Measurements for

water

Rolf Hut

Meten aan water: filters

Challenge the future

DelftUniversity ofTechnology

Meten aan WaterFilters

Rolf Hut

Friday, November 18, 2011

h (t) =

�1, 0 < t < t00, else

g (t) =

� ∞

−∞f (τ)h (t− τ) dτ ↔ G (iω) = F (iω)H (iω)

Signalen

Filters

2

Friday, November 18, 2011

Signalen

Filters

3

Friday, November 18, 2011

Signalen

Filters: ideal low pass

4

Friday, November 18, 2011

Signalen

Filters: ideal low pass

4

Friday, November 18, 2011

Signalen

Filters: ideal low pass

4

Friday, November 18, 2011

Signalen

Filters: ideal low pass

4

Friday, November 18, 2011

Signalen

Filters: ideal low pass

4

Friday, November 18, 2011

Signalen

Filters ideal low pass

5

Friday, November 18, 2011

Signalen

Fourier transformatie

•Differentiate

•RC network, Low pass filter!

6

g (t) =d

dtf (t) ↔ G (iω) = iωF (iω)

H (iω) =1

1 +RCiω

Friday, November 18, 2011

Signalen

Filter = Systeem

•mass spring system

7

md2y (t)

dt2= x (t)− ky (t)− b

dy (t)

dt

ωn =

�k

m

ξ =b

2√km

H (iω) =1

�iωωn

�2+ 2ξ

�iωωn

�+ 1

Friday, November 18, 2011

x (t)

X (iω)

y (t)

Y (iω)

h (t)

H (iω)

y (t) =

� ∞

−∞x (τ)h (t− τ) dτ

Y (iω) =X (iω)H (iω)

Signalen

Filter = Systeem

8

LTI Systeeminput output

Friday, November 18, 2011