Signal processingLesson 2 of 2 in the course Sampling

Sampling Theory: Aliasing, Reconstruction, and Extensions

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

This lesson introduces the Nyquist–Shannon sampling theorem, which explains when regularly spaced samples can preserve all the information in a continuous signal.

Here, TT is the sample period, the time between adjacent samples, and the sampling frequency is fs=1/Tf_s=1/T samples per second. A simple analogy is taking regularly spaced snapshots of a moving object: whether the snapshots capture its motion depends on how quickly it changes and how often the snapshots are taken.

All flashcards

Aliasing
Frequency ambiguity caused when shifted copies of a sampled signal's spectrum overlap.
Sinc interpolation
Ideal reconstruction method that sums sample-scaled, shifted sinc functions for a properly sampled band-limited signal.
Zero-order hold
A DAC output method that holds each sample value as a rectangular pulse until the next sample.
Nyquist frequency
Half the sampling frequency, fs/2f_s/2, in the usual baseband sampling setup.
Compressed sensing
A recovery approach that can use sparse signal structure to enable recovery below the conventional sampling rate.

Quiz questions

  1. What causes aliasing when a continuous signal is sampled?Answer: Shifted spectral copies overlap, making some frequency components indistinguishable.
  2. What is the main purpose of an anti-aliasing filter placed before sampling?Answer: To reduce input frequencies that would otherwise cause aliasing.
  3. How does a zero-order hold produce a digital-to-analog converter's initial output?Answer: It holds each sample value as a rectangular pulse until the next sample.
  4. Why can oversampling make practical reconstruction-filter design easier?Answer: It creates more frequency space for the filter's transition from passband to stopband.
  5. Under what condition can compressed sensing support recovery below the conventional sampling rate?Answer: When the signal has suitable sparse structure and the measurement process supports recovery.

Based on the Wikipedia article Nyquist–Shannon sampling theorem, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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