Is the Imaginary Part of QAM Real?
Вставка
- Опубліковано 7 сер 2021
- Explains Quadrature Amplitude Modulation (QAM) from a signals perspective, showing how signals are sent in the passband. Also explains how xDSL sends QAM signals over the baseband channel without a carrier.
Related videos: (see www.iaincollings.com)
• How do complex numbers relate to real signals?: • How do Complex Numbers...
• What is a Constellation Diagram? • What is a Constellatio...
• OFDM and the DFT • OFDM and the DFT
• Fourier Transform of cos function: • Fourier Transform of Cos
• Convolution with a Delta function: • Convolution with Delta...
• How does OFDM Overcome ISI? • How does OFDM Overcome...
• What is a Cyclic Prefix in OFDM? • What is a Cyclic Prefi...
• How does the Discrete Fourier Transform DFT relate to Real Frequencies? • How does the Discrete ...
For a full list of Videos and Summary Sheets, goto: www.iaincollings.com
.
Love your videos. There is always something new to learn.
I'm so glad you're finding them helpful.
it gives immense satisfaction and relief to the mind after understanding such complex things in such a easy and synchronized manner...on day if possible i want to be a teacher like you ...cheers
I'm so glad to hear that you found the video helpful.
@@iain_explains sir you are not a teacher you are magician 😊
Amazing information as always! Complex numbers in baseband becoming a reality in RF due to π/2 phase offset between sin and cos carrier waves..
Yes, exactly! You got it. Glad you liked the video.
Outstanding!
Glad you like it!
Hi Iain, could you make a video about spectral leakage? I heard from a colleague that this was an important topic when he wrote tests for some high-speed digitizers.
Great suggestion for a topic, thanks. I'll add it to my "to do" list. In general, spectral leakage happens for nonlinear systems. It refers to energy being spread out in the frequency domain. One example of spectral leakage occurs in sampling, and is shown in this video at the 7min10sec mark: "Discrete / Fast Fourier Transform DFT / FFT of a Sinusoid Signal" ua-cam.com/video/lwQTNcWtN7w/v-deo.html
Hi Iain. Great video! Maybe some small clarification is required for real signal production for DMT. Just concatenating C and time reverse conj(C) might not always work - ADSL standard suggests to put 0 into DC and N/2 points on top of adding time reverse conj C.
Yes, but that's so that the DC component is 0 (ie. no DC offset) and also because the voice channel is carried on the same UTP wires over the 0-4 kHz spectrum. It's not to do with whether the vector is "real" or not.
Hi Iain, you might be able to explain in a video why a radio signal (electricity in an antenna) is a complex number. What is the physical background to that. Great videos! 👍
Great suggestion! Thanks. I'll add it to my "to do" list.
In summary, the radio signal that an antenna radiates is a sinusoidal EM wave (physics and Maxwell's equations tell us this). And sinusoidal signals have three parameters: amplitude, phase and frequency. For a given frequency, the amplitude and phase parameters can be represented mathematically as a complex number. For more insights into this, see my video: "How do Complex Numbers relate to Real Signals?" ua-cam.com/video/TLWE388JWGs/v-deo.html
Please make videos on up sampling and download sampling.
Also include SNR aspect when we down sample or up sample.
Thanks for the suggestion regarding the SNR. For videos on the basics of up sampling (interpolation) and down sampling (decimation) see: "Interpolation of Discrete Time Signals" ua-cam.com/video/C5HoWirRQiU/v-deo.html and "Decimation of Discrete Time Signals" ua-cam.com/video/jP267ZoMChw/v-deo.html
pencil and papers is a really a good way to capture audience attention. Could you do LDPC for QPSK next ?
Thanks for the suggestion. LDPC is on my "to do" list already. I'll move it up the priority order.
So for my understanding here, this would be a multi carrier case at f0, with multiple orthogonal sync functions assuming proper size N,Fs? We have C0 to Cn where these are i/q values representing the frequency domain (C0 low band, Cn high band, each representing 4 bits of data), then we ifft it into a time domain where each sample is now an i/q voltage? In this case, are the original i/q values before going into the ifft chosen in such a way that they will be valid in the time domain to be converted and sent over the air or is there more post processing?
Hi. I'm not exactly sure what you're asking. Yes, c_0 to c_N are the I/Q values that are to be sent in each of the N+1 sub channels. And yes, in this example, they each represent 4 bits of data (although it could be more, if we use a larger QAM constellation). But they are not chosen in any special way. The time domain signal will be "valid" for any choice of c_0 to c_N. This video might help: "OFDM and the DFT" ua-cam.com/video/Z4LIgNgNAlI/v-deo.html
Hello Sir, could you please make a video on detailed explanation of digital communication block diagram...Thanks
Thanks for the suggestion. I've added it to my "to do" list.
Hi, I've just made the video you've asked for. I hope it helps: "How is Data Sent? An Overview of Digital Communications" ua-cam.com/video/MAddbFfCsIo/v-deo.html
Thank you. In DMT, complex samples can be transmitted in baseband by concatenating the original sequence with its conjugate. This makes the resulting spectrum symmetric (around 0), which makes the time domain signal real when using IFFT at the transmitter and FFT at the receiver. However, why go through this complicated process when we can simply convert the complex valued sequence into a real valued sequence by splitting the original sequence into two parts (real and imaginary), pulse shaping, and sending it through the baseband channel? Is the reason that bandwidth is twice in the latter? Is there any application for it?
It depends on what you mean by "sending it through the baseband channel". Do you mean sending the "real" part first, and then sending the "imaginary" part? If so, then yes, you could do this. But you'd have to equalise each of them at the receiver. The benefit of sending data "in frequency domain subchannels" is that the equalisation task is easy in the frequency domain. This video might also be of interest: "How are OFDM and xDSL (DMT) Related?" ua-cam.com/video/CET2UuGeEqs/v-deo.html
Yes exactly to send real parts first followed by imaginary . Your answer is satisfying for me.. Thank you!
Also can you make a video on interleaving benefits in physical layer of NR?
Great suggestion. I've had "interleaving" on my mind for some time as a potential video topic, so I'll add it to my "to do" list.
@@iain_explains thanks for your response
Hi lain....can you please tell me why we use only QPSK for NR PDCCH and why not other modulation schemes like 16,64 256QAM?
I'm not intimately familiar with the details of the design of the control channels in the Standard, but in general, control channels carry (relatively) low rate data that is very important to be received with zero errors (or as close to zero errors as possible). Therefore it is common to use a low order constellation (low rate, with constellation points far apart).
@@iain_explains okay...I too expected the same reason...but some more points may be there... anyways thanks for that
Dear Professor,
Why do you consider only positive frequencies for bandwidth ( 0- 1/T) at @3.07 . ? I saw your other videos. Negative frequencies are just the signals that operates in different clockwise direction. Please explains..
Thanks again for great videos
Great question. As I explained in that other video you mentioned, the "negative frequencies" are not really "negative" frequency waveforms, they relate to real (ie. positive) frequencies, but with a counter-rotating phase. In terms of "bandwidth", it does not "increase the bandwidth" to have negative frequencies. They are the same frequencies as their "positive frequency" counterparts, just with different phase. So we only measure "bandwidth" over the positive half of the Fourier transform (ie. for f>0). Also, note that we normally define the "bandwidth" to be the range of (positive) frequencies that the signal is composed of (or "the main bulk of the frequencies" eg. in the case of the sinc function in the frequency domain, it actually includes infinite frequencies, but we define the "bandwidth" to be the frequencies up to the first "zero" in the sinc function). For a _baseband_ signal (such as the one I showed in the video), the bandwidth extends from f=0 up to some positive value. And as I mentioned at the @5:34 min mark of this video, for _passband_ signals the "bandwidth" will be double the "baseband bandwidth", since the passband signal is generated by multiplying the baseband signal by a sinusoid.
@@iain_explainsso counter clockwise means that the carrier has higher frequency?
sorry i m confused. @6:43 two degree of freedom? the 2/T bandwidth will result even if we don't transmit imaginary part of QAM? Also, what about OOK signal which has baseband bandwidth of 1/T and its passband BW becomes 2/T?
I think you're mixing up the existence of a resource, with the efficient use of that resource. Yes, you're right, the 2/T bandwidth will result even if we only transmit amplitude shift keying (ASK) (ie. we don't transmit the imaginary part of QAM), but in that case we are not using the (passband) bandwidth to its maximum efficiency/capacity (in the general sense of those two terms). ASK and OOK both use double the baseband bandwidth (ie. double the necessary bandwidth), but that just means they are not efficiently using the passband. It doesn't mean the passband (full) "degrees of freedom" don't exist.
Is the Imaginary Part of QAM Real? That's a complex question...
😁