How can create partitions and aggregates against them on Trino?

Question

I have a dataset with a unique identifier (ID) and timestamp date stored in trino table.

UID	Timestamp
1	2023-09-01 10:28
1	2023-09-01 18:28
2	2023-09-02 08:15
2	2023-09-02 18:30

I want to create a window with specfic date range for example, from 18:28 of 09/01 to 18:30 of 09/02. For the subsequent dates, the desired resulting data will be aggregated and grouped as the following

Unique Count	Timestamp
1	2023-09-01
2	2023-09-02

I heard that window function can partition the data to specfic range chunks and apply window functions to it? Will it work? Or any other way to approach this problem?

I tried executing without window, but resulted in receiving no data, or incorrect data.

SELECT
  COUNT(DISTINCT UID) AS count,
  timestamp AS time
FROM
  (SELECT UID, timestamp 
  FROM logs_based_on_time
  WHERE timestamp BETWEEN (timetsamp - INTERVAL '1' DAY) + INTERVAL '18' HOUR + INTERVAL '30' MINUTE
  AND (timestamp- INTERVAL '1' DAY) + INTERVAL '1' DAY + INTERVAL '18' HOUR + INTERVAL '30' MINUTE + INTERVAL '1' DAY) AS t
GROUP BY
  EXTRACT(DAY FROM t.time) AS day,
  EXTRACT(HOUR FROM t.time) AS hour
ORDER BY
  EXTRACT(DAY FROM t.time) AS day,
  EXTRACT(HOUR FROM t.time) AS hour

Any other way to appraoch this problem? Should i consider trying window functions?