# How to find Z Transform of the function which is on S domain?

Given a $s$ domain function $$F(s)=\frac{3\, e^{-0.2s}+3}{s(s+3)}$$ and i have to find the Z-Transform of the function for (1)T=0.1 sec (2) T=0.3 sec For T=0.1 sec i can write $$3(e^{-0.2s}+1)\rightarrow 3(z^{-2}+1)$$ and then i can use partial fraction for the denominator part and take ZT .

But for the second part can i write $$3(e^{-0.2\,s}+1)=3(e^{-0.3\,s \cdot \frac{2}{3}}+1)\rightarrow 3(z^{-\frac{2}{3}}+1)$$ is it valid ? i think it's not because ZT can't be valid in between any fractional interval . then how to solve this ?

• This might be a question to ask for the Math SE because you're asking about properties and mathematical computation, rather than theory or application of the the Z-Transform. – KingDuken Aug 21 '17 at 16:19
• You need the 'modified z transform' – Chu Aug 21 '17 at 16:24
• @KingDuken still it is pretty much related with EE , i don't think it's a misfit – Zeno San Aug 21 '17 at 16:30
• @Chu , never heard of a modified ZT , is there any good source or material you can recommend ? – Zeno San Aug 21 '17 at 16:31
• Plenty of references on google - it's a very well known method – Chu Aug 21 '17 at 16:32