Demodulate using FM method
Communications Toolbox / Modulation / Analog Baseband Modulation
The FM Demodulator Baseband block demodulates a complex input signal and returns a real output signal.
Data Types 

Multidimensional Signals 

VariableSize Signals 

Represent a frequency modulated passband signal, Y(t), as
$$Y(t)=A\mathrm{cos}\left(2\pi {f}_{c}t+2\pi {f}_{\Delta}{\displaystyle {\int}_{0}^{t}x(\tau )d\tau}\right)\text{\hspace{0.17em}},$$
where A is the carrier amplitude, f_{c} is the carrier frequency, x(τ) is the baseband input signal, and f_{Δ} is the frequency deviation in Hz. The frequency deviation is the maximum shift from f_{c} in one direction, assuming x(t) ≤ 1.
A baseband FM signal can be derived from the passband representation by downconverting it by f_{c} such that
$$\begin{array}{c}{y}_{s}(t)=Y(t){e}^{j2\pi {f}_{c}t}=\frac{A}{2}\left[{e}^{j\left(2\pi {f}_{c}t+2\pi {f}_{\Delta}{\displaystyle {\int}_{0}^{t}x(\tau )d\tau}\right)}+{e}^{j\left(2\pi {f}_{c}t+2\pi {f}_{\Delta}{\displaystyle {\int}_{0}^{t}x(\tau )d\tau}\right)}\right]{e}^{j2\pi {f}_{c}t}\\ =\frac{A}{2}\left[{e}^{j2\pi {f}_{\Delta}{\displaystyle {\int}_{0}^{t}x(\tau )d\tau}}+{e}^{j4\pi {f}_{c}tj2\pi {f}_{\Delta}{\displaystyle {\int}_{0}^{t}x(\tau )d\tau}}\right]\text{\hspace{0.17em}}.\end{array}$$
Removing the component at 2f_{c} from y_{s}(t) leaves the baseband signal representation, y(t), which is expressed as
$$y(t)=\frac{A}{2}{e}^{j2\pi {f}_{\Delta}{\displaystyle {\int}_{0}^{t}x(\tau )d\tau}}.$$
The expression for y(t) is rewritten as
$$y(t)=\frac{A}{2}{e}^{j\varphi (t)}\text{\hspace{0.17em}},$$
where $$\varphi (t)=2\pi {f}_{\Delta}{\displaystyle {\int}_{0}^{t}x(\tau )d\tau}$$, which implies that the input signal is a scaled version of the derivative of the phase, ϕ(t).
A baseband delay demodulator is used to recover the input signal from y(t).
A delayed and conjugated copy of the received signal is subtracted from the signal itself,
$$w(t)=\frac{{A}^{2}}{4}{e}^{j\varphi (t)}{e}^{j\varphi (tT)}=\frac{{A}^{2}}{4}{e}^{j\left[\varphi (t)\varphi (tT)\right]}\text{\hspace{0.17em}},$$
where T is the sample period. In discrete terms, w_{n}=w(nT), and
$$\begin{array}{l}{w}_{n}=\frac{{A}^{2}}{4}{e}^{j\left[{\varphi}_{n}{\varphi}_{n1}\right]}\text{\hspace{0.17em}}\text{,}\\ {v}_{n}={\varphi}_{n}{\varphi}_{n1}\text{\hspace{0.17em}}.\end{array}$$
The signal v_{n} is the approximate derivative of ϕ_{n}, such that v_{n} ≈ x_{n}.
[1] Chakrabarti, I. H., and I, Hatai. “A New HighPerformance Digital FM Modulator and Demodulator for SoftwareDefined Radio and Its FPGA Implementation.” International Journal of Reconfigurable Computing. Vol. 2011, No. 10.1155/2011, 2011, p. 10.
[2] Taub, Herbert, and Donald L. Schilling. Principles of Communication Systems. New York: McGrawHill, 1971, pp. 142–155.