Waves Slides adapted from Nirupam Roy Sound Visible light - - PowerPoint PPT Presentation

▶
waves
SMART_READER_LITE
LIVE PREVIEW

Waves Slides adapted from Nirupam Roy Sound Visible light - - PowerPoint PPT Presentation

Jan 30, 2023 211 likes •1.29k views

Waves Slides adapted from Nirupam Roy Sound Visible light Physical vibrations WiFi signal Ripples in water Infrared Mechanical Wave Electromagnetic Wave Sound Visible light Physical vibrations WiFi signal Ripples in water

slide-1
SLIDE 1

Waves

Slides adapted from Nirupam Roy

slide-2
SLIDE 2

Sound WiFi signal Physical vibrations Visible light Ripples in water Infrared … …

slide-3
SLIDE 3

Sound WiFi signal Physical vibrations Visible light Ripples in water Infrared … … Mechanical Wave Electromagnetic Wave

slide-4
SLIDE 4

Waves made this possible

slide-5
SLIDE 5

Waves made this possible

slide-6
SLIDE 6

Equation of waves in time and space

slide-7
SLIDE 7

Equation of waves in time and space

Temporal variation of the wave’s amplitude

slide-8
SLIDE 8

Equation of waves in time and space

slide-9
SLIDE 9

Frequency, Amplitude, and Phase

slide-10
SLIDE 10

Time

Frequency, Amplitude, and Phase

𝑔 𝑑𝑧𝑑𝑚𝑓𝑡 𝑞𝑓𝑠 𝑡𝑓𝑑𝑝𝑜𝑒 2𝜌 𝑏𝑜𝑕𝑚𝑓𝑡 𝑞𝑓𝑠 𝑑𝑧𝑑𝑚𝑓

slide-11
SLIDE 11

𝚺

A . sin(𝜄(𝑢))

A

= = A . sin(2𝜌𝑔𝑢)

time = t second

Frequency, Amplitude, and Phase

𝑔 𝑑𝑧𝑑𝑚𝑓𝑡 𝑞𝑓𝑠 𝑡𝑓𝑑𝑝𝑜𝑒 2𝜌 𝑏𝑜𝑕𝑚𝑓𝑡 𝑞𝑓𝑠 𝑑𝑧𝑑𝑚𝑓

Phase

Ψ(t) = A . sin(2𝜌 𝑈 𝑢)

𝑃𝑜𝑓 𝑔𝑣𝑚𝑚 𝑑𝑧𝑑𝑚𝑓 𝑗𝑜 𝑈 𝑡𝑓𝑑𝑝𝑜𝑒𝑡 i.e., 𝑔 =

! "

slide-12
SLIDE 12

Equation of waves in time and space

slide-13
SLIDE 13

Equation of waves in time and space

slide-14
SLIDE 14

Equation of waves in time and space

slide-15
SLIDE 15

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓

slide-16
SLIDE 16

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓 Amplitude here is a delayed version of the amplitude here.

slide-17
SLIDE 17

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓 Amplitude here is a delayed version of the amplitude here.

slide-18
SLIDE 18

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓 Amplitude here is a delayed version of the amplitude here. The delay depends

  • n the distance.
slide-19
SLIDE 19

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓 Amplitude here is a delayed version of the amplitude here. The delay depends

  • n the distance.

= A . sin(2𝜌𝑔𝑢) Ψ(t) = A . sin(2𝜌 𝑈 𝑢)

slide-20
SLIDE 20

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓 Amplitude here is a delayed version of the amplitude here. The delay depends

  • n the distance.

= A . sin(2𝜌𝑔𝑢 − 𝜄(𝑦)) Ψ(t, x)

Why is this negative?

slide-21
SLIDE 21

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓

= A . sin(2𝜌𝑔𝑢 − 𝜄(𝑦)) Ψ(t, x)

w𝑏𝑤𝑓𝑚𝑓𝑜𝑕𝑢ℎ = λ

slide-22
SLIDE 22

Equation of waves in time and space w𝑏𝑤𝑓𝑚𝑓𝑜𝑕𝑢ℎ = λ 𝑔 𝑜𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑑𝑧𝑑𝑚𝑓𝑡 𝑞𝑓𝑠 𝑡𝑓𝑑𝑝𝑜𝑒 𝐷 𝑛𝑓𝑢𝑓𝑠𝑡 𝑝𝑔 𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑞𝑓𝑠 𝑡𝑓𝑑𝑝𝑜𝑒 (𝑡𝑞𝑓𝑓𝑒 𝑝𝑔 𝑢ℎ𝑓 𝑥𝑏𝑤𝑓) 𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑞𝑓𝑠 𝑑𝑧𝑑𝑚𝑓 = λ = 𝐷 / 𝑔

slide-23
SLIDE 23

Equation of waves in time and space w𝑏𝑤𝑓𝑚𝑓𝑜𝑕𝑢ℎ = λ 𝑔 𝑜𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑑𝑧𝑑𝑚𝑓𝑡 𝑞𝑓𝑠 𝑡𝑓𝑑𝑝𝑜𝑒 𝐷 𝑛𝑓𝑢𝑓𝑠𝑡 𝑝𝑔 𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑞𝑓𝑠 𝑡𝑓𝑑𝑝𝑜𝑒 (𝑡𝑞𝑓𝑓𝑒 𝑝𝑔 𝑢ℎ𝑓 𝑥𝑏𝑤𝑓) 𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑞𝑓𝑠 𝑑𝑧𝑑𝑚𝑓 = λ = 𝐷 / 𝑔 2𝜌 𝑠𝑏𝑒𝑗𝑏𝑜𝑡 𝑝𝑔 𝑏𝑜𝑕𝑚𝑓 𝑗𝑡 𝑑𝑝𝑤𝑓𝑠𝑓𝑒 𝑞𝑓𝑠 𝑑𝑧𝑑𝑚𝑓

slide-24
SLIDE 24

w𝑏𝑤𝑓𝑚𝑓𝑜𝑕𝑢ℎ = λ 𝑔 𝑜𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑑𝑧𝑑𝑚𝑓𝑡 𝑞𝑓𝑠 𝑡𝑓𝑑𝑝𝑜𝑒 𝐷 𝑛𝑓𝑢𝑓𝑠𝑡 𝑝𝑔 𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑞𝑓𝑠 𝑡𝑓𝑑𝑝𝑜𝑒 (𝑡𝑞𝑓𝑓𝑒 𝑝𝑔 𝑢ℎ𝑓 𝑥𝑏𝑤𝑓) 𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑞𝑓𝑠 𝑑𝑧𝑑𝑚𝑓 = λ = 𝐷 / 𝑔 2𝜌 𝑠𝑏𝑒𝑗𝑏𝑜𝑡 𝑝𝑔 𝑏𝑜𝑕𝑚𝑓 𝑗𝑡 𝑑𝑝𝑤𝑓𝑠𝑓𝑒 𝑞𝑓𝑠 𝑑𝑧𝑑𝑚𝑓 Equation of waves in time and space 2𝜌 λ 𝑠𝑏𝑒𝑗𝑏𝑜𝑡 𝑝𝑔 𝑏𝑜𝑕𝑚𝑓 𝑗𝑡 𝑑𝑝𝑤𝑓𝑠𝑓𝑒 𝑞𝑓𝑠 𝑣𝑜𝑗𝑢 𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓

slide-25
SLIDE 25

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓

= A . sin(2𝜌𝑔𝑢 − 𝜄(𝑦)) Ψ(t, x)

w𝑏𝑤𝑓𝑚𝑓𝑜𝑕𝑢ℎ = λ

= A . sin(2𝜌𝑔𝑢 − 2𝜌 λ 𝑦)

slide-26
SLIDE 26

Model for a signal (frequency, amplitude, and phase)

𝑓𝑘 2πft

slide-27
SLIDE 27

Presenting real signal with the complex model

𝑑𝑝𝑡 2πft

=

𝑓𝑘 2πft 𝑓

_𝑘 2πft

+

2

𝑡𝑗𝑜 2πft

=

𝑓𝑘 2πft 𝑓

_𝑘 2πft

−

2j

𝑑𝑝𝑡 2πft + 𝑘 sin 2πft =

𝑓𝑘 2πft

𝑑𝑝𝑡 2πft − 𝑘 sin 2πft =

𝑓

_𝑘 2πft

slide-28
SLIDE 28

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓

Ψ(t, x)

w𝑏𝑤𝑓𝑚𝑓𝑜𝑕𝑢ℎ = λ

= A . sin(2𝜌𝑔𝑢 − 2𝜌 λ 𝑦)

slide-29
SLIDE 29

Equation of waves in time and space

𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝑔𝑠𝑝𝑛 𝑢ℎ𝑓 𝑡𝑝𝑣𝑠𝑑𝑓 (𝑦) 𝑡𝑞𝑏𝑑𝑓

Ψ(t, x)

w𝑏𝑤𝑓𝑚𝑓𝑜𝑕𝑢ℎ = λ

= A . e 𝑘(2𝜌𝑔𝑢 − 2𝜌

λ 𝑦)

slide-30
SLIDE 30

Time and space

Cycles per sec = frequency = f Hz Distance per second = speed = C meters/sec Distance per cycle = wavelength = λ meters

C = f . λ

Speed of sound in air: 343 m/s Speed of sound in water: 1493 m/s Speed of sound in iron: 5130 m/s Speed of electromagnetic waves: 3*108 m/s (~ a million times faster than sound)

slide-31
SLIDE 31

Time and space

A . sin(2𝜌𝑔𝑢)

slide-32
SLIDE 32

Time and space A . e

𝑘(2𝜌𝑔𝑢)

slide-33
SLIDE 33

Time and space

Distance = d meter

A . e

𝑘(2𝜌𝑔𝑢)

slide-34
SLIDE 34

Distance = d meter

Time and space A . e

𝑘(2𝜌𝑔𝑢 − 2𝜌 λ 𝑒)

A . e

𝑘(2𝜌𝑔𝑢)

slide-35
SLIDE 35

Distance = d meter

d meter

Time and space A . e

𝑘(2𝜌𝑔𝑢 − 2𝜌 λ 𝑒)

A . e

𝑘(2𝜌𝑔𝑢 − 2𝜌 λ 𝑒)

A . e

𝑘(2𝜌𝑔𝑢)

slide-36
SLIDE 36

Distance = d meter

d meter

Time and space A . e

𝑘(2𝜌𝑔𝑢 − 2𝜌 λ 𝑒)

A . e

𝑘(2𝜌𝑔𝑢 − 2𝜌 λ 𝑒)

A . e

𝑘(2𝜌𝑔𝑢)

slide-37
SLIDE 37

Time and space A . e

𝑘(2𝜌𝑔𝑢)

slide-38
SLIDE 38

Time and space A . e

𝑘(2𝜌𝑔𝑢)

X meters

slide-39
SLIDE 39

𝚺

Time and space

X meters

A . e

𝑘(2𝜌𝑔𝑢)

slide-40
SLIDE 40

𝚺

X.sin(𝚺)

Time and space

X meters

A . e

𝑘(2𝜌𝑔𝑢)

slide-41
SLIDE 41

d = X.sin(𝚺)

𝚺

Time and space

X meters

A . e

𝑘(2𝜌𝑔𝑢)

slide-42
SLIDE 42

d = X.sin(𝚺)

𝚺

Time and space

X meters

A . e

𝑘(2𝜌𝑔𝑢)

slide-43
SLIDE 43

Reflection of waves

slide-44
SLIDE 44

Reflection

slide-45
SLIDE 45

𝚺 𝚺

Reflection

slide-46
SLIDE 46

𝚺 𝚺

d1 d2

Reflection

slide-47
SLIDE 47

echo

Absorption + Reflection

Reflection

slide-48
SLIDE 48

Time = t1

Reflection

slide-49
SLIDE 49

Time = t1

Absorption + Reflection

Reflection

slide-50
SLIDE 50

t2 Time = t1 echo

Absorption + Reflection

Reflection

slide-51
SLIDE 51

Sound travelled (2d) distance d t2 Time = t1 echo

Absorption + Reflection

Reflection

slide-52
SLIDE 52

Sound travelled (2d) distance d t2 Time = t1 C.(t2-t1) = 2d echo

Absorption + Reflection

Reflection

slide-53
SLIDE 53

Sound travelled (2d) distance d t2 Time = t1 C.(t2-t1) = 2d echo

Echolocation

Absorption + Reflection

Reflection

slide-54
SLIDE 54

Echolocation in nature

Bat

slide-55
SLIDE 55

Echolocation in nature

Beluga whale

slide-56
SLIDE 56

Waves for gesture detection [Project Soli]

slide-57
SLIDE 57

57

LiDAR (Light Detection and Ranging)

slide-58
SLIDE 58

58

LiDAR (Light Detection and Ranging)

slide-59
SLIDE 59

Acoustic imaging

slide-60
SLIDE 60

Acoustic imaging

Sonogram

slide-61
SLIDE 61

Acoustic imaging

Sonogram

slide-62
SLIDE 62

Multipath

slide-63
SLIDE 63

Multipath

slide-64
SLIDE 64

Multipath

slide-65
SLIDE 65

Multipath: Convolution

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

slide-66
SLIDE 66

Multipath: Convolution

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

Direct path

slide-67
SLIDE 67

Multipath: Convolution

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

Direct path Echo

slide-68
SLIDE 68

Multipath: Convolution

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

Direct path Echo

slide-69
SLIDE 69

Multipath: Convolution

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

Direct path Echo

slide-70
SLIDE 70

Multipath: Convolution

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

Amplitude

0.25 0.50 0.75 1.00 1.25

Time (sec)

0.00

slide-71
SLIDE 71

Multipath: Convolution

Amplitude

0.75

Time (sec)

0.00

slide-72
SLIDE 72

Multipath: Convolution

Amplitude

0.75

Time (sec)

0.00

slide-73
SLIDE 73

Amplitude Time (sec) Impulse/ Dirac delta function

Impulse response

a 𝜀(x-a)

Environment (reflections, absorption, attenuation etc.) Impulse Response

slide-74
SLIDE 74

Linear Time Invariant (LTI) System

slide-75
SLIDE 75

Linear Time Invariant (LTI) System

Amplitude

0.75

Time (sec)

0.00

+ + =

slide-76
SLIDE 76

Impulse response

slide-77
SLIDE 77

SYSTEM Impulse Response Impulse

Impulse response

slide-78
SLIDE 78

SYSTEM Impulse Response Input Input

* Impulse response

Convolution

  • perator
slide-79
SLIDE 79

Convolution operator

slide-80
SLIDE 80

Convolution operator: Definition

slide-81
SLIDE 81

Convolution operator: Properties

slide-82
SLIDE 82

Convolution operator

slide-83
SLIDE 83

A simple acoustic ranging technique

BeepBeep – SenSys 2007

slide-84
SLIDE 84

Device A Device B Distance = d

slide-85
SLIDE 85

Device A Device B Distance = d

Time = t1

slide-86
SLIDE 86

Device A Device B Distance = d

Time = t1 Time = t2

slide-87
SLIDE 87

Device A Device B Distance = d

Time = t1 Time = t2 Time = t1

Bluetooth/WiFi

slide-88
SLIDE 88

Device A Device B Distance = d

Time = t1 Time = t2 Time = t1

Bluetooth/WiFi

d = C . (t2-t1)

slide-89
SLIDE 89

Device A Device B Distance = d

Time = t1 Time = t2 Time = t1

Bluetooth/WiFi

d = C . (t2-t1)

Problem: Clock synchronization

slide-90
SLIDE 90

The root cause of inaccuracy – three uncertainties

  • Clock synchronization uncertainty

time

slide-91
SLIDE 91

The root cause of inaccuracy – three uncertainties

  • Clock synchronization uncertainty
  • Sending uncertainty

time

slide-92
SLIDE 92

Sound production and recording

slide-93
SLIDE 93

Sound

Sound recording with microphone

slide-94
SLIDE 94

Sound Analog signal (voltage) ADC

Sound recording with microphone

ADC = Analog-to-Digital Converter

slide-95
SLIDE 95

Sound Analog signal (voltage) ADC Audio Sample Buffer S6 S5 S4 S3 S2 S1 S0

Sound recording with microphone

ADC = Analog-to-Digital Converter

slide-96
SLIDE 96

Audio Sample Buffer S6 S5 S4 S3 S2 S1 S0

Sound production with speaker

slide-97
SLIDE 97

Audio Sample Buffer S6 S5 S4 S3 S2 S1 S0 DAC Analog signal (voltage)

Sound production with speaker

DAC = Digital-to-Analog Converter

slide-98
SLIDE 98

Audio Sample Buffer S6 S5 S4 S3 S2 S1 S0 DAC Analog signal (voltage) Sound

Sound production with speaker

DAC = Digital-to-Analog Converter

slide-99
SLIDE 99

The root cause of inaccuracy – three uncertainties

  • Clock synchronization uncertainty
  • Sending uncertainty

time

... t0 = wall_clock(); write(sound_dev, signal); ...

software issuing command

slide-100
SLIDE 100

The root cause of inaccuracy – three uncertainties

  • Clock synchronization uncertainty
  • Sending uncertainty

time

... t0 = wall_clock(); write(sound_dev, signal); ...

software issuing command sound leaves speaker

unknown delays (software, system, driver, hardware, …)

?

slide-101
SLIDE 101

The root cause of inaccuracy – three uncertainties

  • Clock synchronization uncertainty
  • Sending uncertainty

time

... t0 = wall_clock(); write(sound_dev, signal); ...

software issuing command sound leaves speaker

unknown delays (software, system, driver, hardware, …)

?

  • Receiving uncertainty
slide-102
SLIDE 102

The root cause of inaccuracy – three uncertainties

  • Clock synchronization uncertainty
  • Sending uncertainty

time

... t0 = wall_clock(); write(sound_dev, signal); ...

software issuing command sound leaves speaker

unknown delays (software, system, driver, hardware, …)

?

sound reaches mic

  • Receiving uncertainty
slide-103
SLIDE 103

The root cause of inaccuracy – three uncertainties

  • Clock synchronization uncertainty
  • Sending uncertainty

time

... t0 = wall_clock(); write(sound_dev, signal); ...

software issuing command sound leaves speaker

unknown delays (software, system, driver, hardware, …)

?

sound reaches mic

unknown delays (hardware, interrupt, driver, scheduling, …)

?

  • Receiving uncertainty
slide-104
SLIDE 104

The root cause of inaccuracy – three uncertainties

  • Clock synchronization uncertainty
  • Sending uncertainty

time

... t0 = wall_clock(); write(sound_dev, signal); ...

software issuing command sound leaves speaker

unknown delays (software, system, driver, hardware, …)

?

... read(sound_dev, signal); t1 = wall_clock(); ...

software aware of arrival sound reaches mic

unknown delays (hardware, interrupt, driver, scheduling, …)

?

  • Receiving uncertainty
slide-105
SLIDE 105

Beepbeep’s basic procedure

Device A Device B

A’s recording B’s recording

ETOAA ETOAB

  • 1. Device A emits a beep

while both recording

  • 2. Device B emits another

beep while both continue recording

  • 3. Both devices detect TOA
  • f the two beeps and
  • btain respective ETOAs
  • 4. Exchange ETOAs and

calculate the distance

slide-106
SLIDE 106

Dx,y is distance between x’s speaker to y’s microphone