Ideal sampling of audio signals-Periodic spectrum [duplicate]

1. What is sampled signal spectrum?
2. How a band-limited signal can be sampled without aliasing?
3. What is sampling and aliasing?
4. How band-limited signal can be reconstructed from its samples?

What is sampled signal spectrum?

The sampled signal has a spectrum that is periodic at the sampling frequency (20 Hz) and has an even symmetry about 0.0 Hz, as well as symmetry about the sampling frequency, f_s. Since the sampled spectrum is periodic, it goes on forever and only a portion of it can be shown.

How a band-limited signal can be sampled without aliasing?

Thus, band-limited signals can be sampled and fully recovered only when observing the Nyquist criterion. For bandpass signals the Nyquist criterion will ensure no aliasing only when the recovery of the signal is done with a bandpass filter; otherwise a higher sampling frequency will be required.

What is sampling and aliasing?

Aliasing is when a continuous-time sinusoid appears as a discrete-time sinusoid with multiple frequencies. The sampling theorem establishes conditions that prevent aliasing so that a continuous-time signal can be uniquely reconstructed from its samples. The sampling theorem is very important in signal processing.

How band-limited signal can be reconstructed from its samples?

Nyquist Sampling Theorem:

If a signal is band limited and its samples are taken at sufficient rate then those samples uniquely specify the signal and the signal can be reconstructed from those samples. The condition in which this is possible is known as Nyquist sampling theorem and is derived below.