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For example, to interpolate by a factor of 15, you could interpolate by 3 then interpolate by 5. For example you could interpolate by 16 in: The result (assuming an ideal interpolation filter) is a signal at L times the original sampling rate which has the same spectrum over the input Nyquist (0 to Fs/2) range, and with zero spectral content above the original Fs/2.
This idea is appealing because, intuitively, this “stairstep” output seems more similar to the original than the zero-stuffed version.
It is usually symbolized by “L”, so output rate / input rate=L.
Tip: You can remember that “L” is the symbol for interpolation factor by thinking of “interpo-L-ation”. Since interpolation relies on zero-stuffing you can only interpolate by integer factors; you cannot interpolate by fractional factors.
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“Interpolation”, in the DSP sense, is the process of upsampling followed by filtering.
(The filtering removes the undesired spectral images.) As a linear process, the DSP sense of interpolation is somewhat different from the “math” sense of interpolation, but the result is conceptually similar: to create “in-between” samples from the original samples.
Therefore, interpolation is far more common that upsampling alone.