How Nyquist Sampling Theorem Works?
The Nyquist Sampling Theorem explains the relationship between the sample rate and the frequency of the measured signal. It is used to suggest that the sampling rate must be twice the highest frequency in the signal. It is used to reconstruct any signal from samples. A sample is basically the number of times an analog signal is measured per value of time (typically seconds).
Nyquist Sampling Theorem
- Relationship Between Sampling Rate and Signal Frequency: T he Theorem States that Sampling rate(fs) should be greater than or equal to the twice the highest frequency component(fm) in the signal.
- Preventing Aliasing: When the Sampling rate is double the highest frequency of the signal, Aliasing can be avoided. Aliasing occurs when the high frequency parts of the signal occurs in the lower frequency, causing distortion.
- Reconstruction of Signals: The Nyquist theorem tells us that if we sample a signal at a rate higher than twice its highest frequency, we can reconstruct the original analog signal from these samples. This is done using methods like interpolation and reconstruction algorithms, ensuring we don’t lose important information from the original signal.
- Concept of Sampling: Sampling is simply capturing the strength of an analog signal at specific moments in time. These captured strengths, or samples, create a digital version of the original signal. So, by taking enough samples, we can accurately represent the analog signal in digital form.
For example, If we were to store sound like music in a CD, the audio signal must be sampled at a rate of at least 40,000 Hz to reproduce the 20,000 Hz signal.
The sampling rate must be at least twice the highest frequency in the signal.
Let
Original frequency be 20,000 Hz
Since fs >= 2fm
The reproduced sample rate must be 40,000 Hz.
Nyquist Sampling Theorem
Nyquist Theorem also referred to as the Sampling Theorem is a principle of reproducing a sample rate, that is at least twice the frequency of the original signal. This principle is very important in all analog-to-digital conversion and is applied in digital audio and video to minimize a problem referred to as Aliasing.
In digital communication, signals are representations of information that are transmitted from one point to another in a digital format. Nyquist Sampling is a critical theorem that is used to derive the frequency of the signal to reconstruct without aliasing. Aliasing refers to the distortion or unwanted noise that may destroy a signal’s integral value.