Since the discrete Fourier series, the Sampling rate, would be the equivalent of the inverse of the passage of time, that is, to the frequency, mathematically this can be written as,
[tex]\frac{1}{\Delta t} = 10000Hz[/tex]
In turn, the time can be described depending on the period and the amount of data samples taken. This would be,
[tex]\Delta t = \frac{T}{m}[/tex]
Here,
m = Data Samples
T = Period
Replacing,
[tex]\Delta t = \frac{T}{1024}[/tex]
Replacing the value of the time from the first equation,
[tex]\frac{1024}{T} = 10000[/tex]
[tex]T = 102.4ms[/tex]
At the same time, the range then will be given between the basic frequency to the half of the sample, that is,
[tex]f_{min} = \frac{1}{T} = 9.165Hz[/tex]
[tex]f_{max} = \frac{1024}{2} (9.165Hz)[/tex]
[tex]f_{max} = 5000Hz[/tex]
Therefore the lowest frequency is 5000Hz and highest 9.165Hz