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Compresses length of vector vsrc by an integer factor.
The stretch operator is used to describe and analyze upsampling, that is, increasing the sampling rate by an integer factor.
We found that ''stretching" a discrete-time signal by the integer factor (filling in between samples with zeros) corresponded to the spectrum being repeated times around the unit circle.
The sampling theorem is easier to show when applied to sampling-rate conversion in discrete-time, i.e., when simple downsampling of a discrete time signal is being used to reduce the sampling rate by an integer factor.
In analogy with the continuous-time aliasing theorem of §D.2, the downsampling theorem (§7.4.11) states that downsampling a digital signal by an integer factor produces a digital signal whose spectrum can be calculated by partitioning the original spectrum into equal blocks and then summing (aliasing) those blocks.
For the synchronization purpose, we search on all discrete values of τ as a multiple integer factor of N + D and ε as a multiple integer factor of inter carrier frequency spacing.
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Most of the cryptographic protocols used in everyday life are based on number theoretic problems such as integer factoring.
It is best to use a number with small integer factors in order for the FFT to be computed efficiently.
If the program balks at increasing the zoom factor again due to limitation on the screen size, it will instead zoom in on the images using integer factors.
All of these relationships are precise only for integer stretch/downsampling/aliasing/repeat factors; in continuous time and frequency, the restriction to integer factors is removed, and we obtain the (simpler) scaling theorem (proved in §C.2).
To assess the robustness of an algorithm involving both methods, different sensor densities are simulated by reducing the input deflection shapes by integer factors.
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