Coherent sampling
Encyclopedia
Fast Fourier Transform
(FFT) is a common tool to investigate performance of for data converters and other sampled systems. Coherent sampling refers to a certain relationship between input frequency
,
, sampling frequency, 
, number of cycles, 
, in the sampled set and number of samples, 
. With coherent sampling one is assured that the signal power in an FFT is contained within one FFT bin, assuming single input frequency.
The condition for coherent sampling is given by
If we have
and 
and we want an input frequency close to 
, let's say 
, then 
which is close to an integer, so we could round it down to 
and we would get 
. This is an input frequency that satisfies coherent
sampling and makes sure that we get an integer number of cycles.
This integer number should be chosen carefully. We have three possible types of integers, even, odd, and prime. Even is not a good idea since we would hit the same code every M
samples, where M can be much less than N. Odd is a better idea since it takes longer to hit the same code. According to some sources http://www.maxim-ic.com/appnotes.cfm/appnote_number/1040/ a prime number
of cycles is the best (with the exception of the prime 2) because it takes a long time before the same code repeats.
Fast Fourier transform
A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...
(FFT) is a common tool to investigate performance of for data converters and other sampled systems. Coherent sampling refers to a certain relationship between input frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
,
, sampling frequency, , number of cycles, , in the sampled set and number of samples, . With coherent sampling one is assured that the signal power in an FFT is contained within one FFT bin, assuming single input frequency.The condition for coherent sampling is given by
If we have
and and we want an input frequency close to , let's say , then which is close to an integer, so we could round it down to and we would get . This is an input frequency that satisfies coherentsampling and makes sure that we get an integer number of cycles.
This integer number should be chosen carefully. We have three possible types of integers, even, odd, and prime. Even is not a good idea since we would hit the same code every M
samples, where M can be much less than N. Odd is a better idea since it takes longer to hit the same code. According to some sources http://www.maxim-ic.com/appnotes.cfm/appnote_number/1040/ a prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
of cycles is the best (with the exception of the prime 2) because it takes a long time before the same code repeats.