Measurements for Water: Meten aan water, signalen

Measurements for

water

Rolf Hut

Meten aan water: signalen

Challenge the future

DelftUniversity ofTechnology

Meten aan WaterSignalen

Rolf Hut

Friday, November 18, 2011

Signalen

Signalen

2

Friday, November 18, 2011

Signalen

Signalen

2

Friday, November 18, 2011

0 5 10 15 20 25 30 35 40 45 501

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

1

time in seconds

Ampl

itude

Signalen

Signalen

2

Friday, November 18, 2011

Signalen

Signalen

2

Friday, November 18, 2011

Signalen

Signalen

2

Friday, November 18, 2011

Signalen

Signalen

2

Friday, November 18, 2011

Signalen

Signalen

•signaal = verzameling (meet)waarden waarbij ordening van belang is

3

f : Cn → C

Friday, November 18, 2011

Signalen

Signalen

•signaal = verzameling (meet)waarden waarbij ordening van belang is

3

f : Cn → Cf : Rn → Cf : R → R 1-D real signal

Friday, November 18, 2011

•periodic signals

•Complex exponential functions

•Periodic Complex Signals

Signalen

Speciale Signalen

4

f (t) = f (t+ T )

f (t) = Ceat

f (t) = eiω0t

eiω0t = cosω0t+ j sinω0t

Friday, November 18, 2011

•Periodic Complex Signals

Signalen

Speciale Signalen

5

f (t) = eiω0t

eiω0t = cosω0t+ j sinω0t

Friday, November 18, 2011

•Periodic Complex Signals

Signalen

Speciale Signalen

5

f (t) = eiω0t

eiω0t = cosω0t+ j sinω0t

A cos (ω0t+ φ) =A

2eiφeiω0t +

A

2e−iφe−iω0t

Friday, November 18, 2011

Signalen

Speciale Signalen

•Step function

•Impulse function

6

u (t) =

�0, t < 0

1, t > 0

u (t) =

� t

−∞δ (t) dt

Friday, November 18, 2011

fp (t) =∞�

−∞f (nT ) δ (t− nT )

Signalen

Meet Signalen

7

Friday, November 18, 2011

fp (t) =∞�

−∞f (nT ) δ (t− nT )

Signalen

Meet Signalen

7

Friday, November 18, 2011

fp (t) =∞�

−∞f (nT ) δ (t− nT )

Signalen

Meet Signalen

7

Friday, November 18, 2011