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SPL will be calculated as described below:

  1. collect $N$ samples
  2. do FFT for the $N$ samples collected: the signal is now in the frequency domain.
  3. get magnitude of the FFT
  4. get RMS value of the FFT
  5. apply a time-weight filter to the RMS value
  6. apply a frequency-weight filter to the RMS value
  7. compute the SPL using the RMS value
  8. output data

Using variable as described below:

  • $N = 65536$
  • Sampling rate: 48KHz
  • calculate cycle: 0.5sec

In some documents, the method of adding time weights uses exponential moving averages:

$$y = \alpha y + (1 - α)y_{new}$$

What does $\alpha$ mean? How to add time weights in SPL operation?

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  • $\begingroup$ The time weightings Fast (0.125s) and Slow (1s) are done by using Exponential Weighted Moving Average. Basically, you don't want your SPL reading to jump around a lot. In analog domain this would be a simple RC low pass filter with a cut-off frequency $f_0=\frac{1}{2\pi\tau}$. In digital domain you would use an EWMA filter: $L_{N+i} = L_N e^{-i\cdot dt/\tau}$, where $\tau$ is your time constant and $dt$ is a sampling period. $\endgroup$
    – jojeck ♦
    Aug 10, 2022 at 18:31

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There are few things to consider here

  • After step 1 you probably want to apply a window (hanning, for example)
  • The choice or parameters is odd. The FFT is quite long with an FFT resolution of less than 1 Hz and an overlap of 63%. More common would be N = 8192 or N = 16384 with 50% overlap.
  • You need to apply the frequency weighting before calculating the RMS.
  • The whole thing will need to be calibrated. This depends on microphone sensitivity, pre-amp gain, ADC sensitivity, any OS-based preprocessing, choice window, etc. If you run it always on the same hardware, it's easiest to calibrate against a "known good" SPL meter.

What does α mean?

The operation is a low pass filter. It determines how quickly the meter will react to changes in the physical SPL. It's a trade-off between being able follow quick events but not be so jittery that it's hard to read.

$\alpha$ determines the cutoff frequency and/or time constant of that lowpass filter. Depending on your application these may be prescribed in the standard IEC 61672-1. See for example https://www.nti-audio.com/en/support/know-how/fast-slow-impulse-time-weighting-what-do-they-mean

The relationship between $\alpha$ depends on the desired time constant and your "cycle rate".

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