Question

A signal is sampled at 10000 Hz and a total of 1024 data samples are taken, what are the highest and lowest frequencies that can be resolved by discrete Fourier analysis. What is the time period T?

Answer 1

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,

$\frac{1}{\Delta t} = 10000Hz$

In turn, the time can be described depending on the period and the amount of data samples taken. This would be,

$\Delta t = \frac{T}{m}$

Here,

m = Data Samples

T = Period

Replacing,

$\Delta t = \frac{T}{1024}$

Replacing the value of the time from the first equation,

$\frac{1024}{T} = 10000$

$T = 102.4ms$

At the same time, the range then will be given between the basic frequency to the half of the sample, that is,

$f_{min} = \frac{1}{T} = 9.165Hz$

$f_{max} = \frac{1024}{2} (9.165Hz)$

$f_{max} = 5000Hz$

Therefore the lowest frequency is 5000Hz and highest 9.165Hz