Functions > Vector and Matrix > Array Characteristics > Example: Downsampling a Vector
Example: Downsampling a Vector
Use the following method for picking every nth element from a data vector, starting with the first element. This demonstrates the effects of excessive downsampling (Nyquist's theorem).
1. Define the period and the sampling frequency.
2. Create a signal vector.
3. Define an integer n which is smaller than the length of vector v.
4. Use vector indexing to extract every nth element of vector v.
5. Plot the original and downsampled traces.
When the new sampling rate is too slow (infrequent), the signal can look very distorted (try n = 15), disappear entirely (only sampling the 0 points - try n = 16), or aliasing can occur, that is, the signal appears to be of an incorrect frequency (n = 28, shown), because there aren't enough samples to accurately represent the information in the signal.
Sampling has consequences for any numerical algorithm which is approximating a result at discrete intervals, such as the fast fourier transform, or differential equation solvers.
To downsample a signal properly without aliasing, the signal must be lowpass filtered with a cutoff of p/n before removing every nth point. For details, see Oppenheim and Schafer, Discrete Time Signal Processing, Prentice Hall, pp 102-105, ©1989.