Relationship Between Frequency And Domain_3

If a point is sampled at a given sampling rate, the post-obit equation defines the time interval between the samples, or the sampling interval.

where Δt is the sampling interval and f _s is the sampling rate in samples per 2nd (South/southward).

The sampling interval is the smallest frequency that the system tin can resolve through the DFT or related routines.

The following equation defines the DFT. The equation results in X[k], which is the frequency-domain representation of the sample bespeak.

where x[i] is the time-domain representation of the sample signal and N is the total number of samples. Both the fourth dimension domain 10 and the frequency domain Ten have a total of North samples.

Similar to the time spacing of Δt between the samples of x in the fourth dimension domain, you lot have a frequency spacing, or frequency resolution, between the components of Ten in the frequency domain, every bit the following equation defines.

where Δf is the frequency resolution, f _south is the sampling rate, N is the number of samples, Δt is the sampling interval, and NorthΔt is the total acquisition time.

To improve the frequency resolution, that is, to decrease Δf, you must increase N and keep f _s constant or subtract f _s and keep Northward abiding. Both approaches are equivalent to increasing NΔt, which is the time duration of the acquired samples.