How are Correlation and Convolution Related in Digital Communications?

[@adonis7419]

The best teacher for all telecom students 😍I wish I had a teacher like this during my classes

[@iain_explains]

Thanks. I'm glad you're finding the videos helpful. I'm enjoying making them.

[@Max-hf7fx]

Thank you from germany. Very nice explanations.

[@iain_explains]

Glad it was helpful!

[@bkquanvu3228]

Thank you from Việt Nam. 😍😍😍

[@bitcubeRL]

Thank you Professor for these videos. Your explanations are very clear and concise. So if we take f(t) = transmitted waveform in the correlation receiver, we will get maximum SNR and we can always use correlation receiver instead of matched filter. Is there any scenario in which one receiver architecture is more beneficial over the other?

[@iain_explains]

It all depends on the electronics you prefer to use in order to implement it. Generally correlator structures are easier to implement.

[@jaiwilson8047]

Thanks mate your videos are always a great help

[@iain_explains]

Glad you like them!

[@ibrahimshikdaher7551]

Thanks a lot. Amazing videos

[@emileduvernois6680]

I do not get the matched filter part. Why do you integrate between 0 and t, when the convolution formula tells you to integrate between -∞ and +∞ ?

[@iain_explains]

Ah, good question. I forgot to mention it, but in the video, we are considering only the part of the received signal that arrives between time t=0 and t=T. In other words, we are looking at demodulating and detecting a single digital symbol (the one that was sent on a signal/modulation waveform between time t=0 and t=T), and hence we are only integrating over that time interval. The same analysis will hold for all other digital symbols in a digital communications data sequence (sent at other times), but with the range of the integral shifted in time to correspond to the time over which each of those other symbols is sent.

[@emileduvernois6680]

@@iain_explains I think I got it : when you pass the function f through a filter with an impulse response g, if your function f is null for negative values of time, (a reasonable hypothesis) you only integrate over [0, infty[, and if your impulse response is null for negative values of time, then g(t-u) is null for u>t. and therefore, integrating f(u)g(t-u)du on the whole real axis boils down to integrating between 0 and t. Thank You! That was my moment of epiphany about the convolution !

[@rishabhkumar1050]

sir in real communication which Is more preferred matched filter receiver or coorelator receiver if both performing same task?

[@iain_explains]

Often the correlation receiver is easier to implement, so it is generally preferred.

[@malini50]

@@iain_explains Hello again. As per your explanation(in current video) both the receivers seems to be simple. Please describe why implementing convolution receiver is more complex??

[@harrysvensson2610]

Somewhat off-topic, It would be fun to see how coherence is related to correlation and a case where coherence is not equal to 1.

[@iain_explains]

Thanks for the suggestion. I've added it to my "to do" list.

[@gamingandmusic9217]

Thanks again sir.

[@iain_explains]

Always welcome

[@sadeqebrahimi2925]

MY HERO

[@Jedlmind]

Thank you.

[@iain_explains]

You're welcome!

[@AJ-fo3hp]

h(m) = f(T-m) h(m-tau)=f(T-m+tau) ---------------------------- h(tau) = f(-tau+T) h(-tau)=f(+tau +T) h(-tau+t)=f(tau+T+t)