I absolutely *LOVED* this presentation! I graduated in 1976 with a BSEE, but all of this was a practical impossibility due to the relative slowness of existing compute power. Imagine trying to implement these ideas with an 8 bit microprocessor (think Z-80) running at a _”leisurely”_ 4 mHz.! And yet … all of the *COMPLEX MATH* was possible, just nothing fast enough to run it! Perhaps we ought to think ahead and create (theoretical) concepts, even if they have to wait *DECADES* to be practical. You know, the old humorous chemical equations that had a block labeled *_”An then a miracle occurs…”_* 😀
Good explanation to the basics. i would like to add that you also need another band pass filter at the RF stage to counteract the signals at image frequencies
Looking for a detailed overview of the Tyloe quadrature demodulator that shows how the recombination of the 4 samples, 0/270, 90/180, results in the I and Q signals.
Yeah, sorry if it's there and I've just missed it, but but how seems like you left out something major, i.e. HOW does this "digital complex mixer" get I and Q from just the sampled amplitude values? From what I could gather from the source code of uSDX (seemingly the only source on the subject), what it does is sample at 2 * Fs, treating even samples as I, odd as Q, but linearly interpolates the Is, replacing each one with the average of it and the next one. What this clearly does do is shift one of the streams in time by one sample period, so that the synthetic Is coincide with Qs. While the thing does work in the end, - the device does seem to receive SSB, which is the only use for the I/Q data there, as far as I can tell, - I can't possibly see a) how can those I values be correct beyond the simple assumption that both domains are (-1; 1), and, more importantly, b) any basis for the downright strange assumption that a shift by one sample in the array is equivalent to a 90 degree phase shift. This technique, which quacks like a dirty hack for the anemic 8-bit MCU it's written for, is called a "Hilbert transform" in the comments. Whatever. Correct or not, the whole transition from amplitude samples to I, Q pairs doesn't seem like an "implementation detail" you can just omit here, especially when the end result of the formulation is supposed to be a general SDR, and not some special case transceiver.
At 4:45 you say sin of f2 is real and cosin of f2 is imaginary, but in the previous slide this was reversed; sin was imaginary and cosin was real. Can you explain this discrepancy?
Excellent presentation. But the devil is in the details. Where do I get an ADC and a DAC breakout board at a cheap enough price( < $20) that will handle 200 MSPS ?
Very nice presentation but... 5:12: there is a mistake in the first formula. You say: cos(f1)sin(f2) = 1/2*{sin(f1-f2) + sin(f1+f2)} which is wrong. It should be: cos(f1)sin(f2) = 1/2{sin(f2-f1) + sin(f1+f2)}. Second one is OK. Both formula should be presented in this way: cos(f1)sin(f2) = 1/2{sin(f2-f1) + sin(f2-f1)} cos(f1)cos(f2)=1/2{cos(f2-f1) + cos(f2+f1)}
Actually this is not really wrong since a negative frequency in the cos is the same as a cos with the positive frequency. Negative frequencies get "mirrored" up in the spektrum. Its only better to undertand in this case.
5:35 I don’t understand what you mean on simplify it by removing the high frequency component. Why don’t you simplify it by multiplying by 0? That would be more simple.
So the reason you multiply/mix the input by an analog RF tuner, is only to bring the signal to the area of the band-pass hardware filter? Would Direct-Sampling remove this Intermediate-Frequency requirement, and if so, why isn't it the preferred approach? However, it still feels like a free lunch that you can sample and get a *single* ADC value, but then digitally mix (DDC) to get 2 baseband samples (the cosine (Q) and sine data (I))! After-all, couldn't more operations be done on the same sample to get even more bandwidth?
