Can someone explain the relationship between high impedances and noise?
Thermal noise is generated in any conductor or resistor at all times.
https://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noiseIt originates from the thermal agitation of the charge carriers (electrons) within the resistor. Just sitting on a desk, a resistor is generating a wide-band, white noise called Johnson or Nyquist noise voltage with power equal to
P = v^2 = 4kTBR Watts where:
k is Boltzmanns constant, 1.38064852×10−23 J/K
T is absolute temperature in degrees kelvin above absolute zero,
B is the frequency bandwidth in Hertz that the noise voltage may be limited to by external circuitry, and
R is the resistor value in Ohms.
The noise voltage appears in series with the resistor if the resistor is considered as ideal and noiseless.
So a 100K resistor at room temp generates 128 nV RMS if limited to 10 Hz bandwidth. A typical audio system with a 47K input impedance and 20KHz bandwidth has an input noise level about 3.9 uV RMS or -108dB with respect to 1V RMS.
https://daycounter.com/Calculators/Thermal-Noise-Calculator.phtmlEven if the system is absolutely noiseless (impossible) it can't get any quieter than that.
This is why wide-band transmission systems are designed around a low impedances such as 50 or 75 Ohms.
Since you are dealing with a BW of only 10 Hz and driving LEDs you should not be worrying about noise levels in op-amp circuits at all. The noise voltages are just way too small to be bothered with.
Finally, what are your opinions on what approach is best?
1. Use high-R and low-C parts in the filter so C0G caps are an option
2. Distortion from X7R/X5R etc. caps are fine for this application, so use low-R and high-C parts
3. Do ramping and smoothing in the MCU so the filter can have a higher cutoff frequency and lower-valued parts all around
#1 - Sure - go for it.
#2 - Depends on the linearity you need. If you are making a precision VU meter then I would worry about distortion.
#3 - Depends on your sensitivity to parts cost and how much spare MCU compute-bandwidth you have. If doing that will allow you to use only a 1st-order filter and save 30 precious cents in parts in a high-volume device then there's that option, too.
Hope this helps