# MODFM

## Purpose:

Performs frequency modulation of a series.

## Syntax:

MODFM(series, fmin,
fmax)

series |
- |
A series, the input to modulate. |

fmin |
- |
Optional, a real. The minimum modulation frequency.
Defaults to 0.0. |

fmax |
- |
Optional, a real. The
maximum modulation frequency. Defaults to **rate(series)/2**. |

## Returns:

A series, the frequency modulated output.

## Example:

W1: gtriwave(1000,.001, 4)

W2: modfm(w1)

W3: demodfm(w2)

W4: specgram(w2, 64, 63, 1024)

The triangle series of W1 is frequency
modulated between 0 Hz and 500 Hz in W2. W3 recovers the modulated series
and W4 displays the joint time-frequency plot of the frequency
modulated series.

## Example:

W1: gtriwave(1000,.001, 4)

W2: modfm(w1, 100, 300)

W3: demodfm(w2)

W4: specgram(w2, 64, 63, 1024)

Same as above except
the series is frequency modulated between 100 Hz and 300 Hz.

## Remarks:

A frequency modulated series is defined
by:

where *f*(*τ*)
is the modulating function.

The maximum modulation frequency, **fmax**, should be set to:

rate(series) / 2

or less.

See DEMODFM
to demodulate a frequency modulated series.

See GSWEEP
to generate a simple swept sinewave.

See MODAM
to amplitude modulate a series.

## See Also:

DEMODAM

DEMODFM

GSWEEP

MODAM

SPECGRAM