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If every delay element in the transfer function of the IIR filter designed in (a) is replaced with a subsystem described by the following difference equation,

Options:
a) The filter becomes an FIR filter.
b) The filter becomes a high-pass filter.
c) The filter becomes a notch filter.
d) The filter becomes a Butterworth filter.

User YSbakker
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1 Answer

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Final answer:

Replacing a capacitor with an inductor in a filter circuit will shift its characteristics from high-frequency to low-frequency filtering or vice versa depending on the initial design of the circuit.

Step-by-step explanation:

The replacement of capacitors with inductors in a circuit fundamentally alters its filtering characteristics. In a low-frequency filter, capacitors impede the flow of low-frequency signals and allow high-frequency signals to pass. Conversely, inductors impede the flow of high-frequency signals and allow low-frequency signals to pass through a high-frequency filter. Hence, replacing a capacitor with an inductor in a circuit originally designed as a low-frequency filter will transform it into a high-frequency filter, and vice versa.

Specifically, in Figure 23.52(a), the capacitor acts as a low-frequency filter, or high pass filter, allowing high-frequency signals to pass while attenuating low frequencies. If the capacitor in this figure is replaced with an inductor, the filter would become a low-frequency, or low pass filter, attenuating high-frequency signals. Conversely, the capacitor in Figure 23.52(b) functions as a high-frequency filter or low pass filter, allowing low-frequency signals through while blocking high frequencies. Substituting the capacitor with an inductor in this figure will result in it becoming a high-frequency filter, or high pass filter, which attenuates low-frequency signals.Understanding the fundamental behavior of capacitors and inductors in AC circuits is essential for grasping why such substitutions affect the filter characteristics. The inherent properties of these components - capacitors storing energy in an electric field and inductors in a magnetic field - determine how they will react to different frequencies of electrical signals within a circuit.

User Mark Rowlands
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