For time discretization, the Nyquist–Shannon sampling theorem[1] says a band-limited, continuous-time signal can be perfectly reconstructed from a discrete-time signal with a sufficiently high (but finite) sampling frequency. Human hearing is naturally band limited to about the range 20Hz to 20kHz, and audio recordings typically use sufficient sampling frequency to losslessly recontruct thos bandwidth.
For quantization, any recorded analog signal is a true signal plus some level of measurement noise. Quantization of a signals can also be thought of as adding some noise to a continuous amplitude signal[2]. If the "quantization noise" is much smaller than the measurement noise of the signal, then the discretization is effectively lossless. Typical audio formats have a maximum quantization error far, far smaller than typical audio recording hardware's measurment error (and the human ear's).
So typical quantized, discrete-time audio formats can be considered lossless representations of the anolog sound signals humans can hear (assuming proper capture and processing). On the other hand, no quantized or discretized signal can losslessly represent a non-band-limited, zero-noise audio signal.
For time discretization, the Nyquist–Shannon sampling theorem[1] says a band-limited, continuous-time signal can be perfectly reconstructed from a discrete-time signal with a sufficiently high (but finite) sampling frequency. Human hearing is naturally band limited to about the range 20Hz to 20kHz, and audio recordings typically use sufficient sampling frequency to losslessly recontruct thos bandwidth.
For quantization, any recorded analog signal is a true signal plus some level of measurement noise. Quantization of a signals can also be thought of as adding some noise to a continuous amplitude signal[2]. If the "quantization noise" is much smaller than the measurement noise of the signal, then the discretization is effectively lossless. Typical audio formats have a maximum quantization error far, far smaller than typical audio recording hardware's measurment error (and the human ear's).
So typical quantized, discrete-time audio formats can be considered lossless representations of the anolog sound signals humans can hear (assuming proper capture and processing). On the other hand, no quantized or discretized signal can losslessly represent a non-band-limited, zero-noise audio signal.
[1]: https://en.wikipedia.org/w/index.php?title=Nyquist%E2%80%93S...
[2]: https://en.wikipedia.org/wiki/Quantization_(signal_processin...