week 5 Flashcards
which is more effective: sampling MORE times per cycle or less?
sampling more times per cycle
aliasing
when a signal is discretely sampled at an insufficient range to catch changes in the signals
2 faults with aliasing
- different signals become indistinguishable
- components of digitized signals at high frequencies get mistaken for components at low freuencies
how to avoid aliasing?
sampling rate should be greater than or equal to TWICE the highest frequency present in the signal
what sampling frq should be used to digitize this signal?
A(t) = 5sin(4pit) + 2sin(8pit) + 3sin(12pi*t)
use 12 sampling frequency and sample 6 times per signal
highest frequency component
signal that defines the sampling frequency (fs)
smallest frequency component
signal that defines the period of the signal (T)
what does lower sampling frequency look like graphically?
the graph is jagged
what does higher sampling frequency look like graphically?
the graph is loopy (too curvy/wavy)
common post-processing operations
shifting, scaling, and noise reduction
shifting/offsetting/DC shifting
adding a constant value to each data point
F2(t) = F(t) + C
scaling
multiplying each data point by a constant value to amplify or attenuate the signal
F2(t) = F(t) * C
scaling
C>1 does what?
amplifies the signal
scaling
C<1 does what?
attenuates the signal
noise reduction
reduce noise in measured signal
2 methods of noise reduction
signal averaging and signal smoothing/filtering
signal averaging
reduces noise power of a signal, best when frequency spectra of the signal and noise overlap
2 steps of signal averaging
1) average all even numbered signals
2) average all odd numbered signals
equation for estimation of noise in signal averaging
noise = average_odd - average_even
how do you calculate the average of even data points in matlab?
avg_even = mean(noisy_signal(2:2:end, :))
how do you calculate the average of odd data points in matlab?
avg_odd = mean(noisy_signal(1:2:end, :))
how do you calculate SNR in matlab
rmsy = sqrt(mean(y2 .^ 2))
rmsnoise = sqrt(mean(error.^2))
SNR = 20* log10(rmsy/rmsnoise)
filters
used to remove unwanted parts of data
moving average filter
most common digital signal processing method replaces each data value with the average of itself and nearby data points
types of moving average filters
symmetrical, asymmetrical, weighted, and unweighted
symmetrical moving average filter
replace data point with average of itself and next door neighbors
asymmetrical moving average filter
replace data point with average of itself and future OR past values, its asymmetric so it’s one way or the other
when are moving average filters useful?
for time domain encoded signals
it smooths data
reduces energy occupying the high-frequency end of the signal frequency spectrum.
removes random noise
weighted moving average filter
replaces each value with average of nearby data points and fives MOST weight to data point being replaces and LEAST to points further away
weighted moving average filter weight example
*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)
in signal averaging
noise average will approach ___ while number of signals in average approaches _____
0
inf
