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Signal Processing > Building Signals with Blocks > Flashcards

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?

A

sinusoids

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
Q

sinusoidal output to LTI system

A

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

26
Q

what do LTI systems modify?

A

the amplitude and the phase of the sinusoid, angle H(w), applied to the input

27
Q

define wavelet

A

limited duration oscillatory signals

28
Q

frequency of a wavelet is inversely related to…

A

the duration in time of the wavelet

29
Q

what forms a bases?

A

a collected of wavelets of characteristic shape, but with different durations and onset locations

30
Q

how are different wavelet bases made?

A

by changing the shape of the oscillations

31
Q

what are some example wavelets?

A

Haar, Daubechies, Coiflet

32
Q

define long duration wavelet

A
  • broad in time
  • narrow in frequency
  • accurately captures frequency
33
Q

define short duration wavelet

A
  • narrow in time
  • broad in frequency
  • accurately captures location of transient events
  • good for representing signals that differ in time/space
34
Q

what do good bases do?

A

concentrate energy into a few significant weights

35
Q

how do signals get turned to weights?

A

signals get transformed to weights using bases

36
Q

what is the goal of signal processing?

A

to concentrate component signals into relatively small number of bases signals

37
Q

how do you separate signals?

A

1) transform signal mixture into weights using bases
2) set the weights of non-relevant signals to zero
3) reconstruct separate signals

38
Q

how do you denoise a signal?

A

1) transform noisy signal into weights using bases
2) set small weights to zero
3) reconstruct cleaned signal

39
Q

how do you compress a signal?

A

1) transform signal into weights using bases
2) store only the significant weights
3) reconstruct signal from significant weights

40
Q

define bases expansion

A

express weighted sum of component signals

Signal Processing (5 decks)

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