1. Filters filters

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

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

4. Filter Distortion of a Signal Figure 6.11 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 What are M and  for signal C? Note: digital filters can be designed to have zero phase shift M (magnitude ratio) = E o /E i

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

6. Undesirable filter effects 1.Overfiltering: reducing / eliminating the desired signal How does one avoid this?

7. Undesirable filter effects 2.Phase lag / time shift How does one avoid this?

8. Undesirable filter effects 3.Transient filter ring-down (initial portion of data looks different) All filters have this, just something to watch for

9. Analog vs. Digital filters

10. Analog-to-Digital Conversion A/D converters

11. A/D Conversion Process Figure 6.15 possible binary values for 12-bit A/D converter (10 V / 2 12 = 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 analog, discrete and digital signals

12. In-Class Example A: What is the flow velocity if  p = 58 Pa ? U = √(2  p/  ) = √[(2)(58)/1.16] = 10 m/s A-B: Wheatstone bridge (pp. 72-75) where E o =E i [ R 1 /(R 1 +R 2 ) - R 3 /(R 3 +R 4 )] (Eqn.4.26) Here, R 2 =R 3 =R 4 =R= 100 Ω; E i = 5 V with R s = 200 Ω at U = 0 m/s

13. In-Class Example A-B: What is R x needed to give E o =0 V at U = 0 m/s ? Eqn. 4.26 gives E o = 0.23 V B-C: What is the amplifier gain to achieve 80 % of the full-scale range of the A/D board at the highest U ? Assume a 0 V to 10 V A/D board → G = (0.8)(10)/0.23 = 35 B-C: If a non-inverting opamp is used (see p. 147), what should be the values of its resistances ? G = 35 = E o /E i = 1 +R 2 /R 1 → R 2 /R 1 = 34 A-B: At the highest U, R 1 increases by 20 % because of an increase in R s. What is E o at the highest U? R 1 must be 100 Ω and 1/R 1 =1/R x + 1/R s → R s = 200 Ω

14. In-Class Example C-D: What type of filter would be appropriate to use ? A low-pass (anti-aliasing) filter with f cutoff = 1/(2  RC). 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 ? At the highest-U condition, E = 8 V → absolute quantization error (=Q/2) < (0.002)(8) = 0.016 V = 16 mV Now M = 8 → Q/2 = 19.6 mV and M = 12 → Q/2 = 1.22 mV So, a 12-bit A/D board will suffice.