# Documentation

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# FM Modulator Passband

Modulate using frequency modulation

## Library

Analog Passband Modulation, in Modulation

## Description

The FM Modulator Passband block modulates using frequency modulation. The output is a passband representation of the modulated signal. The output signal's frequency varies with the input signal's amplitude. Both the input and output signals are real scalar signals.

If the input is u(t) as a function of time t, then the output is

`$\mathrm{cos}\left(2\pi {f}_{c}t+2\pi {K}_{c}{\int }_{0}^{t}u\left(\tau \right)d\tau +\theta \right)$`

where:

• fc represents the Carrier frequency parameter.

• $\theta$ represents the Initial phase parameter.

• Kc represents the Frequency deviation parameter.

Typically, an appropriate Carrier frequency value is much higher than the highest frequency of the input signal.

By the Nyquist sampling theorem, the reciprocal of the model's sample time (defined by the model's signal source) must exceed twice the Carrier frequency parameter.

This block works only with real inputs of type `double`. This block does not work inside a triggered subsystem.

## Parameters

Carrier frequency (Hz)

The frequency of the carrier.

Initial phase (rad)

The initial phase of the carrier in radians.

Frequency deviation (Hz)

The frequency deviation of the carrier frequency in Hertz. Sometimes it is referred to as the "variation" in the frequency.

## Pair Block

FM Demodulator Passband

#### Introduced before R2006a

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