Sampling Theorem Demo

The Nyquist-Shannon Sampling Theorem states that a continuous signal can be perfectly reconstructed from its samples if the sampling rate is greater than twice the highest frequency present in the signal. This minimum sampling rate is called the Nyquist rate.

Key Points:

• Nyquist Rate = 2 × Maximum Signal Frequency
• Sampling above the Nyquist rate preserves all information
• Sampling below the Nyquist rate causes aliasing (information loss)

Aliasing occurs when a signal is sampled below its Nyquist rate. The sampled signal appears to be a different (lower) frequency than the original. This is because there aren't enough samples to capture the true oscillations of the signal.

Example: If you sample a 10 Hz signal at only 15 Hz (below Nyquist rate of 20 Hz), the reconstructed signal will appear to be 5 Hz instead of 10 Hz.

Experiment with different scenarios:

• Proper Sampling: Set signal frequency to 5 Hz and sampling rate to 50 Hz (10x Nyquist). Notice perfect reconstruction.
• Minimum Nyquist: Set signal to 5 Hz and sampling to 11 Hz (just above Nyquist). Reconstruction works but barely.
• Aliasing: Set signal to 10 Hz and sampling to 15 Hz. Watch the reconstructed signal appear as 5 Hz!
• Severe Aliasing: Set signal to 15 Hz and sampling to 20 Hz. The apparent frequency will be very different.

• Digital Audio: CD-quality audio samples at 44.1 kHz to capture frequencies up to ~22 kHz (human hearing limit)
• Video: Frame rate must be sufficient to capture motion without aliasing (wagon wheel effect)
• Communications: Signal bandwidth determines minimum sampling rate for digital transmission
• Medical Imaging: MRI and CT scans must sample at appropriate rates to avoid artifacts
• Data Acquisition: Sensor sampling rates must exceed twice the maximum expected signal frequency