with given Sampling rate, what max frequency human voice can be captured?

Question

I'm new to signal processing and sampling rate, I was asked interview question related to this.

This is the exact question asked:

With 8Khz of sampling rate, whats the max frequency that human voice can be captured ?

Options provided:

a) 4Khz

b) 8Khz

c) 16Khz

d) 32Khz

I have checked few Q/A websites but couldn't find anything helpful. I did find something similar in this SP stack --> link

And I've also found that for human voice range are upto 8Khz for male and 17 Khz for female. I don't know if it's helpful but I thought I should add this in the question.

Any help, would be really appreciated thank you :)

Answer 1

Without more details, when a signal is properly recorded at $F_n$ Hz, one is entitled to expect that all information below the half of it, namely $F_n/2$ Hz, can be recovered, somehow. This is an application of the classical Shannon Sampling Theorem. Twice the maximum frequency is sufficient to sample a signal... in theory. The question says: max frequency that human voice can be captured; don't expect this max frequency (and others) be capture with full accuracy, as suggested in comments by David.

In some cases, this can be extended, as long as the bandwidth can be shrunk. If the actual bandwidth is smaller, like $F_n/4$-$F_n/2$, one might expect to sample it at $2\times (F_n/2-F_n/4) = F_n/2$ without loss, yet I don't think it is the expected answer, cf. Voice Frequency :

The bandwidth allocated for a single voice-frequency transmission channel is usually 4 kHz, including guard bands, allowing a sampling rate of 8 kHz to be used as the basis of the pulse code modulation system used for the digital PSTN. Per the Nyquist–Shannon sampling theorem, the sampling frequency (8 kHz) must be at least twice the highest component of the voice frequency via appropriate filtering prior to sampling at discrete times (4 kHz) for effective reconstruction of the voice signal.