Building Signals with Blocks

Question 1

what are bases?

Answer 1

elementary signals

Question 2

a complex signal gets ________ into elementary signals

Answer 2

decomposed

Question 3

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

Answer 3

weights

Question 4

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

Answer 4

bases

Question 5

what are the building blocks of signals?

Answer 5

bases

Question 6

what do bases represent?

Answer 6

arbitrary signals as weighted products

Question 7

how are bases scaled?

Answer 7

with different weights

Question 8

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

Answer 8

sufficiently different from each other

Question 9

how are complex/arbitrary signals represented?

Answer 9

by weighted integrals/sums of bases signals

Question 10

define integral (as defined by this video)

Answer 10

sum of large number of terms; limiting form

Question 11

define integral (as defined by mathematics)

Answer 11

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.

Question 12

define transform

Answer 12

conversion of signal amplitudes to weighted bases

Question 13

what are some example transforms?

Answer 13

discrete, fourier, wavelet, and cosine transforms

Question 14

any signal with N values can be represented by…

Answer 14

N linearly independent bases signals

Question 15

is there an optimal bases technique?

Answer 15

No

Question 16

what are some examples of bases techniques?

Answer 16

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

Question 17

what bases are used in Fourier transform analysis?

Answer 17

sinusoids

Question 18

define sinusoids

Answer 18

Eigenfunctions of Linear Time Invariant systems

Question 19

define Eigenfunctions

Answer 19

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

Question 20

define LTI

Answer 20

Linear Time Invariant system

Question 21

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

x[n] = Acos(wn)

Answer 21

also a sinusoid

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

Question 22

define x[n] = Acos(wn)

Answer 22

sinusoidal input to LTI system

Question 23

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

Answer 23

sinusoidal output to LTI system

Question 24

sinusoidal input to LTI system

Answer 24

x[n] = Acos(wn)

Question 25

sinusoidal output to LTI system

Answer 25

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

Question 26

what do LTI systems modify?

Answer 26

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

Question 27

define wavelet

Answer 27

limited duration oscillatory signals

Question 28

frequency of a wavelet is inversely related to...

Answer 28

the duration in time of the wavelet

Question 29

what forms a bases?

Answer 29

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

Question 30

how are different wavelet bases made?

Answer 30

by changing the shape of the oscillations

Question 31

what are some example wavelets?

Answer 31

Haar, Daubechies, Coiflet

Question 32

define long duration wavelet

Answer 32

- broad in time - narrow in frequency - accurately captures frequency

Question 33

define short duration wavelet

Answer 33

- narrow in time - broad in frequency - accurately captures location of transient events - good for representing signals that differ in time/space

Question 34

what do good bases do?

Answer 34

concentrate energy into a few significant weights

Question 35

how do signals get turned to weights?

Answer 35

signals get transformed to weights using bases

Question 36

what is the goal of signal processing?

Answer 36

to concentrate component signals into relatively small number of bases signals

Question 37

how do you separate signals?

Answer 37

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

Question 38

how do you denoise a signal?

Answer 38

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

Question 39

how do you compress a signal?

Answer 39

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

Question 40

define bases expansion

Answer 40

express weighted sum of component signals