Final answer:
The question concerns the calculation of capacitance based on desired reactance at different frequencies and the relationships between cut-off frequency, phase delay, and group delay in filter design. It requires an understanding of AC circuit concepts such as reactance and filter parameters.
Step-by-step explanation:
The student's question involves calculating the capacitance required to achieve a specific reactance at different frequencies and discussing the implications of these results. Reactance is frequency-dependent, and it's critical to understand how it changes with frequency to design appropriate filter circuits. To find the capacitance that results in a 100 kΩ reactance at 120 Hz, we use the formula ℝ(X) = 1 / (2πfC) and solve for C. The cut-off frequency of a filter is the frequency at which the output signal power is reduced to half the power of the input signal, and it's a critical parameter in filter design.
At a frequency of 1.00 MHz, the reactance of the capacitor can also be calculated using the same formula, which illustrates how the capacitance effectively impedes different frequencies. The student is also asked to explore the relationship between group delay, phase delay, and the order of a FIR filter, which is an advanced concept in electrical engineering. Group delay often relates to the rate of change of the phase response with frequency, and the order of the FIR filter affects the filter's complexity and behavior.