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Sample Rate and Discrete Frequency

Sample Rate and Discrete Frequency

Discover how sampling a signal leads to a new set of frequencies.

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 fsf_s is known, there’s little that can be done.

Determining the frequency

With the available information about fsf_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 2020 samples. In terms of real time in seconds, this period depends on fsf_s.

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A discrete-time signal in memory
A discrete-time signal in memory
  • fs=10f_s=10 Hz implies that Ts=0.1T_s = 0.1 seconds, so:

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