# upsampling for a signal

We have a signal $$s(t)$$.

1. If we do an upsampling, does the signal duration increase?
2. What is the point of upsampling if the signal time increases?
3. Can we do an upsampling if we don't use a shaping filter?

## 1 Answer

No, if you upsample a signal, its duration (i.e. measured in real-world units like "seconds") does not change.

• If your signal $$s[n]$$ is sampled at a rate $$f_s$$ Hz, and it is $$N$$ samples long, then the total duration of the signal is $$\frac{N}{f_s}$$ seconds.

• Say you upsample the signal by a factor $$M$$, yielding a new signal $$s_u[n]$$. It will be $$MN$$ samples long, but it will be sampled at a new rate $$Mf_s$$. Its duration is therefore $$\frac{MN}{Mf_s} = \frac{N}{f_s}$$. You can see that the signal duration is the same as $$s[n]$$.

It's not clear what you mean by a "shaping filter" in your third question.

• In the third question, 'shaping filter' is for example a root raised cosine filter: Can we do an upsampling if we don't use a shaping filter (for example a root raised cosine filter)? – user39389 Dec 8 '18 at 19:25
• upsampling has not necessarily something to do with pulse shaping, so yes. – Marcus Müller Dec 9 '18 at 0:06