X(e j ω ) denotes the Fourier transform of the complex-valued signal x[n], where the...

X(e ^{j ω} ) denotes the Fourier transform of the complex-valued signal x[n], where the real and imaginary parts of x[n] are given in Figure P2.44. (Note: The sequence is zero outside the interval shown.)

Perform the following calculations without explicitly evaluating X(e^jω).

(d) Determine and sketch the signal (in the time domain) whose Fourier transform is X(e −^jω).

(e) Determine and sketch the signal (in the time domain) whose Fourier transform is jIm{X(e^jω)}.