Friday, June 21, 2013

Undersampling causes Aliasing!

The earthquake data from the CSN stations (in SAC format) is at a sampling rate of 50Hz. We put some thought into the possibility of something going wrong because of the sampling rate. We figured that it might be the case; undersampling causes aliasing!

If a 60 Hz sine wave is sampled at 50 Hz and then the Discrete Fourier Transform is taken (by the FFT algorithm), one might expect no data in the plot since there is no frequency in the range 0 Hz - 25 Hz. (25 Hz is 50/2 Hz, the Nyquist rate). But that is not the case. Since the data has been undersampled the 60 Hz signal distorts the Frequency Transform to bring up a peak at 10 Hz (60 Hz - 50 Hz). This is demonstrated in the plot below.

Aliasing caused by the 60 Hz signal sampled at 50 Hz

This could make a lot of the analysis go wrong, a peak at 1 Hz could have been caused by signals of 1 Hz, 49 Hz, 51 Hz, 99 Hz, 101 Hz etc. Further analysis in the frequency domain thus requires more information about the different frequencies the stations could possibly catch.

No comments:

Post a Comment