Question 1

What is ADC and DAC?

Accepted Answer

ADC (analogue-to-digital conversion) turns a continuous voltage into a stream of numbers by sampling it in time and rounding each sample to a fixed number of levels. DAC (digital-to-analogue conversion) reverses the process, rebuilding an analogue waveform from those numbers. This page visualises the original signal, the sampled ADC output and the reconstructed DAC output stacked together.

Question 2

What is the Nyquist theorem?

Accepted Answer

The Nyquist-Shannon sampling theorem states that a band-limited signal can be reconstructed perfectly only if the sample rate is at least twice its highest frequency, written f_ADC at least 2 times f_signal. The Nyquist frequency is half the sample rate, so it is the maximum signal frequency the system can represent without error.

Question 3

What causes aliasing in this simulation?

Accepted Answer

Aliasing appears when you drop the sample rate below 2 times f_signal. Too few samples per cycle make a high-frequency tone masquerade as a lower one. The simulation computes the alias as the value of the absolute difference of f_signal and k times f_ADC that falls below f_ADC over 2, turns the sample stems red and flags the warning badge.

Question 4

What do the three sliders control?

Accepted Answer

The signal frequency slider sets the input tone from 100 to 5000 Hz. The sample rate slider sets f_ADC from 500 to 20000 Hz, deciding how often the wave is measured. The bit depth slider, from 1 to 12 bits, sets how many amplitude levels (2 to 4096) are available for quantisation.

Question 5

What is bit depth and quantisation noise?

Accepted Answer

Bit depth N determines the number of discrete amplitude levels, equal to 2 to the power N. With fewer bits the steps between levels are larger, so each sample is rounded more coarsely and the rounding error appears as quantisation noise. At 1 bit the wave becomes a crude two-level staircase; at 12 bits the 4096 levels make the staircase almost smooth.

Question 6

What does SQNR mean and how is it calculated?

Accepted Answer

SQNR is the signal-to-quantisation-noise ratio, a measure of how cleanly the converter represents a signal. The simulation uses the standard approximation SQNR approximately 6.02 times N plus 1.76 dB, where N is the bit depth. Each extra bit adds roughly 6 dB, so 8 bits give about 50 dB and 16 bits about 98 dB.

Question 7

What is the sampling ratio shown in the stats?

Accepted Answer

The sampling ratio is f_ADC divided by f_signal, displayed as a multiple such as 4.00x. A ratio of 2 sits exactly at the Nyquist limit, so anything above 2 satisfies the theorem and anything below it causes aliasing. Higher ratios give more samples per cycle and a more faithful reconstruction.

Question 8

Why does the reconstructed signal sometimes look wrong?

Accepted Answer

When aliasing occurs, the DAC can only rebuild the signal from the samples it received, and those samples are consistent with a lower alias frequency rather than the true tone. The reconstructed row therefore shows the alias, not the original, demonstrating that aliasing destroys information that no later processing can recover.

Question 9

Is this simulation physically accurate?

Accepted Answer

It captures the core ideas faithfully: uniform sampling, mid-tread quantisation to 2 to the power N levels, the Nyquist condition and the 6.02 times N plus 1.76 dB SQNR rule are all standard. It simplifies by using an ideal sine input and omitting anti-aliasing filters, sample-and-hold artefacts and reconstruction filtering, so it is a teaching model rather than a circuit-level emulator.

Question 10

Why does CD audio use 44.1 kHz?

Accepted Answer

Human hearing tops out near 20 kHz, and the Nyquist theorem requires sampling above twice that, so at least 40 kHz. The 44.1 kHz rate leaves headroom for a practical anti-aliasing filter and has historical roots in early digital video tape storage. You can mimic this by setting f_signal near the audio limit and f_ADC just above twice it.

Question 11

How can I avoid aliasing in a real system?

Accepted Answer

Place an analogue anti-aliasing low-pass filter before the ADC to remove any content above the Nyquist frequency, then choose a sample rate comfortably above twice the highest frequency of interest. Oversampling further eases the filter requirements. In this simulation you simply raise the sample rate until the green Nyquist-satisfied badge appears.

🌊 ADC / DAC 采样

📊 ADC / DAC — 信号采样与混叠

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