Final answer:
The power spectral density (PSD) of a polar line code using a sinc function can be found by calculating the Fourier transform of the autocorrelation function of the sinc function, resulting in a rectangular function in the frequency domain. To sketch it, plot a 'top-hat' shape with a frequency range from -1/2Tβ to 1/2Tβ.
Step-by-step explanation:
The student is asking about finding the power spectral density (PSD) of a polar line code that uses a sinc function to represent the 1's. Firstly, we need to understand that the PSD represents how the power of a signal or time series is distributed with frequency. Given the function p(t) = sinc(πt/Tβ), we can note that this is a baseband signal representation of the polar line code. One way to find the PSD is to calculate the Fourier transform of the autocorrelation function of p(t). The sinc function, being the time domain representation, is the Fourier transform of the rectangular pulse in the frequency domain. Therefore, the PSD can be expressed as a squared magnitude of the Fourier transform of the sinc function, which results in a rectangular function in the frequency domain.
To sketch the PSD, one would plot frequency on the horizontal axis and power on the vertical axis. The sinc function will lead to a rectangular shape, representing constant power over the band of frequencies from -1/2Tβ to 1/2Tβ and zero elsewhere. The PSD plot would then resemble a top-hat function with its peak aligning with the level of power of the signal and its width determined by 1/Tβ.