Calculate Nyquist frequency.
Understand the Problem
The question is asking to calculate the Nyquist frequency, which is the maximum frequency that can be accurately sampled given a certain sampling rate. It is typically calculated as half of the sampling rate.
Answer
The Nyquist frequency is $f_N = \frac{f_s}{2}$.
Answer for screen readers
The Nyquist frequency is given by $f_N = \frac{f_s}{2}$.
Steps to Solve
- Identify the Sampling Rate
Determine the given sampling rate. For this example, let's say the sampling rate is $f_s$ Hz.
- Calculate the Nyquist Frequency
Use the formula for the Nyquist frequency, which is given by:
$$ f_N = \frac{f_s}{2} $$
This equation tells us that the Nyquist frequency is half of the sampling rate.
- Substitute the Sampling Rate
If we know the sampling rate, we can substitute it into the formula. For example, if the sampling rate is 1000 Hz:
$$ f_N = \frac{1000}{2} = 500 \text{ Hz} $$
This means the Nyquist frequency is 500 Hz.
The Nyquist frequency is given by $f_N = \frac{f_s}{2}$.
More Information
The Nyquist frequency is important in signal processing and communications because it determines the highest frequency that can be accurately represented and prevents aliasing, which occurs when higher frequencies are sampled improperly.
Tips
- Using the wrong sampling rate in calculations. Always double-check the given value.
- Forgetting to divide by two when calculating the Nyquist frequency.
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