$ sudo apt install cuetools shntool flac
$ shnsplit -f input.cue -t %n-%t -o flac output.flac

You'll need flac, bchunk and ffmpeg. If you run Debian or Ubuntu, just type

$ sudo apt-get install flac ffmpeg

The first step is to convert the whole .ape into .wav.

$ ffmpeg -i input.ape output.wav

And convert to flac.

  $ flac --best output.wav

Then you split the .wav into individual tracks.

  $ shnsplit -f cuefile.cue -t %n-%t -o flac output.flac

You can then remove the .ape, .cue and interim .wav files.

$ ffmpeg -i input.flac -sample_fmt s16 -ar 44100 output.flac

List sample formats: ffmpeg -sample_fmts List additional flac encoding options: ffmpeg -h encoder=flac

FFmpeg supports two resamplers: the default swresample library, and the external SoX resampler (soxr).

$ ffmpeg -i input.flac -af aresample=out_sample_fmt=s16:out_sample_rate=44100 output.flac

Either example will result in the same output: you can verify with the hash muxer. Changing the dithering method See the -dither_method option for a list of available dithering methods and additional resampling options. Example:

$ ffmpeg -i input.flac -dither_method triangular_hp -sample_fmt s16 -ar 44100 output.flac

To use soxr your ffmpeg must be compiled with –enable-libsoxr. Then choose it with the -resampler option:

$ ffmpeg -i input.flac -resampler soxr -sample_fmt s16 -ar 44100 output.flac

Or use the aresample filter to do it all:

$ ffmpeg -i input.flac -af aresample=resampler=soxr:out_sample_fmt=s16:out_sample_rate=44100 output.flac