PPM Signal Analyzer
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PPM Spectrum
In Pulse Position Modulation (PPM), the position of each pulse within its time slot is varied according to the instantaneous amplitude of the message signal, while the pulse amplitude and width remain constant.
\[ s_{PPM}(t) = A_p \sum_{n=-\infty}^{\infty} p\left(t-nT_c-\tau_n\right) \]
The pulse position displacement is proportional to the message signal. It can be represented as:
\[ \boxed{\tau_n = k_p\,m(nT_c)} \]
The PPM spectrum consists of a DC component and spectral components around harmonics of the pulse repetition frequency. For a sinusoidal message, sidebands occur around these harmonics and are spaced by the message frequency.
\[ \boxed{f = kf_s \pm nf_m} \]
Frequency Components
Therefore, the PPM spectrum contains components around integer multiples of the pulse repetition frequency:
\[ \boxed{f = kf_s \pm nf_m} \]
where \(k = 0,\pm1,\pm2,\ldots\) and \(n = 1,2,3,\ldots\) .
In PPM, the pulse amplitude and pulse width remain constant. The information is carried by the displacement of the pulse position from its reference position. Consequently, the spectrum is related to the pulse repetition frequency and contains sidebands whose spacing is determined by the message frequency.
Here, \(f_s = 1/T_c\) is the pulse repetition frequency, \(f_m\) is the message frequency, \(A_p\) is the pulse amplitude, and \(\tau_n\) represents the position displacement of the \(n\)-th pulse. Unlike PWM, where information is represented by pulse-width variation, PPM represents the information through pulse-position variation.