Sample Rate and Discrete Frequency

An ADC samples a continuous-time signal to produce discrete-time samples. From the viewpoint of a digital signal processor, this signal is represented in computer memory as a series of numbers. Unless the sample rate $f_s$ is known, there’s little that can be done.

Determining the frequency

With the available information about $f_s$, we can discover the frequency by first computing the period. For example, the figure below shows a discrete-time sinusoid with a period of $20$ samples. In terms of real time in seconds, this period depends on $f_s$.

• $f_s=10$ Hz implies that $T_s = 0.1$ seconds, so:

$$\begin{align*} T &= 20 ~\frac{\textmd{samples}}{\textmd{period}}~ \cdot ~ 0.1 ~\frac{\textmd{seconds}}{\textmd{sample}} = 2~ \textmd{seconds} \end{align*}$$ ...