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What does Nyquist theorem do?
Nyquist’s theorem states that a periodic signal must be sampled at more than twice the highest frequency component of the signal. In practice, because of the finite time available, a sample rate somewhat higher than this is necessary.
What is the difference between Shannon’s Law and Nyquist’s theorem?
The Nyquist theorem concerns digital sampling of a continuous time analog waveform, while Shannon’s Sampling theorem concerns the creation of a continuous time analog waveform from digital, discrete samples.
How is the Nyquist sampling theorem related to waveforms?
For demonstrations and explanations, we’ll look at three closely related waveforms: y = sin (2 π t), a 1 cycle per second or 1 Hertz sine wave. y = sin (2 π t * 0.9), a 0.9 Hertz sine wave. y = sin (2 π t * (1+ 0.02t)), a “chirped pulse,” where the frequency continuously increases with time.
What is the significance of the Nyquist-Shannon theorem?
The Nyquist sampling theorem, or more accurately the Nyquist-Shannon theorem, is a fundamental theoretical principle that governs the design of mixed-signal electronic systems. Modern technology as we know it would not exist without analog-to-digital conversion and digital-to-analog conversion.
What happens when we sample a signal lower than the Nyquist rate?
If we sample an analog signal at a frequency that is lower than the Nyquist rate, we will not be able to perfectly reconstruct the original signal. The next two plots demonstrate the loss of cyclical equivalency that occurs when the sampling frequency drops below the Nyquist rate.
When do we need to use the sampling theorem?
If we apply the sampling theorem to a sinusoid of frequency f SIGNAL, we must sample the waveform at f SAMPLE ≥ 2f SIGNAL if we want to enable perfect reconstruction. Another way to say this is that we need at least two samples per sinusoid cycle. Let’s first try to understand this requirement by thinking in the time domain.