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

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.

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

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

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

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

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

Analog vs. Digital filters

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

In-Class Example A: What is the flow velocity if Dp = 58 Pa ? A-B: Wheatstone bridge (pp. 72-75) where Eo=Ei [ R1/(R1+R2) - R3/(R3+R4)] (Eqn.4.26)

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 ?

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 ?