Final answer:
The power spectral density of a PAM signal with a rectangular transmit pulse can be sketched by considering the Fourier Transform of the pulse, resulting in a sinc function, and then accounting for the white nature of the symbols, which have a flat spectrum across the frequency band.
Step-by-step explanation:
The question involves sketching the power spectral density (PSD) of a passband Pulse Amplitude Modulation (PAM) signal with a specific transmit pulse shape. Given the transmit pulse g(t) as rect(t; Ts/2), the symbols A[k] are zero-mean and white with variance σ2/A. To sketch the PSD, we would first obtain the Fourier Transform of the transmit pulse g(t), which would give us the frequency spectrum of the single pulse. In the case of a rectangular pulse, this would yield a sinc function. The PSD of the PAM signal would then be shaped by the spectrum of the individual pulses and the power spectral characteristics of the symbol sequences.
Since the symbols A[k] are white, the frequency components of these symbols are flat across the frequency band. However, in the time domain, these symbols are convolved with the transmit pulse g(t), which means in the frequency domain, their spectrum is multiplied with the sinc function resulting from the Fourier Transform of g(t). To complete the sketch, the PSD is shaped by the combination of the sinc function and the flat spectrum of the white symbols, and it should reflect the variance as the power of the signal.