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

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 (fs) of twice the information bandwidth of the analog input signal is used (Nyquist sampling).

Why is band limiting necessary?

For data communications, a signal, which is to be transmitted, has an infinite number of terms in its Fourier transform. However, when this signal needs to be transmitted through a channel of fixed bandwidth, band-limiting is required.

Why signals should be limited to sample?

The reasons are both mathematical and physical, as we discuss later. 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. For one such signal, G(f) in Figure 1, we see that the spectrum is zero for frequencies above α.

What is a band limit?

The maximum number of members you can have in your band before no one can agree on anything. But seriously, band limit refers to limiting the range of frequencies allowed to pass in a system. In audio, filters are often employed to band limit sounds.

What are time limited and band limited signals?

Band-limited signals have infinite time duration and time-limited signals have infinite bandwidth.

When can a signal be reconstructed?

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.

What is band limited signal?

Bandlimiting is the limiting of a signal’s frequency domain representation or spectral density to zero above a certain finite frequency. A band-limited signal is one whose Fourier transform or spectral density has bounded support. A bandlimited signal may be either random (stochastic) or non-random (deterministic).

What happens if a band limited function is under sampled?

Not allowing the sampling of these frequencies may result in their reappearance disguised as lower frequencies; resulting in an aliasing artifact.

What is a band-limited oscillator?

Bandlimiting is the limiting of a signal’s frequency domain representation or spectral density to zero above a certain finite frequency. A band-limited signal is one whose Fourier transform or spectral density has bounded support.

What happens if a band-limited function is under sampled?

What is band-limited signal?

What is band limiting process?

How is a bandlimited signal reconstructed from a sample?

A bandlimited signal can be fully reconstructed from its samples, provided that the sampling rate exceeds twice the maximum frequency in the bandlimited signal. This minimum sampling rate is called the Nyquist rate.

Can a bandpass signal permit a lower sampling frequency?

Consider a baseband and a bandpass signal, each with the same value of maximum frequency. The bandpass signal permits a lower sampling frequency only if the recovery method includes a bandpass filter that isolates the original signal spectrum (the white rectangles in Figure 5).

Why do you band limit a continuous time signal?

To avoid contamination of the signal by the aliased frequencies, you would first band-limit (lowpass filter) the continuous-time signal and only then sample it. All the frequency component above W will be aliased, but if they are small, it would be nothing more than noise, everything below will be properly sampled.

When to use Nyquist criterion for band limited sampling?

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.