Why do we use Shannon and Nyquist theorem?
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. The theorem also leads to a formula for perfectly reconstructing the original continuous-time function from the samples.
Why is it important to follow Nyquist when sampling?
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.
What is the need for sampling?
Sampling is done because you usually cannot gather data from the entire population. Even in relatively small populations, the data may be needed urgently, and including everyone in the population in your data collection may take too long.
How is the sampling theorem of Shannon expressed?
Sampling theorem can be expressed as given below: fs≥2fm Where, fs is the sampling frequency and fm is the maximum modulating signal frequency Sampling is a process of translating continuous analog signal into discrete analog signal, where the sampled signal is the discrete time representation of the original analog signal.
How is the analog signal defined in Shannon’s theorem?
Fig. 2.2 shows an analog (continuous-time) signal (solid line) defined at every point over the time axis (horizontal line) and amplitude axis (vertical line). Hence, the analog signal contains an infinite number of points. Fig. 2.2. Display of the analog (continuous) signal and display of digital samples vs. the sampling time instants.
How is the sampling theorem used to reconstruct a signal?
According to the sampling theorem ( Shannon, 1949 ), to reconstruct a one-dimensional signal from a set of samples, the sampling rate must be equal to or greater than twice the highest frequency in the signal.
What happens if an analog signal is not sampled?
If an analog signal is not appropriately sampled, aliasing will occur, which causes unwanted signals in the desired frequency band. The sampling theorem guarantees that an analog signal can be in theory perfectly recovered as long as the sampling rate is at least twice of the highest-frequency component of the analog signal to be sampled.