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final exam studying Flashcards

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1
Q

linspace

A

generates row vector of n-points (default is 100) between and including a & b
linspace(a, b, n)

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2
Q

transpose (special case)

A

.’ conjugates complex numbers

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3
Q

to conduct operations on vectors/matrices, the dimensions must be _______

A

the same

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4
Q

random function

A

generates random numbers based on input specifications

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5
Q

rand(3)

A

3 by 3 matrix with random numbers 0-1

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6
Q

rand(10, 1, 5)

A

10 by 10 of random numbers between 1-5

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7
Q

find function

A

locates non-zero elements and outputs indices

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8
Q

min/max functions

A

returns smallest/largest in each vector (for matrices, it’s for each column)

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9
Q

[M, I] = min(x)
what are M and I

A

M is the values, I is the indices

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10
Q

sortrows function

A

sorts matrix by specified column from smallest to largest (add ‘descend’ to flip)

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11
Q

symmetric error-bar function

A

errorbar(x, y, e)
e is the error

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12
Q

asymmetric error-bar function

A

errorbar(x, y, d, u)
histograms –> d is low error and u is high error
line graph–> d is negative error and u is positive

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13
Q

meshgrid function

A

creates 2d matrix for input vectors, (repeats the vector over and over)
[ X, Y] = meshgrid(x,y)

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14
Q

how to generate Z with results of meshgrid function?

remember [X, Y] = meshgrid(x,y)

A

Z = sin(X) .* cos(Y)

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15
Q

linear interpolation

A

estimating values at certain points based on existing ones
interp1(x,y, new_x)

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16
Q

cubic spline interpolation

A

smooths curve and minimizes errors (fitting interpolation)

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17
Q

least squares fitting

A

line of best fit for data based on the slope and intersection (goal is to minimize R)

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18
Q

linear regression

A

finds the linear function that best fits the data

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19
Q

polyfit function

A

returns coefficients of degree n that’s the best fit with least squares
polyfit(x, y, n)

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20
Q

polyval function

A

evaluates polynomial at each point of x
polyval(p, x)

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21
Q

diff function

A

calculates difference between consecutive elements

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22
Q

resistance and current (I = )

A

I = V/R

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23
Q

systems (in bioengineering)

A

groups of things that affect signal of interest

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24
Q

model (in bioengineering)

A

symbolic representations of process, system, or data collection

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25
signals (at their core)
variations in energy that carry info
26
types of signals
chemical, mechanical, electrical, and thermal energy
27
signals for communication in body?
chemical and bioelectrical energy
28
biotransducer
converts non-electrical energy to electrical signal
29
sensitivity
change in output for given change in input (dy/dx)
30
resolution
smallest change in input that changes the measurement
31
linearity
consistency of input/output relationship
32
repeatability
expected change in output for repeated changes in input
33
noise
change in output not related to input, unrelated to signal
34
measured signal
biosignal of interest + noise
35
encoding
step of processing signals, transducing body signals so they can be read, can be analog or digital
36
continous/analog signal
in terms of amplitude, has a defined amplitude at every point
37
continuous/analog signal
x(t)
38
continuous/analog domain
uncountable, may or may not be finite
39
discrete/digital signal
defined over discrete time domain
40
discrete/digital signal
x[t]
41
Ts
sample interval
42
t =
n*Ts = n/fs
43
fs =
1/Ts
44
signal measurement system
signal (analog)--> sensor/transducer --> signal processing --> sampling (digital)
45
sampling
slicing the signal into sequences at time interval (Ts)
46
systematic error
each measurement deviates from the value by a fixed amount (DC shift)
47
random error
noise (random variations)
48
biomedical sources of noise
physiological variability noise, environmental noise/interference, artifact, electronic noise (thermal, shot, white noise)
49
sinusoidal wave
Asin(w*t) = Asin(2*pi*f*t) = Asin(2*pi*t/T) w = frq in radians
50
root mean squared (RMS)
square the signal, calculate the mean, take sqrt
51
SNR (signal noise ratio)
higher SNR is better system
52
positive SNR means...
signal > noise
53
negative SNR means...
noise > signal
54
aliasing
when signal isn't sampled enough to capture changes, different signals become indistinguishable and high frq components and mistaken for low frq components
55
nyquist sampling theorum
to avoid aliasing, the sample rate should e twice the highest frequency component in signal ex: if highest is 12, signal should be sampled 24 times per cycle
56
smallest frequency component
defines the period of a signal (T), too low = jagged graph, too high= loopy graph
57
post-processing
operations after digitization, like shifting, scaling, and noise reduction
58
2 methods of noise reduction
signal averaging and signal filtering
59
signal averaging
reduces the noise power, best when the frq spectra of noise and signal overlap noise = average_odd - average_even
60
moving average filters
replace each data point with value of average and itself and nearby points
61
symmetrical moving average filter
3 point moving average: (Xt-1 + Xt + Xt+1) /3
62
asymmetrical moving average filter
3 point moving average: (Xt-2 + Xt-1 + Xt) / 3
63
weighted moving average
more weight to point being replaced and less to furthest away ((Xt-2 * 1) + (Xt-1 * 2) + (Xt * 3) + (Xt+1 * 2) (Xt+2 *1) / 9
64
3 classes of signal
periodic, aperiodic, transient (step-like)
65
periodic signals
every phase is the same, biosignals can be taken as periodic for analysis
66
aperiodic signals
exists over finite time frame, treated as periodic
67
transient signal
increases infinitely, hardest to treat
68
interpolate before averages
[rxy, lags] = xcorr(x, y, 'coeff')
69
correlation
comparison of two signals
70
correlation coefficient
number that signifies the correlation (-1 to 1)
71
crosscorrelation
correlating over many shifts/lags
72
lag
continuous variable of time to shift x(t) with respect to y(t)
73
peak correlation
tells us where signals are most similar
74
multiple correlations
shift wave to find best match for signal
75
autocorrelation
correlating signal with itself
76
plotting crosscorrelation
[rxy, lags] = xcorr(x,y, 'coeff') figure; plot(lags*Ts, rxy)
77
max correlation
[max_corr, max_shift] = max(rxy)
78
crosscovariance
similarity in deviation of two signals about the mean
79
covariance
similar to correlation but has the mean subtracted from the signal
80
frequency domain
shows how signal energy is distributed over a range of frequencies
81
2 components of frequency domain
magnitude (abs(Xf)) and phase (angle(Xf))
82
fourier series theorum
any periodic signal can be represented as a sum of sinusoids, more sinusoids = better summation X(f) = fft(x)
83
bandwidth
range of frequency domain
84
filters in frequency domain
reduce noise by limiting the bandwidth of range of interest
85
filter properties
filter type, bandwidth, attenuation slops
86
multiplication value
dependent on instantaneous frequency, (1 = keep, 0 = pass)
87
pass band
part of input signal you want to keep, passed to output without change
88
stop band
part of input signal you want to discard, ideally reduced to 0
89
cut-off frequency
between pass and stop bands
90
inverse fourier analysis
going back to time domain from frequency domain ifft(Xf, n) --> n-point trandformation
91
low pass filter
passes frequency (below fc) with minimal attenuation and attenuates higher frequency
92
high pass filter
passes frequency (above fc) with minimal attenuation and attenuates lower frequency
93
band-pass filter
allows specific interval of frequency to pass and stops the rest
94
band-stop filter
attenuates specific interval of frequency and passes the rest
95
notch-filter
attenuates signal within very narrow range of frequencies
96
filtfilt
digital filtering by processing x data forwards and backgrounds filfilt(B, A, X) filters in X direction w filter described in A and B
97
[B, A] = butter(N, Wn)
designs nth order butterworth filter with 0.0 < Wn < 1.0 (cut-off frq) returns numerator B and denominator A
98
butter(N, Wn, 'high')
high pass filter, removes low frequencies
99
butter(N, Wn, 'low')
low pass filter, removes high frequencies
100
butter(N, Wn, 'stop')
band-stop filter of WN [W1, W2]
101
event time
when signal passes the threshold
102
relative timing
time passed in between events
103
single events
time of physiological response to stimulus
104
latency
time of peak response
105
event detection
detect by setting and finding the threshold (min or max), jump forward by interval time
106
false negative
missing an event
107
identification features of events
amplitude, slopes, peaks
108
how do you avoid false positives/negatives?
with a good system and measurement system
109
false positive
detecting an event when none occurred
110
spatial data
data in space-time domain
111
digital images
represented as 2D matrix of pixels
112
resolution (in imaging)
number of pixels per unit length
112
voxel
3D pixel
113
dynamic range
number of gray levels in an image (2^bits)
113
histogram function
represents grayscale distribution (x = gray level, y = frequency)
114
115
quantization
digitizing the amplitude
116

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