Electronic – Resonant frequency in parallel

The problem is, I feel, in your thinking. The unit impulse does contain all frequencies and therefore, the RMS value of the particular frequency that corresponds with your filter's resonant frequency is infinitely small.

But, you might say that your filter's bandwidth is still quite wide so the energy of the spectrum around your resonance is not infinitely small. However, all the "in-band" frequencies that are "stimulating" your filter are incoherent and you can't expect to see those energies translated to one clear and obvious sinewave.

If you are connecting a resistor in series with 1 or more LEDs do this:

You will need to know the voltage drop beetwen LEDs (normally around 2V per LED) and the voltage input. The voltage that gonna drop beetwen your resistor is what didn't drop in the LEDs. So:

$$V_{in} = V_r + V_{led}$$

$$V_r = V_{in} - V_{led}$$

Then the current going thought the resistor gonna be the current you want to flow in the LEDs, most of the time I use 10mA, the max the LED can handle is normally around 20mA. That will determine how much bright your LED gonna be.

With your resistor voltage and current you can use ohms law to calculate its resistance.

$$V=R \cdot I$$

One thing to pay attention is the power dessipated in the resistor.

$$P=V_r\cdot I_r$$

If you have parallel LED association I would consider using this to calculate a resistor for each parallel. The problem with using only one resistor is that all the current from each LED will go though this resistor, so it may need to have a better power rate. Even if you get a resistor that has a good power rate you may consider calculating separated LED resistors because power rate won't prevent it from heating up.