Math  /  Algebra

QuestionA binary PAM wave is to be transmitted over a low-pass channel with bandwider of 75 kHz . The bit duration is 10μ s10 \mu \mathrm{~s}. Find a raised-cosine pulse spectrum that satisfies these requirements.

Studdy Solution
The raised-cosine pulse spectrum H(f) H(f) is defined by the roll-off factor β \beta and the Nyquist bandwidth BN B_N . The spectrum is:
H(f)={1,fBN12[1+cos(π(fBN)βBN)],BN<f(1+β)BN0,f>(1+β)BN H(f) = \begin{cases} 1, & |f| \leq B_N \\ \frac{1}{2} \left[ 1 + \cos\left(\frac{\pi (|f| - B_N)}{\beta B_N}\right) \right], & B_N < |f| \leq (1 + \beta)B_N \\ 0, & |f| > (1 + \beta)B_N \end{cases}
For this problem, BN=50kHz B_N = 50 \, \text{kHz} and β=0.5 \beta = 0.5 .
The raised-cosine pulse spectrum that satisfies these requirements is defined by the above equations with the given parameters.

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