What is the corresponding time constant for a low frequency filter cutoff frequency of 3 Hz?

To determine the time constant corresponding to a low-frequency filter cutoff frequency of 3 Hz, it's essential to understand the relationship between cutoff frequency and time constant in filter design.

The time constant (τ) can be calculated using the formula:

[

\tau = \frac{1}{2\pi f_c}

]

where ( f_c ) is the cutoff frequency in hertz (Hz). In this case, the cutoff frequency is given as 3 Hz.

Substituting the value into the formula:

[

\tau = \frac{1}{2\pi \times 3}

]

Calculating this gives:

[

\tau = \frac{1}{6.2832} \approx 0.159 \text{ sec}

]

This value can be rounded to 0.2 sec, which corresponds to the time constant calculated for a cutoff frequency of 3 Hz. Therefore, the correct answer is indeed the one that represents the time constant closest to this calculated value.

This approach demonstrates understanding of both the mathematical concept involved and the practical application in signal processing, particularly in the context of EEG where filter settings are crucial for analyzing brain waves accurately. The time constant indicates how quickly the filter