Question

According to the Nyquist sampling criterion (see Section 5C-2), a signal must be digitized at a rate at least twice that of the highest frequency in the signal to avoid a sampling error. If a particular 12-bit ADC has a conversion time of $5\mu \mathrm{s}$, what is the highest frequency that can be accurately digitized while satisfying the Nyquist criterion?

Short answer

The highest signal frequency is 100 kHz

Step-by-step solution

Step 1. Given information

The converter is 12-bit ADC.

The conversion time is$\Delta t=5\mu \text{s}$

Step 2. Explanation

According to the Nyquist criterion, the maximum or highest signal frequency is half of the conversion frequency.

The highest signal frequency,$f=\frac{1}{2}\left(\frac{1}{\Delta t}\right)$

Step 3.  Calculation

The highest signal frequency is

$\begin{array}{l}f=\frac{1}{2}\left(\frac{1}{\Delta t}\right)\\ =\frac{1}{2}\left(\frac{1}{5\times {10}^{-6}\text{\hspace{0.17em}s}}\right)\\ =100\text{\hspace{0.17em}kHz}\end{array}$

Therefore. the highest signal frequency is 100 kHz