1. Filters
A filter removes a signal’s unwanted frequency components.
Figure 6.18

2. Simple RC Filters Low Pass Filter: Passes low-frequencies
Figure 6.10
Low Pass Filter:
Passes low-frequencies
Removes high-frequencies
High Pass Filter:
Passes high-frequencies
Removes low-frequencies
The time constant, t, of a simple RC filter equals RC.

3. Filter Distortion of a Signal
A filter alters both the magnitude and the phase of the signal.
A: input signal
B: input signal with attenuation (amplitude reduction)
C: output signal with attenuation and phase lag
M (magnitude ratio)
= Eo/Ei
Figure 6.11
What are M and f for signal C?
Note: digital filters can be designed to have zero phase shift

4. Simple Low-Pass RC Filter with Sinusoidal-Input Forcing
Figures 5.3 and 5.4

5. Undesirable filter effects
Overfiltering: reducing / eliminating the desired signal
How does one avoid this?

6. Undesirable filter effects
Phase lag / time shift
How does one avoid this?

7. Undesirable filter effects
Transient filter ring-down (initial portion of data looks different)
All filters have this, just something to watch for

8. Analog vs. Digital filters

9. A/D Conversion Process
analog, discrete and digital signals
possible binary values
for 12-bit A/D converter
(10 V / 212 = 10 V / 4096
= 2.44 mV increments)
range of possible
analog amplitudes
assigned 2.44 mV
range from 1.22 mV
to 3.66 mV, which is
2.44 mV ± Q/2 for
12-bit A/D converter
Figure 6.15

10. In-Class Example A: What is the flow velocity if Dp = 58 Pa ?
A-B: Wheatstone bridge (pp ) where
Eo=Ei [ R1/(R1+R2) - R3/(R3+R4)] (Eqn.4.26)

11. In-Class Example A-B: What is Rx needed to give Eo =0 V at U = 0 m/s ?
A-B: At the highest U, R1 increases by 20 % because of
an increase in Rs. What is Eo at the highest U?
B-C: What is the amplifier gain to achieve 80 % of the
full-scale range of the A/D board at the highest U ?
B-C: If a non-inverting opamp is used (see p. 147), what
should be the values of its resistances ?

12. In-Class Example
C-D: What type of filter would be appropriate to use ?
D-E: What bit A/D board is required to have less than 0.2 %
error in the voltage reading of the highest-U condition ?