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Comment on Frequency Modulation (FM) and Demodulation Using DSP Techniques by YouTube Premium
['Qasim Chaudhari']
Comments for Wireless Pi
Analog modulation schemes, on the other hand, vary the desired parameter in a continuous fashion according to the message signal.
\begin{equation}\label{equation-frequency-deviation}\Delta f = k_f A_m\end{equation}Peak frequency deviation represents how far the modulated signal frequency can stretch in either direction as compared to the carrier frequency.
$$\begin{equation}\begin{aligned}\theta(nT_s) &= 2\pi k_f \int_{0}^{nT_s} x(\tau) d\tau \\&= 2\pi k_f \int_{0}^{(n-1)T_s} x(\tau) d\tau + 2\pi k_f \int_{(n-1)T_s}^{nT_s} x(\tau) d\tau \\ \\&=\theta[(n-1)T_s] + 2\pi k_f T_s x[(n-1)T_s]\end{aligned}\end{equation}\label{equation-fm-phase-baseband}$$where the continuous-time integral has been replaced with the backward difference version of a discrete-time integrator.
\begin{equation}\label{equation-fm-demodulation}z[n] = e^{j\theta(nT_s)} = e^{j \left\{\theta[(n-1)T_s] + 2\pi k_f T_s x[(n-1)T_s]\right\}}\end{equation}From here, the FM demodulation techniques can be divided into three different categories.
Differentiate and Access PhaseA conventional demodulation technique used in old analog FM receivers is to differentiate the FM signal $y(t)$ in Eq (\ref{equation-fm-modulation}).