SELECT v,  backfilled_rolling_median(v::double precision, 5) over() FROM generate_series(1, 10) as t(v);
 v  | backfilled_rolling_median 
----+---------------------------
  1 |                         3
  2 |                         3
  3 |                         3
  4 |                         3
  5 |                         3
  6 |                         4
  7 |                         5
  8 |                         6
  9 |                         7
 10 |                         8
(10 rows)

SELECT v,  backfilled_rolling_median(v::double precision, 5) over() FROM generate_series(1, 3) as t(v);
 v | backfilled_rolling_median 
---+---------------------------
 1 |                          
 2 |                          
 3 |                          
(3 rows)

SELECT v,  backfilled_rolling_median(v, 3) over() FROM (VALUES (1), (1.1), (0.9), (1.1), (0.95), (2.1), (1.95), (2.0), (2.05), (3.11), (2.99), (3.05), (3.0)) as t(v);
  v   | backfilled_rolling_median 
------+---------------------------
    1 |                         1
  1.1 |                         1
  0.9 |                         1
  1.1 |                       1.1
 0.95 |                      0.95
  2.1 |                       1.1
 1.95 |                      1.95
  2.0 |                         2
 2.05 |                         2
 3.11 |                      2.05
 2.99 |                      2.99
 3.05 |                      3.05
  3.0 |                         3
(13 rows)

SELECT v,  backfilled_rolling_median(v, 3) over() FROM (VALUES (1), (1.1)) as t(v);
  v  | backfilled_rolling_median 
-----+---------------------------
   1 |                          
 1.1 |                          
(2 rows)

SELECT v,  backfilled_rolling_median(v::double precision, 3) over() FROM (VALUES (NULL), (NULL), (NULL)) as t(v);
 v | backfilled_rolling_median 
---+---------------------------
   |                          
   |                         0
   |                         0
(3 rows)

SELECT v,  backfilled_rolling_median(v, 3) over() FROM (VALUES (1), (1.1), (0.9), (1.1), (NULL), (NULL), (1.95)) as t(v);
  v   | backfilled_rolling_median 
------+---------------------------
    1 |                         1
  1.1 |                         1
  0.9 |                         1
  1.1 |                       1.1
      |                          
      |                          
 1.95 |                          
(7 rows)