Interpolate missing values when joining two tables - sql-server

Question

I have two tables of different density data and I'd like to be able to join them but interpolate this values in the lower frequency table to fill in the gaps.
I have no idea how to approach this other than it's a lag/lead thing but the differences are irregular.
Here is my set up below:
CREATE TABLE #HighFreq
(MD INT NOT NULL,
LOSS float)
INSERT INTO #HighFreq
VALUES
(6710,0.5)
,(6711,0.6)
,(6712,0.6)
,(6713,0.5)
,(6714,0.5)
,(6715,0.4)
,(6716,0.9)
,(6717,0.9)
,(6718,0.9)
,(6719,1)
,(6720,0.8)
,(6721,0.9)
,(6722,0.7)
,(6723,0.7)
,(6724,0.7)
,(6725,0.7)
CREATE TABLE #LowFreq
(MD INT NOT NULL
,X FLOAT
,Y FLOAT)
INSERT INTO #LowFreq
VALUES
(6710,12,1000)
,(6711,8,1001)
,(6718,10,1007)
,(6724,8,1013)
,(6730,11,1028)
And I want my output to look like this:

Answer 1

Here is an approach using a recursive cte and window functions. The recusive cte generates the list of mds from values available in both tables. Then, the idea is to put adjacent "missing" #LowFreq records into groups, using gaps-and-island technique. You can then do the interpolation in the outer query, by projecting values between the first (and only) non-null value in the group and the next one.
with cte as (
select min(coalesce(h.md, l.md)) md, max(coalesce(h.md, l.md)) md_max
from #HighFreq h
full join #LowFreq l on l.md = h.md
union all
select md + 1, md_max from cte where md < md_max
)
select
md,
loss,
coalesce(x, min(x) over(partition by grp)
+ (min(lead_x) over(partition by grp) - min(x) over(partition by grp))
* (row_number() over(partition by grp order by md) - 1)
/ count(*) over(partition by grp)
) x,
coalesce(y, min(y) over(partition by grp)
+ (min(lead_y) over(partition by grp) - min(y) over(partition by grp))
* (row_number() over(partition by grp order by md) - 1)
/ count(*) over(partition by grp)
) y
from (
select
c.md,
h.loss,
l.x,
l.y,
sum(case when l.md is null then 0 else 1 end) over(order by c.md) grp,
lead(l.x) over(order by c.md) lead_x,
lead(l.y) over(order by c.md) lead_y
from cte c
left join #HighFreq h on h.md = c.md
left join #LowFreq l on l.md = c.md
) t
Demo on DB Fiddle:
md | loss | x | y
---: | ---: | ---------------: | ---------------:
6710 | 0.5 | 12 | 1000
6711 | 0.6 | 8 | 1001
6712 | 0.6 | 8.28571428571429 | 1001.85714285714
6713 | 0.5 | 8.57142857142857 | 1002.71428571429
6714 | 0.5 | 8.85714285714286 | 1003.57142857143
6715 | 0.4 | 9.14285714285714 | 1004.42857142857
6716 | 0.9 | 9.42857142857143 | 1005.28571428571
6717 | 0.9 | 9.71428571428571 | 1006.14285714286
6718 | 0.9 | 10 | 1007
6719 | 1 | 9.66666666666667 | 1008
6720 | 0.8 | 9.33333333333333 | 1009
6721 | 0.9 | 9 | 1010
6722 | 0.7 | 8.66666666666667 | 1011
6723 | 0.7 | 8.33333333333333 | 1012
6724 | 0.7 | 8 | 1013
6725 | 0.7 | 8.5 | 1015.5
6726 | null | 9 | 1018
6727 | null | 9.5 | 1020.5
6728 | null | 10 | 1023
6729 | null | 10.5 | 1025.5
6730 | null | 11 | 1028