In the field of digital signal processing, the Nyquist sampling theorem establishes the fundamental criterion for signal digitization— to accurately reconstruct a continuous signal, the sampling frequency must be at least twice the highest frequency of the signal.However, engineers have observed an interesting phenomenon: in practical applications, we often generate signals exceeding 500MHz using a DAC with a sampling rate of 1GHz. This seems to contradict the sampling theorem, but in reality, it does not. So, what is the scientific principle behind this?
⬇ Daily software comprehensive RF knowledge sharing⬇
⬆RF & Radar simulation expert scenario interpretation ⬆
The core of the Nyquist sampling theoremWhat is the essential requirement of the sampling theorem?
The Nyquist-Shannon sampling theorem clearly states:
To reconstruct a band-limited continuous signal without distortion, the sampling frequency must be greater than twice the highest frequency of the signal.
This “twice” relationship is the mathematical lower limit for signal reconstruction.
The actual working characteristics of DACs
How do real DACs achieve high-frequency signal reconstruction?The way real DACs operate differs from the ideal model, and these differences can be reasonably utilized:Zero-order hold effect:
- Ideal reconstruction should use sinc function interpolation
- Real DACs use zero-order hold output
- This is equivalent to approximating the ideal reconstruction
Frequency response characteristics:
- The hold operation introduces a (sin x)/x type amplitude-frequency response
- Leading to signal mirroring in higher Nyquist zones
Characteristics of mirrored signals:
- Although these mirrors contain distortion, they retain the information of the original signal
- With appropriate processing, they can be used for signal reconstruction
The scientific method of engineering implementationHow to correctly utilize these characteristics?Engineers have developed a rigorous technical scheme:Multi-Nyquist zone signal design:
- Place the target signal in the second or higher Nyquist zone
- Utilize the inherent mirroring characteristics of the DAC to reconstruct high-frequency signals
Digital pre-emphasis processing:
- Pre-compensate the digital signal with inverse sinc
- Offset the frequency response introduced by the DAC’s zero-order hold
Precise band selection:
- Design high-performance reconstruction filters
- Accurately extract the target frequency band signal
Non-linear distortion management:
- Optimize the frequency band position of the signal
- Ensure harmonic components fall within the filterable region
The Nyquist sampling theorem, as the theoretical cornerstone of signal processing, is undoubtedly scientific and important.
The brilliance of modern engineering technology lies not in “breaking through” physical laws, but in deeply understanding the full implications of these laws and developing innovative engineering implementation methods based on this understanding. This combination of adherence to fundamental principles and engineering creativity is the inexhaustible driving force of technological progress.
#Science #Popular Science #Radar #Instrumentation #Knowledge Sharing #Electronic Warfare
 |
|
