Show that the time-dependent Fourier transform, as defined by Eq. (10.18), has the following properties:
(a) Linearity:
If x[n] = ax1[n] + bx2[n], then X[n, λ) = aX1[n, λ) + bX2[n, λ).
b) Shifting: If y[n] = x[n − n0], then Y [n, λ) = eX[n − n0, λ).
(c) Modulation: If y[n] = ejω0nx[n], then Y [n, λ) = ejω0n X[n, λ − ω0).
(d) Conjugate Symmetry: If x[n] is real, then X[n, λ) = X ∗[n,−λ).
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