# What do you call it when you add zeros between the elements of a vector?

What do you call it when you add zeros between the elements of a vector?

let's say you have x =[1 2 3 4]

and x_2 = [0 1 0 2 0 3 0 4]

what do you call this process?

In the context of filter banks, simply upsampling (without filtering, or with the trivial all-pass filter, as Wikipedia relates it to interpolation), denoted by an up-arrow, as illustrated below fro a 2-fold or order-2 upsampling:

This is described in Filter banks: Decimation, Interpolation, and Modulation, and the interpolation filter associated with upsampling is called synthesis filter.

As noted by @Jason R, one also finds "expansion". Expansion is also found as a streching for continuous signals, while compression is the effect in the dual Fourier domain. Sometimes, one can find "zero-insertion" or "zero-stuffing".

Actually in image processing some use "upsampling" as a proxy for pixel increase with filtering.

• is it still called up sampling if you intend to use it as part of hermitian symmetry? – HappyBee Apr 18 '16 at 16:20
• @HappyBee One can upsample a complex signal. However, I am not sure I understand how you want to use it in Hermitian symmetry – Laurent Duval Apr 18 '16 at 16:22
• let's say I have x = [m1 m2 m3 m4] I want to generate a signal that would have a hermitian symmetry out of x (in an OFDM system) i.e I would start by doing s =[0 m1 0 m2 0 m3 0 m4] then s_2 = [0 m1 0 m2 0 m3 0 m4 0 m4* 0 m3* 0 m2* 0 m1*] I would say now that s_2 has hermitian symmetry @Laurent – HappyBee Apr 18 '16 at 16:36
• I've also seen this operation described in DSP texts as expansion in contrast to interpolation where you would actually filter the result. – Jason R Apr 18 '16 at 16:39
• @Jason R indeed, thank you, I have given a more precise context. – Laurent Duval Apr 18 '16 at 16:55