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In the PySDR online course, to the question "Why can’t we directly transmit the ethernet signal [directly in the antenna]", one answer is the following :

Square waves take an excessive amount of spectrum for the bits per second – recall from the Frequency Domain chapter that sharp changes in time domain use a large amount of bandwidth/spectrum

The illustration is the following :

The course then goes on showing amplitude shift keying modulation as a way to transmit a signal wirelessly…

But when I look at the spectrum of a ASK signal, using the Fourier transform, I also get something that looks like it occupies the whole spectrum :

I'm wondering whether this argument is a good one, or whether I missed something… I understand that given a small enough window, the spectrum would be a Dirac with the given frequency, but, the argument states that "sharp changes", so I figured out that I had to take the Fourier transform of a few periods.

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  • $\begingroup$ One could easily -- almost trivially -- filter the ASK before modulation and get a spectrally compact signal. Given the host of other reasons you wouldn't transmit Ethernet by just connecting the TX wires to a transmitter, this seems like a strange argument to put forth. $\endgroup$
    – TimWescott
    Feb 5, 2023 at 20:56

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I would agree with you that the argument as presented is a very poor one, if that is indeed what the course intended (or responder to the question). The two points stated on their own are indeed true: Square waves (at baseband or translated to any higher frequency carrier) do indeed require an excessive amount of spectrum. And ASK is indeed a way to transmit the signal wirelessly- however we would importantly pulse shape the square wave before doing the ASK modulation.

The modulation at baseband and it's spectral occupancy is not changed by shifting the carrier frequency from DC (f=0) to any other higher frequency. (As an aside for completeness, for a real modulation and real carrier, we would also have the effects of spectral aliasing when the bandwidth exceeds the carrier, which we see evidence of in the OP's spectral plot.) In order to limit the spectrum, we must pulse shape the baseband signal (or equivalently low pass filter) so that it does not have an abrupt transition in time: to change instantly in time requires an infinite bandwidth, as is observed.

An ethernet signal itself need not be rectangular pulses to be used directly as an ethernet signal, and in fact filtering the sharp edges would help reduce reflection distortion on longer cables. There are two primary reasons we choose a higher frequency and not transmit an ethernet signal directly at the antenna: the antenna design and what it's size and shape would be to efficiently transmit the signal, and regulatory requirements as to what frequencies we can radiate into and at what power. Once we do decide to transmit on a wireless channel, spectral occupancy is very important in which case pulse shaping and other bandwidth efficient modulations would be an important consideration.

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