Sampling of a Periodic Analog Signal #
Sampling is the process of converting a continuous (analog) signal into a discrete (digital) signal by measuring its value at regular intervals.
1. Nyquist-Shannon Theorem #
The sampling frequency must be at least twice the maximum frequency of the signal:
$$f_s \geq 2 \cdot f_{max}$$If this condition is not met, aliasing occurs — the reconstructed signal is distorted.
2. Quantization #
Each sample is rounded to the nearest available digital level. More bits → more levels → higher precision. An n-bit ADC has \(2^n\) levels.
3. ADC (Analog-to-Digital Converter) #
Converts the analog voltage to a binary number. Resolution: \(\Delta V = \frac{V_{ref}}{2^n}\)
4. Practical Example #
Audio CD: sampling at 44,100 Hz (Nyquist for 20 kHz human hearing), 16-bit quantization (65,536 levels).
Conclusion #
Sampling bridges the analog and digital worlds. The Nyquist theorem ensures faithful reproduction; quantization determines precision. These concepts are fundamental for audio, video, sensors and all digital signal processing.
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