In Figure P10.25, a filter bank is shown for which h0[n] = 3δ[n + 1] + 2δ[n] + δ[n...

In Figure P10.25, a filter bank is shown for which

h0[n] = 3δ[n + 1] + 2δ[n] + δ[n − 1],

and

The filter bank consists of N filters, modulated by a fraction 1/M of the total frequency band. Assume M and N are both greater than the length of h₀[n].

(a) Express y_q [n] in terms of the time-dependent Fourier transform X[n, λ) of x[n], and sketch and label explicitly the values for the associated window in the time-dependent Fourier transform. For parts (b) and (c), assume that M = N. Since v_q[n] depends on the two integer variables q and n, we alternatively write it as the two-dimensional sequence v[q, n].

(b) For R = 2, describe a procedure to recover x[n] for all values of n if v[q, n] is available for all integer values of q and n.

(c) Will your procedure in (b) work if R = 5? Clearly explain.