Recall that an FIR filter can be realized in the frequency-sampling form with system fun...

Recall that an FIR filter can be realized in the frequency-sampling form with system function

(a) Suppose that this structure is implemented as an adaptive filter using the LMS algorithm to adjust the filter (DFT) parameters Give the time-update equation for these parameters. Sketch the adaptive filter structure.

(b) Suppose that this structure is used as an adaptive channel equalizer, in which the desired signal is

With this form for the desired signal, what advantages are there in the LMS adaptive algorithm for the DFT coefficients over the direct-form structure with coefficients h(n)? (Hint. Refer to Proakis (1970).)