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state and prove sampling theory as applied to low pass signal

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How do you prevent aliasing while sampling a continuous time signal?

To prevent aliasing when sampling a continuous time signal, you should first apply a low-pass filter to the signal to eliminate frequency components above half the sampling rate (the Nyquist frequency). Then, ensure that the sampling rate is at least twice the highest frequency present in the signal, as dictated by the Nyquist-Shannon sampling theorem. By adhering to these principles, you can accurately reconstruct the original signal from its samples without distortion.


How can you overcome the aliasing effect?

To overcome the aliasing effect, you can increase the sampling rate or use an anti-aliasing filter before sampling the signal. Additionally, you can employ oversampling techniques or apply signal processing algorithms like interpolation or filtering to reduce or eliminate aliasing artifacts in the signal.


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Why continuous time signals are represented by samples?

Continuous time signals are represented by samples to enable their processing and analysis using digital systems, which operate with discrete data. Sampling converts the continuous signal into a finite set of values at specific intervals, allowing for easier storage, manipulation, and transmission. This representation also facilitates the use of digital signal processing techniques, making it possible to apply algorithms that enhance, filter, or compress the signal efficiently. Additionally, sampling aligns with the Nyquist theorem, ensuring that the essential information of the continuous signal is preserved in the sampled version.


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