An ideal Hilbert transformer with impulse response has input x r [n] and output x i [n]
Question:
An ideal Hilbert transformer with impulse response
has input xr[n] and output xi[n] = xr[n] * h[n], where xr[n] is a discrete-time random signal.
(a) Find an expression for the autocorrelation sequence ?xixi[m] in terms of h[n] and ?xrxr[m].
(b) Find an expression for the cross-correlation sequence ?xrxi[m]. Show that in this case ?xrxi[m] is an odd function of m.
(c) Find an expression for the auitocorrelation function of the complex analytic signal x[n] xr[n] + jxi[n].
(d) Determine the power spectrum Pxx(?) for the complex signal in part (c).
Transcribed Image Text:
2 sin (an/2) n +0, n = 0. h[n] = 0.
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Related Book For
Discrete Time Signal Processing
ISBN: 978-0137549207
2nd Edition
Authors: Alan V. Oppenheim, Rolan W. Schafer
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