how to calculate Rms value of a signal having more than two frequencies?

[ksr]

Hi guys,

I want to know how to calculate from a pcm file the following things...

1. Rms value of a signal when it is having single frequency and also multiple frequencies .
2. Rms value of harmonic components of a signal when it is having single frequency and also multiple frequencies .
3 Rms value of noise..

By using above values i want to calculate SNR, THD , THD+N.

Thanks in Advance

[Ray A. Rayburn]

Originally Posted by ksr

Hi guys,

I want to know how to calculate from a pcm file the following things...

1. Rms value of a signal when it is having single frequency and also multiple frequencies .
2. Rms value of harmonic components of a signal when it is having single frequency and also multiple frequencies .
3 Rms value of noise..

By using above values i want to calculate SNR, THD , THD+N.

Thanks in Advance

Take the linear value (not log like dB) of each sample. Square each sample value. Average all the squared values. Take the square root of the result. You have taken the Root, of the Mean, of the Squares, or RMS.

While you can use a simple RMS to determine the unweighted Signal to Noise Ratio (SNR), it is more common to weight the noise using some curve such as A-weighting to adjust for the fact that the ear is not equally sensitive to all frequencies.

To measure THD+N the signal must be a pure sine wave going into the Device Under Test (DUT). Take the output of the DUT and apply a very narrow notch filter that takes out the input frequency. What is left is the THD+N which can be measured with a RMS detector.

To just measure THD is a bit more complex. You need to use a narrow select filter rather than a notch filter, and individually measure the energy in each harmonic, then compare the summed energy of all the harmonics with that of the fundamental. THD (and THD+N) is expressed in percent, and it is possible to have THD in excess of 100% if the harmonics have greater energy than the fundamental.

[ksr]

Thanks for your reply bro..can you suggest any book for knowing this concepts deeply??

[Ray A. Rayburn]

Originally Posted by ksr

Thanks for your reply bro..can you suggest any book for knowing this concepts deeply??

It is hard to point to any one book. There is a lot of good stuff you can download for free from here:

http://ap.com/download/whitepapers

The Handbook for Sound Engineers, Fourth Edition has some good stuff in it (I wrote two of the chapters).

There are tons of AES Journal articles on audio measurements.

[ksr]

Thanks bro.....

[Arlin]

If you understand algebraic notation, attached are the formulas for finding RMS from a discrete time history signal & calculating total RMS from the RMS of multiple signals when combined.
This is taken straight from wikipedia here: http://en.wikipedia.org/wiki/Root_mean_square