Interpolating and expanding time series

Are you comfortable with a VBA solution?

	A	B	C	D	E	F	G
1	Orginal data				Desired data
2	Date time	data
3	5/10/2019 0:00	1000			5/10/2019 0:00	1000.00	F3: =IntIndex($B$3:$B$12, IntMatch(E3, $A$3:$A$12))
4	5/10/2019 1:00	1003			5/10/2019 0:03	1000.15
5	5/10/2019 2:00	1005			5/10/2019 0:06	1000.30
6	5/10/2019 3:00	1002			5/10/2019 0:09	1000.45
7	5/10/2019 4:00	999			5/10/2019 0:12	1000.60
8	5/10/2019 5:00	987			5/10/2019 0:15	1000.75
9	5/10/2019 6:00	996			5/10/2019 0:18	1000.90
10	5/10/2019 7:00	1001			5/10/2019 0:21	1001.05
11	5/10/2019 8:00	1003			5/10/2019 0:24	1001.20
12	5/10/2019 9:00	1007			5/10/2019 0:27	1001.35
13					5/10/2019 0:30	1001.50
14					5/10/2019 0:33	1001.65
15					5/10/2019 0:36	1001.80
16					5/10/2019 0:39	1001.95
17					5/10/2019 0:42	1002.10
18					5/10/2019 0:45	1002.25
19					5/10/2019 0:48	1002.40
20					5/10/2019 0:51	1002.55
21					5/10/2019 0:54	1002.70

If you are in a position to use a spreadsheet other than Excel, this is straightforward in Gnumeric using that spreadsheet's built in INTERPOLATION() function =INTERPOLATION($A$3:$A$12,$B$3:$B$12,E3,0) entered into F3 and copied down as far as needed.

If you cannot use a spreadsheet with a built in interpolation function, then you need to build your own algorithm. I recommend an approach like this (which uses helper columns in the lookup table, so some users don't like it):

1) Add 2 helper columns to the original data that compute slope and intercept for each segment. =SLOPE(B3:B4,A3:A4) in C3, =INTERCEPT(B3:B4,A3:A4) in D3 and copy down.
2) Where you want the interpolation, use lookup functions to return the slope and intercept for the appropriate segment and put them into the standard y=mx+b equation =VLOOKUP(E3,$A$3:$D$12,3,TRUE)*E3+VLOOKUP(E3,$A$3:$D$12,4,TRUE).

That's a pretty good solution.