RMS display

I m working on a project which records acoustic signal and display its true RMS for a certain time period of the signal. for this, I would like to store the signal in RAM or SD card for further processing. Please suggest me, how to do that ?

For a sinusoidal signal or repetitive signal it is very easy to find the RMS value. However for an audio signal, by its very nature it is not fixed and therefore does not have any fixed RMS figure and as you say you have to find the RMS based on a certain time period. However I feel it will be better (and more useful) to determine the average value instead of the RMS. The reason is that RMS value is basically a measure of how hot a piece of resistance will get when fed with a certain repetitive signal - the temperature will stabilise at some fixed value for a sinusoidal or repetitive signal, but will not be fixed (rather will not stabilise) for an audio signal. For a non-repetitive or random signal whatever temperature you measure will basically be an average over time till the instant you measure it. Therefore the average will give a better idea of the signal's history.

The algorithm that comes to mind is:
Assume that you have the samples based on fixed time instances - let's say the sampling frequency is 44100 Hz, so you have 44100 samples in one second. For a time window of 1 second, you simply need to look up the values within that window and average it - this will give you the average over that one second window. For greater time periods, simply determine the start second and end second and average out the values between that interval.

Thanks rohit for your reply.
What you said is correct, but I don't want to use thermocouple for temperature measurements due to its non linear behavior.
I would rather use micro controller and program it to get an accurate value, since this device will be used for research applications. I may need quite a lot of memory than a inbuilt flash memory in micro controller. So, I want to keep an additional SD card or some additional flash memory. But I don't know how to program it or include in my actual circuit. Please suggest me.

I did not imply measuring the temperature - I was merely trying to explain why RMS measurement might not be possible or useful. To program it, you basically need to record the sound and save it either in WAVE or PCM format. WAVE is simply a PCM coded audio file with additional meta data. You need to figure out how to use the PCM data in the file to find each sample.

If you use a standard PC with sound card you can record and save the recording to a WAVE file and then use that file for analysis. For a uC you need to use its analogue input (basically one that connects to its internal ADC) to find the instantaneous value of the input at the sampling interval, convert that to a PCM (could be 8, 16 or 32 bit) number, buffer a fixed number of these samples and output that buffered data to an external capture device - basically the uC would signal this device that data is available and the device would read its buffer - you might use USB or the RS232 interface that the uC board provides to do this.

Hmmm ...
... this is an old question (based on many years of reading 'RMS' values for audio signal power) ... which I after several decades of DSP experience I am not entirely convinced isn't really simple to solve.

The purpose of RMS equivalence is to determine equivalent energy density (power) which is proportional to the square of the voltage applied (the amplitude of the signal) - an average does not help as it is linear with respect to voltage (unlike reality) and for an AC signal it will be zero.

Simple squaring of samples and integrating (accumulating) seems like it should work - and for a sample rate at or below the Nyqvist frequency it clearly works for a sinusoid. Based on the principle of superposition I can't think of a reason why it won't work for complex waveforms provided that the sampling rate is above the Nyqvist limit.

So, sample above the Nyqvist point, square the samples and accumulate them. If you want an RMS equivalent then take the square root of the resulting power value.

I think that's all you need to do.

Thank you Rohit. Your suggestion clarify few concepts for me. I will work on that.

Thank you so much Jeff. I will work on it.

Well, yes if you actually take the amplitude over one cycle then it will be zero for a sinusoid. But for sinusoidal signals, the average value is calculated over half a cycle. That was one point I missed in my earlier reply, and the squaring part .

However, I believe there is a small correction to technique you outlined. We will get instantaneous power at each sample point and integrating them will not yield the correct value. For example, for every sample, the power will never be negative and if you simply accumulate them the resulting value will only increase. Let's say, at t = 0, v = 1V, at t = 2, v =1V, at t = 3, v = 3V, at t = 4, v = -1V. Same thing repeats for t = 5 to t = 9. Note that this is a non-sinusoidal but repetitive signal.

Squaring and accumulating for t=0 to 4, we have
0^2 + 1^2 + 2^2 + 3^2 + (-1)^2 = 0 + 1 + 4 + 9 + 1 = 15
taking the square root, we have, 3.87V

Squaring and accumulating for t = 0 to 9, we have
0^2 + 1^2 + 2^2 + 3^2 + (-1)^2 + 0^2 + 1^2 + 2^2 + 3^2 + (-1)^2 = 30
taking the square root, we have, 5.47V

The above does not look correct. However when we average the squares,
For t =0 to 4, we have 15/5 = 3 (sq. root = 1.732)
For t = 0 to 9 also, we have 30/10 = 3 (sq. root = 1.732, as above)

And this looks much more plausible.