When you see ASX in the URL, most probably it means that Windows Media streams are used.
There are two types of programs you can use to record Windows Media stream from web radio station:
- Direct sound recording software that can record anything from your sound card. You lose some quality when using such programs, 'coz they re-compress audio (Of course you can use lossless audio codecs, but the filesize will be unjustified). The advantage of such programs is that they record no matter what is going on with your internet connection (many stream capture programs will stop recording immediately or after several retries). However they also record any system sounds produced by your PC. Replay AV is one of the programs that have scheduling and direct sound recording.
- Video stream recorders and audio stream rippers that capture / rip / download streams. Make sure the program supports Windows Media streams (MMS and RTSP protocol support is recommended). The most reliable stream capturing software of live Windows Media streams is WM Recorder in the PRO mode. Its "compress time" feature allows to eliminate any gaps in recording due to buffering pauses (The recording will play back without any visible pauses).
If you capture radio stream, you will get .ASF audio file, that can be played by any player supporting Windows Media format.
When you record from sound card, you can choose your favorite format like MP3 or AAC.
The programs offered are not free. Make sure to test free trial versions before buying them!