Sampling?
The process of converting a continuous-time signal into a discrete-time signal is called sampling.
- sampling period: the time between two successive sampling instants.
Nyquist Sampling Principle
It defined the theoretical minimum sampling rate which is related to the maximum of the frequency of the signal.
Effects of under sampling(Aliasing)
If a signal is sampled less than Nyquist sample rate, then it is called under sampled.
\[X_s(\omega)=\frac{1}{T}\sum_{n=-\infty}^{+\infty}X(\omega-n\omega_s)\]The phenomenon in which a high-frequency component in the frequency spectrum of signal takes identity of a lower frequency component in the spectrum of the sampled signal is called aliasing.
If we sample the data in frequency \(\omega_s\) then all the components with a frequency more than \(\omega_s/2\) create aliasing. The low-pass filter (LPF) is commonly known as the anti-aliasing filter.
文档信息
- 本文作者：Shenyao Jin
- 本文链接：https://shenyaojin.github.io/2022/07/18/undersampling/
- 版权声明：自由转载-非商用-非衍生-保持署名（创意共享3.0许可证）