Building Signals with Blocks Flashcards

Understand basis expansion and their role in signal processing

1
Q

what are bases?

A

elementary signals

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2
Q

a complex signal gets ________ into elementary signals

A

decomposed

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3
Q

assuming bases are known, what is an equivalent description for the signal?

A

weights

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4
Q

what must be known for weights to be an equivalent description for the signal?

A

bases

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5
Q

what are the building blocks of signals?

A

bases

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6
Q

what do bases represent?

A

arbitrary signals as weighted products

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7
Q

how are bases scaled?

A

with different weights

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8
Q

bases must be _____ in order for them to be scaled with different weights

A

sufficiently different from each other

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9
Q

how are complex/arbitrary signals represented?

A

by weighted integrals/sums of bases signals

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10
Q

define integral (as defined by this video)

A

sum of large number of terms; limiting form

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11
Q

define integral (as defined by mathematics)

A

a function of which a given function is the derivative, i.e. which yields that function when differentiated, and which may express the area under the curve of a graph of the function.

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12
Q

define transform

A

conversion of signal amplitudes to weighted bases

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13
Q

what are some example transforms?

A

discrete, fourier, wavelet, and cosine transforms

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14
Q

any signal with N values can be represented by…

A

N linearly independent bases signals

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15
Q

is there an optimal bases technique?

A

No

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16
Q

what are some examples of bases techniques?

A

sinusoids, PCA, Haar, Morlet, Synlet, etc…

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17
Q

what bases are used in Fourier transform analysis?

18
Q

define sinusoids

A

Eigenfunctions of Linear Time Invariant systems

19
Q

define Eigenfunctions

A

set of independent functions which are the solutions to a given differential equation.

20
Q

define LTI

A

Linear Time Invariant system

21
Q

what is the output if you put a sinusoid into an LTI system?

x[n] = Acos(wn)

A

also a sinusoid

y[n] = |H(w)|Acos(wn+ angle H(w))

22
Q

define x[n] = Acos(wn)

A

sinusoidal input to LTI system

23
Q

define y[n] = |H(w)|Acos(wn+ angle H(w))

A

sinusoidal output to LTI system

24
Q

sinusoidal input to LTI system

A

x[n] = Acos(wn)

25
sinusoidal output to LTI system
y[n] = |H(w)|Acos(wn+ angle H(w))
26
what do LTI systems modify?
the amplitude and the phase of the sinusoid, angle H(w), applied to the input
27
define wavelet
limited duration oscillatory signals
28
frequency of a wavelet is inversely related to...
the duration in time of the wavelet
29
what forms a bases?
a collected of wavelets of characteristic shape, but with different durations and onset locations
30
how are different wavelet bases made?
by changing the shape of the oscillations
31
what are some example wavelets?
Haar, Daubechies, Coiflet
32
define long duration wavelet
- broad in time - narrow in frequency - accurately captures frequency
33
define short duration wavelet
- narrow in time - broad in frequency - accurately captures location of transient events - good for representing signals that differ in time/space
34
what do good bases do?
concentrate energy into a few significant weights
35
how do signals get turned to weights?
signals get transformed to weights using bases
36
what is the goal of signal processing?
to concentrate component signals into relatively small number of bases signals
37
how do you separate signals?
1) transform signal mixture into weights using bases 2) set the weights of non-relevant signals to zero 3) reconstruct separate signals
38
how do you denoise a signal?
1) transform noisy signal into weights using bases 2) set small weights to zero 3) reconstruct cleaned signal
39
how do you compress a signal?
1) transform signal into weights using bases 2) store only the significant weights 3) reconstruct signal from significant weights
40
define bases expansion
express weighted sum of component signals