I see Claude implemented a very crude upsampling/downsampling algorithm, which is what LLMs usually do when prompted to handle such a problem. But I would suggest restraining the model from implementing DSP processing on their own and instead use battle tested libraries. You can use rubato's FFT Resampler.
Audio processing is genuinely a hard engineering problem, LLMs usually don't get it right. If you decide to get deep into it, the knowledge you'll get is very rewarding.
It's dead simple. Hold the fn key, speak and release. I use a quantized Wisper small.en model for transcription. It inserts the text into the active application. There's also a hands-free model for longer dictation. Audio transcription is kept in memory. There's no account or transcription history. Clipboard contents are restored after it inserts it. GPLv3, Mac-only, English only..still in alpha. Hope you enjoy it! Would love some feedback.