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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 [tex]\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))[/tex] is [tex](5 \times 10^{6}) - (1 \times 10^{6}) = (4 \times 10^{6})[/tex] 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

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# Relationships between bandwidth, Fourier trans & digital modulations

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