Question

Design of a Hilbert transformer Using Hanning window and Kaiser window, design frequency response of a linear-phase Hilbert transformer is given by Hd(e ʲʷ={je⁻ʲᵃʷ 0<ω<π { je⁻ʲᵃʷ - π< ω<0 Choose M 24 and M-25. Plot the resulting amplitude responses and the impulse responses Discuss the results

Answer 1

A Hilbert transformer is a signal-processing filter with a linear-phase response that shifts the phase of the input signal by 90 degrees. The design of a Hilbert transformer can be achieved using windows such as the Hanning window and Kaiser window.

Step-by-step explanation:

A Hilbert transformer is a signal-processing filter with a linear-phase response that shifts the phase of the input signal by 90 degrees across all frequencies. The design of a Hilbert transformer can be achieved using different window functions such as the Hanning window and the Kaiser window.

For the given design frequency response, the amplitude response of the Hilbert transformer is represented by Hd(e ʲʷ={je⁻ʲᵃʷ for 0<ω<π and je⁻ʲᵃʷ for -π<ω<0.

To plot the resulting amplitude response and the impulse response, we can choose a value for M, which represents the number of coefficients in the filter's impulse response. Let's choose M = 24 and M = -25 and calculate the amplitude responses and impulse responses.

The resulting amplitude responses and impulse responses will provide insights into the frequency and phase characteristics of the Hilbert transformer.