[HDTV1080P]

Chip75 answered the question correctly. Since RF channel 3 and 4 coax, composite video, and S-Video are always 480i quality, the cable box 100% of the time will always send a 480i NTSC standard definition image to those connections. The resolution setting on the digital cable box only effects the HDMI and component video outputs.There might be a menu selection in the cable box to choose between letter box and 4:3 ratio. Or the box might automatically convert HD channels to 480i letterbox when using legacy 480i analog video outputs.

Now if your old 4:3 SD CRT TV only has an antenna input for RF channel 3 and 4 then you cannot improve the picture quality. However if you had component video, S-Video, or composite video inputs then you should use one of those.

Also you can find a used 2010 Panasonic or Sony Blu-ray player with analog video and audio jacks if you want to hook up a Blu-ray player to your old TV set (if your old TV has at least one composite video input).

Here is the order of input jacks you should use when connecting a new TV to a cable box or old Blu-ray player

1. HDMI: HDMI offers up to 4K Ultra HD or 8K picture quality, this is the ideal connection if a consumers display supports it. Some old tube 4:3 HDTV’s support HDMI up to 1080i quality. Technically HDMI 2.1 can support between 480i to 8K resolutions.

2. Component video: Component video using 3 separate RCA jacks for video offers up to 1080i picture quality. Many older 4:3 TV’s have at least 480i component video inputs while some tube HDTV’s have 1080i component video inputs. Component video is an analog signal that supports between 480i-1080i quality (Some extremely rare equipment can do 1080P over component video).

3. S-Video: S-Video offers 480i quality and its better quality then composite video since the luminance and chrominance is separated.

4. Composite video: Composite video offers 480i picture quality that is better than RF channel 3 and 4 since the video and audio signals are separated.

5. RF coax channel 3 and 4: is the worse quality connection a consumer can make. Some consumers are forced into this connection since they own very old low cost tube TV’s that do not offer any other video inputs. A TV with only RF inputs is called a TV, however if the TV has at least a composite video input it is called a TV monitor.