| Line 6: | Line 6: | ||
Problems involving Nyquist's Theorem generally require the use of the Fourier Transform. However, being able to compute the Fourier Transform is not required to understand the concepts of Nyquist's Theorem, and thus these computations will not be included in these example problems. For more information about Fourier Series and the Fourier Transform, click [https://www.tutorialspoint.com/signals_and_systems/fourier_series.htm here]. | Problems involving Nyquist's Theorem generally require the use of the Fourier Transform. However, being able to compute the Fourier Transform is not required to understand the concepts of Nyquist's Theorem, and thus these computations will not be included in these example problems. For more information about Fourier Series and the Fourier Transform, click [https://www.tutorialspoint.com/signals_and_systems/fourier_series.htm here]. | ||
| + | <br /> | ||
<br /> | <br /> | ||
1) Through the Fourier Transform, it is revealed that a signal is made up of constituent frequencies 1000 Hz, 1800 Hz, and 2000 Hz. Assuming that this information was collected accurately, what was the minimum sample rate required to find this information? | 1) Through the Fourier Transform, it is revealed that a signal is made up of constituent frequencies 1000 Hz, 1800 Hz, and 2000 Hz. Assuming that this information was collected accurately, what was the minimum sample rate required to find this information? | ||
| − | |||
<br /> | <br /> | ||
Revision as of 20:22, 6 December 2020
Worked Examples Using Nyquist’s Theorem
Problems involving Nyquist's Theorem generally require the use of the Fourier Transform. However, being able to compute the Fourier Transform is not required to understand the concepts of Nyquist's Theorem, and thus these computations will not be included in these example problems. For more information about Fourier Series and the Fourier Transform, click here.
1) Through the Fourier Transform, it is revealed that a signal is made up of constituent frequencies 1000 Hz, 1800 Hz, and 2000 Hz. Assuming that this information was collected accurately, what was the minimum sample rate required to find this information?
A: The minimum sample rate is the Nyquist Rate, which is two times the maximum frequency contained within the signal. Therefore, the answer is 2000 Hz * 2 = 4000 Hz.
2)
