Reading battery voltage via frequency

Maxim has an app note showing how to use their high-side current sensor parts. They also show a basic op-amp circuit as the "traditional" way to do this measurement, and this is probably good enough for your application:

The output from this circuit could be run to a comparator to generate a digital '1' whenever the pulse is "on" and a '0' when the pulse is off. Some low-pass filtering may be required between the sensor circuit and the comparator if there is bounce or noise during the on and off transitions of the current pulse.

Then you have some choices.

In a simple digital logic solution, using probably a fairly modest CPLD, the digital pulse could clock a counter. The size (number of bits) of the counter depends on the maximum frequency you want to measure. A clock circuit would be needed to generate a pulse every 7.5 seconds. The 7.5-second pulse would be used to latch the counter output into a second register, while simultaneously resetting the counter. Some additional refinement would be desirable to avoid latching the counter output while it is the middle of rippling up the result of a newly arrived pulse from the comparator. The latched register, multiplied by 8 (left shifted by 3) would give the pulses-per-minute in the previous 7.5 second interval.

The digital pulse could be input to a microcontroller to count pulses and output how many pulses were seen in the past 7.5 seconds (multiplied by 8 to get pulses per minute). Or, count how many seconds are needed before you receive maybe 10 pulses from the comparator. The micro is more flexible than the CPLD in terms of letting you vary the counting interval depending on the actual frequency, averaging over multiple periods to get a smoother display, being able to change the units of the display, etc., etc.

How you display the output is up to you.

You may think that the bandwidth of an FM signal is \$2\Delta f\$, where \$\Delta f\$ is the frequency deviation (the maximum difference between the instantaneonus frequency \$f(t)\$ and the carrier frequency \$f_c\$).

However, the frequency of a signal cannot be changed in an instant, therefore when frequency modulating a carrier, you will introduce additional frequencies below \$f_c-\Delta f\$ and above \$f_c+\Delta f\$.

The bandwidth of a frequency modulated signal is theoretically infinite, but it can be approximated with the help of Carson's bandwidth rule (http://en.wikipedia.org/wiki/Carson_bandwidth_rule). It's an approximation based on the highest frequency in the modulating signal (\$f_m\$) and the frequency deviation. In your case, the deviation is 1 Hz and \$f_m\$ is 4 Hz, so the approximated bandwidth around the carrier is 10 Hz.