Nyquist Theorem -- Sampling Rate Versus Bandwidth

The Nyquist theorem states that a signal must be sampled at least twice as fast as the bandwidth of the signal to accurately reconstruct the waveform; otherwise, the high-frequency content will alias at a frequency inside the spectrum of interest (passband). An alias is a false lower frequency component that appears in sampled data acquired at too low a sampling rate. The following figure shows a 5 MHz sine wave digitized by a 6 MS/s ADC. The dotted line indicates the aliased signal recorded by the ADC at that sample rate.

The 5 MHz frequency aliases back in the passband, falsely appearing as a 1 MHz sine wave. To prevent aliasing in the passband, a lowpass filter limits the frequency content of the input signal above the Nyquist rate.

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representation changes with frequency
For low frequencies a higher frequency sample rate has a more accurate representation than higher frequencies. For instance in CD sound, size waves at higher frequencies get represented as square waveforms, albeit the right frequency it isn't the right waveform. That's just a drawback of digital sampling. Compressed sound (ala mp3) lose quality representation according to human perception. So data bitrates have no correlation to actual representation. Also audio compression maintains the same bit rate regardless of the quality of sound. Bitrates between raw sampling of sound and compressed sound is only meaninful in comparison for the purposes of data compression. Mp3 data may accurately or inaccurately represent sampled data, but as I said above, sampled data is an approximation to the real analog signal. It's a necessary tradeoff in the use of computers for analysis and storage of signals.
- Feb 25, 2008

Well because the highest frequency determines the bandwidth, then we can say "twice as fast as the bandwidth". However, it is much recommended to say "... as frequency" since many people think that the bandwidth is measured in bits per second (which is not true, that is the data rate!)
- Dec 21, 2007

plz refer once::
Hi,that is not a signal BW,here only consider the Maximam frequency component in that signal,if signal is Bandlimited.Oterwise if the signal is Bandpass then we have been take as u said. Becoz in Base band(or BL) signal may have high freq component more or less than the signal bandwidth.
- Annamnaidu, DA-IICT. annamnaidu_sattaru@daiict.ac.in - Nov 27, 2007

NO - twice as fast as bandwidth. For example, you can sample a 10 MHz wide signal centerred at 100 MHz at a 20 MHz sample rate and preserve the signal. This is sometimes called "digital downconversion" in receiver design.
- Jan 27, 2007

twice as fast as the 'frequency' not bandwidth!
- Apr 29, 2005