Hi, I have hourly time series data and i need to convert it to 15 min time slots

I have hourly time series data and i need to convert it to 15 min time slot, how it is possible ?
By n degree polynomial or any other method plz explain.

data is as follows:

23:30 3.45
00:30 5.65
01:30 6.34
02:30 9.32
03:30 7.32
. .
. .
. .
. .
. .
22:30 1.23
23:30 4.32


and resultant required is as follows:
00:00 ----
00:15 ----
00:30 5.65
00:45 ----
01:00 ----
01:15 ----
01:30 6.34
.
.
.
.
.
23:30
23:45

i don't have data for those slots i need to interpolate (linear interpolation) or Curve fitting.