answer 11

the static behaviour of our signal

Question 12

what does the variance represents

Answer 12

it describes the dynamics of our signal

Question 13

typical application of crest factor index

Answer 13

detect the presence of damage in rotating machineries.
generally the crest factor is usefull to find spikes

Question 14

what is the probability density function P(x)

Answer 14

is the probability that an instantaneous value of a signal is between x and x +delta x divided by the interval amplitude delta x

Question 15

which statistical parameter can i compute knowing the signal probability density function

Answer 15

mean value, mean square value, variance

Question 16

what is the skewness coefficient

Answer 16

it defines any distribution asymmetry around its sample mean value, -negative skewness = data are more on the left side wrt the mean value

Question 17

what is the kurtosis coefficient

Answer 17

is an index of distribution width,
-positive kurtosis = sharper distribution than a normal (gaussian) one
-negative kurtosis = flatter distribution

it’s a good tool to identify the presence of peaks in signals, usually it gives a more stable value than the crest factor since it works on the whole time record

Question 18

usual value of skewness

Answer 18

-1.5<skewness<1.5