How to use recursive CTE to add resolution to a data set - sql-server

Question

I'm attempting to create a recursive CTE statement that adds blank rows in between data points that will later for interpolation. I'm a beginner with SQL and this is my first time using CTE's and am having some difficulty finding the proper way to do this.
I've attempted a few different slight variations on the code I have provided below after some research but haven't grasped a good enough understanding to see my issue yet. The following code should simulate sparse sampling by taking a observation every 4 hours from the sample data set and the second portion should add rows with there respective x values every 0.1 of an hour which will later be filled with interpolated values derived from a cubic spline.
--Sample Data
create table #temperatures (hour integer, temperature double precision);
insert into #temperatures (hour, temperature) values
(0,18.5),
(1,16.9),
(2,15.3),
(3,14.1),
(4,13.8),
(5,14.7),
(6,14.7),
(7,13.5),
(8,12.2),
(9,11.4),
(10,10.9),
(11,10.5),
(12,12.3),
(13,16.4),
(14,22.3),
(15,27.2),
(16,31.1),
(17,34),
(18,35.6),
(19,33.1),
(20,25.1),
(21,21.3),
(22,22.3),
(23,20.3),
(24,18.4),
(25,16.8),
(26,15.6),
(27,15.4),
(28,14.7),
(29,14.1),
(30,14.2),
(31,14),
(32,13.9),
(33,13.9),
(34,13.6),
(35,13.1),
(36,15),
(37,18.2),
(38,21.8),
(39,24.1),
(40,25.7),
(41,29.9),
(42,28.9),
(43,31.7),
(44,29.4),
(45,30.7),
(46,29.9),
(47,27);
--1
WITH xy (x,y)
AS
(
SELECT TOP 12
CAST(hour AS double precision) AS x
,temperature AS y
FROM #temperatures
WHERE cast(hour as integer) % 4 = 0
)
Select x,y
INTO #xy
FROM xy
Select [x] As [x_input]
INTO #x_series
FROM #xy
--2
with recursive
, x_series(input_x) as (
select
min(x)
from
#xy
union all
select
input_x + 0.1
from
x_series
where
input_x + 0.1 < (select max(x) from x)
)
, x_coordinate as (
select
input_x
, max(x) over(order by input_x) as previous_x
from
x_series
left join
#xy on abs(x_series.input_x - xy.x) < 0.001
)
The first CTE works as expected and produces a list of 12 (a sample every 4 hours for two days) but the second produces syntax error. The expected out put would be something like
(4,13.8), (4.1,null/0), (4.2,null/0),....., (8,12.2)

Answer 1

I dont think you need recursive.
What about this:
SQL DEMO
SELECT DISTINCT n = number *1.0 /10 , #xy.x, #xy.y
FROM master..[spt_values] step
LEFT JOIN #xy
ON step.number*1.0 /10 = #xy.x
WHERE number BETWEEN 40 AND 480
This 480 is based on the two days you mention.
OUTPUT
You dont even need the temporal table
SELECT DISTINCT n = number *1.0 /10 , #temperatures.temperature
FROM master..[spt_values] step
LEFT JOIN #temperatures
ON step.number *1.0 / 10 = #temperatures.hour
AND #temperatures.hour % 4 = 0
WHERE number BETWEEN 40 AND 480;

Answer 2

I don't think you need a recursive CTE here. I think a solution like this would be a better approach. Modify accordingly.
DECLARE #max_value FLOAT =
(SELECT MAX(hour) FROM #temperatures) * 10
INSERT INTO #temperatures (hour, temperature)
SELECT X.N / 10, NULL
FROM (
select CAST(ROW_NUMBER() over(order by t1.number) AS FLOAT) AS N
from master..spt_values t1
cross join master..spt_values t2
) X
WHERE X.N <= #max_value
AND X.N NOT IN (SELECT hour FROM #temperatures)

Answer 3

Use the temp table #xy produced in --1 you have, the following will give you a x series:
;with x_series(input_x)
as
(
select min(x) AS input_x
from #xy
union all
select input_x + 0.1
from x_series
where input_x + 0.1 < (select max(x) from #xy)
)
SELECT * FROM x_series;