# Does Increasing Resolution Lead to Have a Poor Resolution?

As it has proven in some paper and books the time and frequency resolution of Morlet wavelet is :
$\Delta t=\frac{f_c\sqrt{f_b}}{2f_i}$ $\Delta f=\frac{1}{2\pi f_c \sqrt{f_b}}$
I don't know how these relations have obtained, I have asked it in detail in here.you can answer that if you want.
but lets accept these relationship for now. there is some misunderstanding for me in here about the concept of resolution.
for this case, by increasing the term $f_c\sqrt{f_b}$ we have finer frequency resolution but poor time resolution. I am sure about finer frequency and poor time resolution because my practical results meet it. but if you look at $\Delta t$ and $\Delta f$ relationships you receive that increasing the term $f_c\sqrt{f_b}$ leads to decrease $\Delta f$ and increase the $\Delta t$.
does it mean that smaller value of resolution spell to have finer resolution and vice verca?

• In your last sentence: Smaller value of what resolution? Finer resolution of what? For each resolution, exactly what are you measuring or describing? – hotpaw2 Apr 11 '14 at 22:01
• I mean does it mean that smaller value of frequency resolution ($\Delta f$)spell to have finer frequency resolution? and moreover does it mean that smaller value of time resolution ($\Delta t$)spell to have finer time resolution? @hotpaw2 – Electricman Apr 12 '14 at 4:42

EDIT: Because you are still trying to understand why it is like that, then please mind that by increasing the frequency of the wavelet ($f_c$), you should also shrink it in time (decrease $f_b$). For more info please refer for example to: Paul Addison - The Illustrated Wavelet Transform Handbook. You can find there a following graphs (Section 2.12):
• @MackTuesday The question is fine, I am just asking something about the concept of resolution. $\Delta f$ is said frequency resolution in many paper. and also they said increasing $fc \sqrt{f_b}$ leads to increase(finer) the frequency resolution. but if you look at $\Delta f$ relationship,you will see that $\Delta f$ is proportional to inverse of $fc \sqrt{f_b}$. this happens for $\Delta t$ as well. – Electricman Apr 12 '14 at 4:54