Does the Nyquist Sampling Theorem Apply to Square Waves?

In summary, in order to reconstruct a square wave, a higher sampling frequency is needed due to the square wave's infinite bandwidth. However, for a sine wave, the sampling frequency only needs to be double the frequency of the sine wave in order to achieve perfect reconstruction. The higher the sampling frequency, the better the reconstruction for both waveforms.
  • #1
yecko
Gold Member
279
15

Homework Statement


In comparison with the sampling sine wave, in order to reconstruct a square wave, do we need to increase or decrease sampling frequency?

Homework Equations


Aliasing effect
Leakage effect

The Attempt at a Solution


No matter square wave or sine wave, the experimental results shown the higher sampling frequency (10kHz, 25kHz, 100kHz, 250kHz, 2.5MHz) construct a clearer waveform (signal freq = 25kHz).

Is there difference between sine and square wave for "increase or decrease sampling frequency"?
Thank you
 
Physics news on Phys.org
  • #2
The square wave is composed of odd harmonic sine waves of the fundamental frequency. What is it you are trying to do with the square wave?
 
  • Like
Likes yecko
  • #3
A square wave has theoretically infinite bandwidth, so you theoretically need infinite sampling frequency to perfectly reconstruct it. This practically means that the higher the sampling frequency, the better reconstruction and there is no upper bound to the sampling frequency.
A sine wave has finite bandwidth and you can perfectly reconstruct it with sampling frequency that is double of the sine wave frequency.
 
  • Like
Likes yecko and scottdave
  • #4
While I normally don't use Wikipedia as a single source for a subject, I think the Square Wave Wikipedia page does a nice job of explaining it. https://en.wikipedia.org/wiki/Square_wave

When you say the higher frequencies construct a clearer waveform for the Sine wave, are you referring to how it looks on the screen? This is different than being able to reconstruct a band limited signal from a set of samples.

While more samples may look nicer to the viewer, many of those extra samples are unnecessary to reconstruct the sine wave.
 
  • Like
Likes Delta2
  • #5
I want to point out that the basic Nyquist theorum applies to the ability to get the correct amplitude given an infinite sample. Infinite samples are rare. There are more complicated versions that give bounds for the possible errors given a limited sample.
 

FAQ: Does the Nyquist Sampling Theorem Apply to Square Waves?

What is Nyquist sampling theorem?

Nyquist sampling theorem is a fundamental concept in digital signal processing that states a signal must be sampled at a rate at least twice its highest frequency component in order to accurately reconstruct the original signal.

Why is Nyquist sampling theorem important?

Nyquist sampling theorem is important because it ensures that the sampled signal contains enough information to accurately reconstruct the original signal. Without following this theorem, the reconstructed signal may contain errors and distortions.

What happens if the Nyquist sampling rate is not followed?

If the Nyquist sampling rate is not followed, the reconstructed signal may contain aliasing, which is the distortion of high frequency components into lower frequencies. This can result in inaccurate and distorted signals.

How is Nyquist sampling theorem used in practical applications?

Nyquist sampling theorem is used in a wide range of practical applications, including audio and video processing, telecommunications, and medical imaging. It ensures that signals are accurately sampled and reconstructed, leading to better quality and more reliable results.

Is Nyquist sampling theorem applicable to all types of signals?

Yes, Nyquist sampling theorem is applicable to all types of signals, including continuous-time signals, discrete-time signals, and digital signals. It is a fundamental principle in digital signal processing and is used in various fields of science and engineering.

Back
Top