Measurements for Water: Meten aan water filters
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Transcript of Measurements for Water: Meten aan water filters
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