A digital resonator is required to be designed including 3 dB bandwidth, with frequency Na, that yield zero magnitude at extreme frequencies. What will be the transfer function of such a resonator? (I)determine the impulse gain. (I1)determine the impulse gain response for the designed filtered (III)Determine the bandwidth?
A digital resonator is required to be designed including 3 dB bandwidth, with frequency Na, that yield zero magnitude at extreme frequencies. What will be the transfer function of such a resonator? (I)determine the impulse gain. (I1)determine the impulse gain response for the designed filtered (III)Determine the bandwidth?
Digital Resonator: A digital resonator is a special kind of bandpass filter having a pair of complex conjugate poles located near the unit circle as shown in the figure below. Digital resonators are second-order recursive filters.
To design a digital resonator with a resonant frequency at
It is required to select the complex conjugate poles at
Now let us select that zeros are located at +1 and -1 such that it eliminates the response at the corner frequencies(
), i.e.,
for getting zero magnitudes at extreme frequencies.
The general transfer function of the digital resonator is given by:
Now, when the zeros are placed at +1 and -1 (
), then the system transfer function will be
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