Relationships between bandwidth, Fourier trans & digital modulations

1. Jun 8, 2010

Eus

HiHo!

W. Stallings's "Wireless Communications & Networks, 2nd edition" explains the relationships between bandwidth and Fourier transformation by depicting a square wave. The square wave is approximated with a Fourier series having several sine terms. The bandwidth is then defined by the difference between the frequency of the last sine term and the first sine term (e.g., the bandwidth of $$\frac{4}{\pi}(sin((2\pi \times 10^{6})t) + \frac{1}{3}sin((2\pi \times 3 \times 10^{6})t) + \frac{1}{5}sin((2\pi \times 5 \times 10^{6})t))$$ is $$(5 \times 10^{6}) - (1 \times 10^{6}) = (4 \times 10^{6})$$ Hz).

Okay, so I understand that the bandwidth is needed to properly approximate the square wave.

However, in the same chapter, the author explains about digital modulation techniques like ASK (Amplitude Shift Keying), FSK (Frequency Shift Keying) and PSK (Phase Shift Keying). I see that in the techniques, binary bits are not encoded as a square wave but as a single sine wave through the manipulation of its amplitude, frequency or phase.

So, I understand that since there is only a single sine wave, there is no bandwidth requirement anymore in ASK and PSK since they only use a single frequency (FSK has a bandwidth requirement since different frequencies are needed to encode different bits).

Is that true? Or, is it to naive? Any pointer to literature to understand the relationships better?

What confuses me is that why I still hear the word bandwidth when talking about QAM that only uses ASK and PSK?

Best regards,
Eus

2. Jun 11, 2010

lostinxlation

I thought of the same thing before and I still don't have an answer to your last question, but I'd guess it might be because QAM is often combined with FDM like ADSL and total bandwidth goes way higher than original carrier wave ?

Last edited: Jun 11, 2010
3. Jun 14, 2010

Eus

Well, in that case, I guess this is an expert question on a transceiver system. No wonder the book has a considerable gap between the FFT explanation and digital signal modulation.

Does anyone have a pointer to understand the matters within the gap?

4. Jun 14, 2010

chroot

Staff Emeritus
The only signal that requires "zero bandwidth" is a pure sine wave -- a wave that lasts indefinitely, and never changes in amplitude, phase, or frequency.

If you change any of those parameters during transmission, you no longer have a pure sine wave. Abrupt changes from one amplitude to another, for example, actually involve frequency components on both sides of the carrier. The spectral content introduced by modulation is usually called the "sidebands."

- Warren

5. Jun 20, 2010

Eus

Hi Warren!

Thank you for the enlightening information. That covers the gap nicely :-)

6. Jun 20, 2010

poor mystic

Yes, in QAM you do start with a single, reference signal, whose timing must be agreed by the terminating modems. However this nominally sinusoidal tone soon gets very rude things done to it ~ the constant chopping and changing of phase and amplitude leaves an oscillogram of visually incomprehensible squiggles.
If a Fourier analyser is attached to the output of a QAM modem, you will see that a wide frequency band is required to convey the QAM signal.