IntermediateTopic 51 of 104Electronics & Embedded
Sampling theorem
Sample at more than twice the highest frequency to avoid aliasing.
In depth
A band-limited signal with highest frequency f_max can be perfectly reconstructed if sampled at f_s>2f_max. Below this, aliasing folds frequencies into the baseband. Oversampling and anti-alias filters relieve requirements.
Key points
- Nyquist frequency f_s/2
- Reconstruction via sinc interpolation
- Bandpass sampling
ExampleAudio CDs sample at 44.1 kHz to capture up to 20 kHz.
What is Sampling theorem?
Sample at more than twice the highest frequency to avoid aliasing.
Why is it important to understand sampling theorem?
The sampling theorem sets the minimum rate to capture a signal, so it determines the sensor and ADC rates a design needs.
What is the Nyquist rate?
Twice the highest frequency in the signal, the minimum rate needed to reconstruct it without aliasing.
Why do real systems sample faster than Nyquist?
Real anti-alias filters are not ideal, so they need a margin, often a sampling rate several times the signal bandwidth.
How is Sampling theorem used in practice?
Typical applications include choosing a sampling rate of at least 2 kHz for a 800 Hz vibration signal, checking that an anti-alias filter is needed before an ADC and setting the sampling rate for an audio recording device.
What should I learn before Sampling theorem?
Study "DAC" first (topic 50 of 104 in Electronics & Embedded). It covers the groundwork this topic builds on.
What are the key points of Sampling theorem?
Nyquist frequency f_s/2. Reconstruction via sinc interpolation. Bandpass sampling.
Can you give an example of Sampling theorem?
Audio CDs sample at 44.1 kHz to capture up to 20 kHz.
What comes after Sampling theorem?
The next topic is "Hardware description languages", which builds directly on this one.
How difficult is Sampling theorem?
It is classed as Intermediate in Electronics & Embedded (topic 51 of 104). It is an intermediate topic. Work through the beginner topics in Electronics & Embedded first.