In order to be able to recover a signal correctly after sampling, then the sampling frequency must be greater than twice the highest frequency in the signal.

For the case of a band pass signal a lower sampling frequency can be used if it is permissible to reproduce the band pass signal with a lower center frequency. In this case the sampling frequency must be greater than twice the bandwidth.

eg parameters:-

(6.0, 8.0, 0.01, 24.78, 70, NA, 70, 343.0, 34.5, 0.25) the band pass signal is between 6 and 8rad/s. The sampling frequency is 17.5rad/s so the signal occurs in the spectrum between 6 and 8 rad/s. ( wL between 246 and 343)

(6.0, 8.0, 0.01, 24.49, 40, NA, 40, 301.0, 34.5, 0.25) the band pass signal is between 6 and 8rad/s. The sampling frequency is 10.0rad/s so the signal occurs in the spectrum between 6 and 8 rad/s. above half the sampling frequency ( wL between 450 and 600). However w

(6.0, 8.0, 0.01, 24.05, 23, NA, 23, 375.0, 34.5, 0.65) w

Setting Nf2 = 50 shows that the original spectrum occurs between the sampling frequency and 1.5 times the sampling frequency. (wL between 360 and 480)

(14.0, 16.0, 0.01, 24.0, 22, NA, 69, 375.0, 34.5, 0.7) w

The original spectrum occurs between the 2.5 times the sampling frequency and 3 times the sampling frequency. (wL between 608 and 695)

(14.0, 16.0, 0.01, 24.21, 27, NA, 69, 294.0, 34.5, 0.7) w

The original spectrum occurs between the 2.0 times the sampling frequency and 2.5 times the sampling frequency. (wL between 608 and 695)

The original spectrum is reproduced correctly between 0 and w

COPYRIGHT © 2007 Cuthbert Nyack.