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Thank you for the detailed response! I just recently picked up an RTL-SDR, and for a moment though that I have this bandwidth thing figured. Nope, more learning

Thank you for the detailed response! I just recently picked up an RTL-SDR, and for a moment though that I have this bandwidth thing figured. Nope, more learning ahead. I'll probably write some simple demodulator to better understand this stuff.

H8crilA 5y ago
PS. I think I can see how to send unbounded data rates through a narrow bandwidth, assuming perfect conditions with no noise. If you want to transfer N bits per second, for half a second transmit plain carrier, then for half a second transmit carrier multiplied by x/2^N DC, where x is the sequence of bits to be transferred in that second. Then repeat the process. The receiver can establish the max reading when pure carrier is being transmitted, and do a readout when the multiplied carrier is transmitted.
- jlokier 5y ago
  That's exactly right, although if you take the Fourier transform of that modulated signal you'll see that it uses infinite bandwidth due to the square-wave modulation steps at each half second. That can be sent through a narrow bandwidth channel, which will filter out the higher harmonics. But then, as the Fourier transform suggests, you'll see at the receiver a different signal, with rounded edges instead of steps in the modulated amplitude. Those half second intervals set what's called the symbol rate to 2sym/s, and the Nyquist frequency for them is 1Hz. If your channel bandwidth (the filter) is > 1Hz, the information will still be there in the modulated, filtered signal to recover, but you'll have an interesting time doing it if the bandwidth is close to 1Hz. If your channel bandwidth is < 1Hz (the filter strictly removes all frequencies above 1Hz), you won't be able to recover all the transmitted bits. I recommend building a demodulator and varying the channel bandwidth to get an intuition for how it gets trickier to demodulate close to 1Hz. Note that making the strict bandwidth filter is also quite an interesting challenge, especially close to 1Hz; this is called a brick wall filter. Doing the Fourier transform on the entire signal before and after filtering is a good way to visualise the bandwidth taken by a modulation scheme and the effects of a channel, and to see if it's correctly removed everything above the threshold frequency. Modifying those Fourier values in the frequency domain then using an inverse Fourier transform to construct a filtered version of the entire signal is a good way to construct an ideal filter for testing the demodulator.

H8crilA 5y ago

PS. I think I can see how to send unbounded data rates through a narrow bandwidth, assuming perfect conditions with no noise. If you want to transfer N bits per second, for half a second transmit plain carrier, then for half a second transmit carrier multiplied by x/2^N DC, where x is the sequence of bits to be transferred in that second. Then repeat the process. The receiver can establish the max reading when pure carrier is being transmitted, and do a readout when the multiplied carrier is transmitted.

jlokier 5y ago
That's exactly right, although if you take the Fourier transform of that modulated signal you'll see that it uses infinite bandwidth due to the square-wave modulation steps at each half second. That can be sent through a narrow bandwidth channel, which will filter out the higher harmonics. But then, as the Fourier transform suggests, you'll see at the receiver a different signal, with rounded edges instead of steps in the modulated amplitude. Those half second intervals set what's called the symbol rate to 2sym/s, and the Nyquist frequency for them is 1Hz. If your channel bandwidth (the filter) is > 1Hz, the information will still be there in the modulated, filtered signal to recover, but you'll have an interesting time doing it if the bandwidth is close to 1Hz. If your channel bandwidth is < 1Hz (the filter strictly removes all frequencies above 1Hz), you won't be able to recover all the transmitted bits. I recommend building a demodulator and varying the channel bandwidth to get an intuition for how it gets trickier to demodulate close to 1Hz. Note that making the strict bandwidth filter is also quite an interesting challenge, especially close to 1Hz; this is called a brick wall filter. Doing the Fourier transform on the entire signal before and after filtering is a good way to visualise the bandwidth taken by a modulation scheme and the effects of a channel, and to see if it's correctly removed everything above the threshold frequency. Modifying those Fourier values in the frequency domain then using an inverse Fourier transform to construct a filtered version of the entire signal is a good way to construct an ideal filter for testing the demodulator.