Final answer:
A bandpass filter allows a certain range of frequencies to pass through, while attenuating others. A bandstop filter attenuates a specific range of frequencies while allowing others to pass through. The quality factor Q for the bandpass filter is 0.75.
Step-by-step explanation:
A bandpass filter is a type of filter that allows only a certain range of frequencies to pass through while attenuating frequencies outside that range. To create a bandpass filter with fc1 = 2 kHz and fc2 = 10 kHz, we need to combine a high-pass filter with a cut-off frequency of fc1 and a low-pass filter with a cut-off frequency of fc2. These filters can be implemented using capacitors, inductors, and resistors.
A bandstop filter, also known as a notch filter, is a type of filter that attenuates a specific range of frequencies while allowing frequencies outside that range to pass through. To create a bandstop filter with fc1 = 2 kHz and fc2 = 10 kHz, we need to combine a low-pass filter with a cut-off frequency of fc1 and a high-pass filter with a cut-off frequency of fc2. These filters can also be implemented using capacitors, inductors, and resistors.
The quality factor Q for a filter determines its selectivity or sharpness of cutoff. It is given by the formula:
Q = fc / (f2 - f1)
where fc is the center frequency of the filter, and f1 and f2 are the lower and upper cutoff frequencies respectively. For the given bandpass filter, the center frequency (fc) is (fc1 + fc2) / 2 = (2 kHz + 10 kHz) / 2 = 6 kHz. Thus, the quality factor Q = 6 kHz / (10 kHz - 2 kHz) = 0.75.