In your own words, explain what Nyquist's sampling theorem says, and explain the importance and implications of it to the storage and transmission of digital sound. In your answer, tell the effect of sample size on reproduced sound and also how sample size relates to storage and transmission.

The Nyquist sampling theorem states that the sampling frequency must be at least twice of the highest frequency component present in the signal.

Mathematically,

Samling rate ≥ 2×fmax

Step-by-step explanation:

We know that sound is an analog signal comprising of several different frequencies. We convert this analog signal into a digital signal by means of an analog-to-digital converter (ADC) for the purpose of storage and transmission.

For accurate and faithful analog to digital conversion, we need to take some samples per second which is basically called "Sampling rate".

So how many samples do we need?

This is where Nyquist sampling theorem comes into the picture.

Nyquist Sampling theorem:

The Nyquist sampling theorem states that the sampling rate must be at least twice of the highest frequency component present in the signal.

Mathematically,

Samling rate ≥ 2×fmax

This is the minimum sampling frequency that is required to avoid distortion of the signal.

If the Nyquist criteria is not followed then some of the information in the analog signal will be lost and the sound will not be accurately converted into the digital signal.

Therefore, a higher sampling rate would result in better reproduction of sound as compared to a lower sampling rate.

On the other hand, a higher sampling rate would also take more storage memory and reduced transmission speed.