week 5

Question 1

which is more effective: sampling MORE times per cycle or less?

Answer 1

sampling more times per cycle

Question 2

aliasing

Answer 2

when a signal is discretely sampled at an insufficient range to catch changes in the signals

Question 3

2 faults with aliasing

Answer 3

1. different signals become indistinguishable
2. components of digitized signals at high frequencies get mistaken for components at low freuencies

Question 4

how to avoid aliasing?

Answer 4

sampling rate should be greater than or equal to TWICE the highest frequency present in the signal

Question 5

what sampling frq should be used to digitize this signal?
A(t) = 5sin(4pit) + 2sin(8pit) + 3sin(12pi*t)

Answer 5

use 12 sampling frequency and sample 6 times per signal

Question 6

highest frequency component

Answer 6

signal that defines the sampling frequency (fs)

Question 7

smallest frequency component

Answer 7

signal that defines the period of the signal (T)

Question 8

what does lower sampling frequency look like graphically?

Answer 8

the graph is jagged

Question 9

what does higher sampling frequency look like graphically?

Answer 9

the graph is loopy (too curvy/wavy)

Question 10

common post-processing operations

Answer 10

shifting, scaling, and noise reduction

Question 11

shifting/offsetting/DC shifting

Answer 11

adding a constant value to each data point
F2(t) = F(t) + C

Question 12

scaling

Answer 12

multiplying each data point by a constant value to amplify or attenuate the signal
F2(t) = F(t) * C

Question 13

scaling
C>1 does what?

Answer 13

amplifies the signal

Question 14

scaling
C<1 does what?

Answer 14

attenuates the signal

Question 15

noise reduction

Answer 15

reduce noise in measured signal

Question 16

2 methods of noise reduction

Answer 16

signal averaging and signal smoothing/filtering

Question 17

signal averaging

Answer 17

reduces noise power of a signal, best when frequency spectra of the signal and noise overlap

Question 18

2 steps of signal averaging

Answer 18

1) average all even numbered signals
2) average all odd numbered signals

Question 19

equation for estimation of noise in signal averaging

Answer 19

noise = average_odd - average_even

Question 20

how do you calculate the average of even data points in matlab?

Answer 20

avg_even = mean(noisy_signal(2:2:end, :))

Question 21

how do you calculate the average of odd data points in matlab?

Answer 21

avg_odd = mean(noisy_signal(1:2:end, :))

Question 22

how do you calculate SNR in matlab

Answer 22

rmsy = sqrt(mean(y2 .^ 2))
rmsnoise = sqrt(mean(error.^2))
SNR = 20* log10(rmsy/rmsnoise)

Question 23

filters

Answer 23

used to remove unwanted parts of data

Question 24

moving average filter

Answer 24

most common digital signal processing method replaces each data value with the average of itself and nearby data points

Question 25

types of moving average filters

Answer 25

symmetrical, asymmetrical, weighted, and unweighted

Question 26

symmetrical moving average filter

Answer 26

replace data point with average of itself and next door neighbors

Question 27

asymmetrical moving average filter

Answer 27

replace data point with average of itself and future OR past values, its asymmetric so it’s one way or the other

Question 28

when are moving average filters useful?

Answer 28

for time domain encoded signals
it smooths data
reduces energy occupying the high-frequency end of the signal frequency spectrum.
removes random noise

Question 29

weighted moving average filter

Answer 29

replaces each value with average of nearby data points and fives MOST weight to data point being replaces and LEAST to points further away

Question 30

weighted moving average filter weight example

Answer 30

*relative to the data point being replaces
2 indices before/after -> multiply by one
1 index before/after -> multiply by two
index of interest -> multiply by 3

average by summing all that up and dividing by (1+2+3+2+1) (sum of multiples)

Question 31

in signal averaging
noise average will approach ___ while number of signals in average approaches _____

Answer 31

0
inf