physicssamplingdefinition

# Sampling frequency for any Continous Signal on a Time Interval

While learning about `Sampling Frequency` I came across two definition

First :

The sampling frequency in a given time interval represents the number of samples taken per unit of time during that interval.

Second :

It is Reciprocal of `Sampling Period`(1/ Sampling Period). Where `Sampling Period` is the time taken between two consecutive samples.

So for Instance we are having Samples at time t=[0, 25, 50, 75, 100] in the time interval 0 - 100

Going by the first definition :

``````Sampling Frequency = (No.of Samples)/ (Time Interval)
= 5/100
= 0.05 Hz
``````

By Second definition :

``````Sampling Period = 25

Sampling Period = (1 / Sampling Period)
= 1/25
= 0.04 Hz
``````

Now I am confused out of both, which one is correct? And what it actually is Sampling Frequency over a Time interval and how does it changes with it..?

Solution

• The second one seems correct. You cannot include both the first and last samples to find the total interval. Choose either one and your calculation will be OK (4/100). To understand this another way, think of a data point being representative of an average time interval, eg what happens between t=12.5 and t=37.5 is encapsulated in the data point corresponding to t=25. Then it becomes clear that your data is basically giving you information from t=-12.5 to t=112.5, in which case you also get the correct answer (5/125)