Before deciding on a design approach you will need to determine some set of specs for what you are trying to do. You started this by specifying the frequency range of the signals but there are some important things missing. Some things that need to be specified are:

a) How fast can the frequency of the input change?

b) Will there be step changes of the input or will it slew slowly?

c) How fast does the output geared up frequency need to track the input?

d) What accuracy does the output to input ratio have to maintain?

e) Does the output frequency need to be edge synchronized with the input?

Yes, it could be a very effective design to measure the input period and then produce an 10X output frequency with a timer on an MCU. Several things to look for in my book are to look for period measurement for the input that gates from edge to edge in hardware instead of having a timer interrupt latency be part of the measurement count. Another thing is to use a timer of the output that supports a full count reload capability similar to a Timer 2.

You may also need to do a little bit of filtering of the input measurements so as to prevent cycle to cycle dither in the output.

If you find an MCU with a 16-bit counter for the output at 10Hz you will need a counter that is clocked by a maximum of 655.3KHz. This will determine the frequency steps that you can attain at the output. A larger counter would afford use of a higher rate clock and permit better resolution.

Michael Karas