Consider a complex sequence h[n] = hr [n] + jhi[n], where hr[n] and hi[n] are both real sequences, and let H(ejω) = HR(ejω) + jHI (ejω) denote the Fourier transform of h[n], where HR(ejω) and HI (ejω) are the real and imaginary parts, respectively, of H(ejω).
Let HER(ejω) and HOR(ejω) denote the even and odd parts, respectively, of HR(ejω), and let HEI(ejω), and HOI(ejω) denote the even and odd parts, respectively, of HI(ejω). Furthermore, let HA(ejω) and HB(ejω) denote the real and imaginary parts of the Fourier transform of hr[n], and let HC(ejω) and HD(ejω) denote the real and imaginary parts of the Fourier transform of hi[n]. Express HA(ejω), HB(ejω), HC(ejω), and HD(ejω) in terms of HER(ejω), HOR(ejω), HEI(ejω), and HOI(ejω).
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