Up-sampling
Consider that x(n) is calculated from the continuous-time signal x(t) by sampling at Fx Hz. We now wish to create a signal y(n) by up-sampling x(n) by a factor of L, that is, we are gaining the sampling rate by a factor of L. That amounts to
1. Changing x(n) to x(t) using a D/A converter.
2. Re-sampling x(t) at LFx Hz to generate y(n).
We can view y(n) as though it were prepareded by sampling an underlying analog signal y(t) (or x(t) for that matter) at a rate Fy = LFx Hz. As in the type of down-sampling we prefer to do that entirely in the digital domain.
Provided the signal x(n) that was obtained at a certain sampling rate we may calculate a new signal y(n) from x(n) with a sampling rate that is L times that of x(n). The signal y(n), an up- sampled type of x(n), is shown by:
and is prepared by placing (L-1) zeros between every pair of consecutive samples of x(n). The time between samples of y(n) is (1/L) of that between samples of x(n), or the sampling frequency of y(n) is raised by a factor of L from that of x(n). The block diagram of an up-sampler is given below.
Example: As an example, if x(n) = an u(n) , a < 1, is the sequence:
then y(n) = x(n/2), with L = 2, is its 2-fold up-sampled version and is obtained by inserting a0 between each pair of consecutive values in x(n)
In this example it is understood that the time between samples of y(n) is one half of that between samples of x(n), or, the sampling rate of y(n) is twice that of x(n).
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