How Do You Calculate Modulation Index and Sideband Amplitudes in FM Synthesis?

AI Thread Summary
The discussion revolves around calculating the modulation index and sideband amplitudes in frequency modulation (FM) synthesis. The carrier signal is a 440 Hz sine wave modulated by another sine wave of the same frequency, with a modulation amplitude of 1760. The deviation is confirmed as 1760, leading to a modulation index of 4, calculated by dividing the deviation by the modulating frequency. Sidebands are identified at various frequencies, including 0, 440, 880, 1320, and others, but the poster struggles with determining their amplitudes and the effects of aliasing. The conversation emphasizes the need for proper calculations and understanding of Bessel functions to complete the task.
MYMLA
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Homework Statement


[/B]
A pure tone (sine) carrier signal of 440 Hz is frequency modulated by another sine wave of frequency 440Hz with an amplitude of 1760.
(a) For the steady-state portion of the output signal generated by synthesis above, calculate: i) the deviation and ii) the Index of modulation.

(b) For the steady-state portion of the output signal generated by synthesis above, calculate the frequency of the carrier and sideband partials.

(c) For the steady-state portion of the output signal generated by synthesis above, and using the Bessel functions represented below, calculate relative amplitude of the carrier and sideband partials, allowing for aliasing.

Could someone please advise me as to how I would go about working through this question?

Thanks in advance
 
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MYMLA said:
A pure tone (sine) carrier signal of 440 Hz is frequency modulated by another sine wave of frequency 440Hz with an amplitude of 1760
Hello Mymla, :welcome:

Please read the guidelines; we aren't supposed/allowed to help if no effort is made by the poster.

In the mean time: check the numbers: modulating 440 Hz with 440 Hz ? 1760 whatkindathings ?
 

Homework Statement


A pure tone (sine) carrier signal of 440 Hz is frequency modulated by another sine wave with a frequency of also 440Hz. The amplitude of the modulating wave (The deviation) is 1760. The amplitude of the carrier is 1.
(a) For the steady-state portion of the output signal generated by synthesis above, calculate: i) the deviation and ii) the Index of modulation.

(b) For the steady-state portion of the output signal generated by synthesis above, calculate the frequency of the carrier and sideband partials.

(c) For the steady-state portion of the output signal generated by synthesis above, and using the Bessel functions represented below, calculate relative amplitude of the carrier and sideband partials, allowing for aliasing.

Homework Equations

The Attempt at a Solution


The deviation is 1760 as this is the amplitude of the modulator
The index of modulation is the deviation/mod frequency = 1760/440 = 4Side bands = 440+fm, 440-fm, 440+2fm, 440-2fm, 440+3fm, 440-3fm……. As far as the deviation. (1760 above and below 440)
So:
First pair: 440+440 and 440-440
Second Pair: 440+880 and 440-880
Third pair: 440+1320 and 440-1320
Forth pair: 440+1760 and 440-1760
So we have side bands at: 880, 0, 1320, -440, 1760, -880, 2200, -1320

This is where I get stuck. How do I work out the amplitudes of these. How does aliasing effect them?
 

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