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How can one find symbol duration if bit rate is 100 kbs (as BPSK is used, symbol rate = bit rate)?

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The symbol duration $T_p$ is related to the symbol rate $R_s$ by the simple relationship $$T_p = \frac{1}{R_p}$$

In the case of BPSK, $R_p$ is equal to the bit rate $R_b$, and $$T_p = \frac{1}{R_b}$$

For constellations with $M$ elements, each symbol encodes $k = \log_2(M)$ bits, the symbol rate is $R_p = R_b / k$, and the symbol duration is $$T_p = \frac{1}{R_p} = \frac{k}{R_b}$$

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