if a signal is band pass signal or band limited signal. you can use the band sampling theory so you dont need to sample the signal at the twice the maximum frequency of the signal. you just need to sample the signal at the twice the signal band.
but application of the band sampling theory have some restriction on the signal. so if RF or the carrier frequency is very high, you can think if it can using the band sampling theory. In the software design, because the AD is near the front, the frequency of the RF signal is very high, practical apllication usually use the band sampling.
The solution to the sampling problem is to sample sound at a little over the Nyquist
rate (page 522), which is twice the bandwidth of the sound (the bandwidth is the difference
between its maximum and minimum frequencies). Thus, if a sound contains
frequencies between 500 Hz and 2 kHz (the bandwidth of the human voice), it should
be sampled at a little more than 3 kHz. (Previous editions of this book, as well as many
other sources, erroneously state that the Nyquist rate is twice the maximum frequency.
The author is indebted to Alfred Fuchs for clearing up this point.
svicent said:David Salomon in his book Data Compression, Third Edition, wrote (page 697):
The solution to the sampling problem is to sample sound at a little over the Nyquist
rate (page 522), which is twice the bandwidth of the sound (the bandwidth is the difference
between its maximum and minimum frequencies). Thus, if a sound contains
frequencies between 500 Hz and 2 kHz (the bandwidth of the human voice), it should
be sampled at a little more than 3 kHz. (Previous editions of this book, as well as many
other sources, erroneously state that the Nyquist rate is twice the maximum frequency.
The author is indebted to Alfred Fuchs for clearing up this point.
Is this theory correct?. My opinion is: not
Exactly. Take for example, the theory of relativity states that nothing can travel faster than light. That does not imply everything travels at the speed of light. Neither does the theory provide the means as to how we can make things travel at the speed of light. As I said, it's just a bound. Sometimes, bounds can be reached in practice. Sometimes, they can't. But in theory, if this bound is violated, no amount of DSP can help you recover the original signal.chandreou said:Niquist says that sampling frequency must be at least two times greater that the frequency of the signal
me2please said:I don't know how you do it in matlab but matlab is a numerical environment which always operates in discrete fashion (unless you do it symbolically).
From my understanding, Nyquist should be valid for =. In the case of continuous spectrum, there shouldn't be any problem getting back the signal at all since the aliasing at the point of the band boundary (periodical points) has zero measure.
The only problem could occur in the case of discrete spectrum. In the bandpass filter to recover original signal spectrum, the discrete spectrum will fall exactly at the boundary points. In this case, if the filtering at boundaries is defined correctly (half of magnitude), the original spectrum will be recovered correctly.
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