Android : How to implement time-weighting in SPL Meter?

I would like to develop an android app to meassure sound pressure level but i am not sure how to implement time weighting. For the moment my algorithm works as follows:

1. Record 20ms of audio (160 samples @ 8000Hz)


2. Compute RMS


3. Calculate SPL


4. Update displayed value and start again

Here you can see the main part of the algorithm:

// The Google ASR input requirements state that audio input sensitivity
// should be set such that 90 dB SPL at 1000 Hz yields RMS of 2500 for
// 16-bit samples, i.e. 20 * log_10(2500 / mGain) = 90.

double Gain = 2500.0 / Math.pow(10.0, 90.0 / 20.0);


// This method is called every 20ms:
@Override
public void processAudioFrame(short[] audioFrame) {

  // Compute the RMS value.
  double rms = 0;
  for (int i = 0; i < audioFrame.length; i++) {
    rms += audioFrame[i]*audioFrame[i];
  }
  rms = Math.sqrt(rms/audioFrame.length);

  final double rmsdB = 20.0 * Math.log10(rms / Gain) + refSPL;
  // refSPL is obtained by calibration with a professional spl meter
}

I know that the grade of sound level meter can be Fast, Slow, or Impulse time weighted. But i am not sure how and where to implement this time weighting in my algorithm.

Q: Does time weighting means after which time i update the meassured dB value?

Q: Should i simply change the update interval to 125ms to get a fast weighted result or am i completly wrong?

Thanks for your support