Why does the bandwidth of a signal need to be half of the sampling rate? [duplicate]

1. How is bandwidth related to sampling rate?
2. Why should your sampling rate be twice the maximum frequency of your signal?
3. Why is it necessary to limit the band of a signal before performing sampling?
4. What does it mean for a signal to be bandlimited?
5. What are the two requirements of sampling theorem?
6. What is the relation between sampling frequency and signal frequency?

How is bandwidth related to sampling rate?

Sampling rate determines the sound frequency range (corresponding to pitch) which can be represented in the digital waveform. The range of frequencies represented in a waveform is often called its bandwidth.

Why should your sampling rate be twice the maximum frequency of your signal?

If the signal contains high frequency components, we will need to sample at a higher rate to avoid losing information that is in the signal. In general, to preserve the full information in the signal, it is necessary to sample at twice the maximum frequency of the signal. This is known as the Nyquist rate.

Why is it necessary to limit the band of a signal before performing sampling?

Band limiting ensures that the original input signal can be reconstructed exactly from the ADC's output samples when a sampling frequency (f_s) of twice the information bandwidth of the analog input signal is used (Nyquist sampling).

What does it mean for a signal to be bandlimited?

A signal is said to be band-limited if the amplitude of its spectrum goes to zero for all frequencies beyond some threshold called the cutoff frequency.

What are the two requirements of sampling theorem?

The sampling theorem essentially says that a signal has to be sampled at least with twice the frequency of the original signal. Since signals and their respective speed can be easier expressed by frequencies, most explanations of artifacts are based on their representation in the frequency domain.

What is the relation between sampling frequency and signal frequency?

The sampling rate must be equal or superior to the double of the highest frequency or the signal .