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What kind of filter is an ideal Hilbert transformer?
Explanation: An ideal Hilbert transformer is a all pass filter.
How much phase shift does an Hilbert transformer impart on the input?
Explanation: An ideal Hilbert transformer is a all pass filter that imparts a 90^{o} phase shift on the signal at its input.
In which of the following fields, Hilbert transformers are frequently used?
Explanation: Hilbert transforms are frequently used in communication systems and signal processing, as, for example, in the generation of SSB modulated signals, radar signal processing and speech signal processing.
The unit sample response of an ideal Hilbert transform is
Explanation: We know that the frequency response of an ideal Hilbert transformer is given as
H(ω)= j ;0 < ω < π
j ;π < ω < 0
Thus the unit sample response of an ideal Hilbert transform is obtained as
The unit sample response of Hilbert transform is infinite in duration and causal.
Explanation: We know that the unit sample response of the Hilbert transform is given as
it sample response of an ideal Hilbert transform is infinite in duration and noncausal.
The unit sample response of Hilbert transform is:
Explanation: We know that the unit sample response of the Hilbert transform is given as
Thus from the above equation, we can tell that h(n)=h(n). Thus the unit sample response of Hilbert transform is antisymmetric in nature.
In this section, we confine our attention on the design of FIR Hilbert transformers with h(n)=h(M1n).
Explanation: In view of the fact that the ideal Hilbert transformer has an antisymmetric unit sample response, we shall confine our attention to FIR designs in which h(n)=h(M1n).
Which of the following is true regarding the frequency response of Hilbert transform?
Explanation: Our choice of an antisymmetric unit sample response is consistent with having a purely imaginary frequency response characteristic.
It is impossible to design an allpass digital Hilbert transformer.
Explanation: We know that when h(n) is antisymmetric, the real valued frequency response characteristic is zero at ω=0 for both M odd and even and at ω=π when M is odd. Clearly, then, it is impossible to design an allpass digital Hilbert transformer.
If f_{l} and f_{u} are the cutoff frequencies, then what is the desired real valued frequency response of a Hilbert transform filter in the frequency range 2π f_{l} < ω < 2πf_{u}?
Explanation: The bandwidth of Hilbert transformer need only cover the bandwidth of the signal to be phase shifted. Consequently, we specify the desired real valued frequency response of a Hilbert transformer filter is
H(ω)=1; 2π f_{l} < ω < 2πf_{u}
where fl and fu are the cutoff frequencies.
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