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From: | Marcus Müller |
Subject: | Re: [Discuss-gnuradio] How to minimize Spillage of energy in neighboring frequencies while transmission |
Date: | Mon, 26 Oct 2015 22:55:38 +0100 |
User-agent: | Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.2.0 |
Hi Abhinav,*breaks out graphics editor* So here's your 200kHz of bandwidth that you know get from the USRP: Obviously, you want to get rid of 198kHz of those 200kHz! Now, I'm assuming that your actual signal "fits" inside the 2kHz, i.e. has a bandwidth <2kHz. Let's focus on what we care for: Hm, how does one go about getting a 2kHz signal out of a 200kHz signal? The answer is surprisingly simple: You just throw away 99 of 100 samples! Obviously, it's not that simple, though. Because if we do that, we'd get 99 aliases in addition to our 1 wanted signal in the resulting 2kS/s stream. Hence, we first need to filter out everything we don't want. Ideally, we'd need a filter that really doesn't touch anything with |f| <= 1kHz and removes everything with |f| > 1kHz. Such a filter, however, is not mathematically possible¹. With filters that inherently have what we call a transition zone, width, or region, we've got to make a compromise between
A little graphic might explain that better: I think the point is clear: the less of interesting signal I cut off, the more out-of-band signal I keep. What happens now with that: Two observations:
And that's exactly what I recommended. I assumed you needed of your new Nyquist bandwidth, meaning that at each edge you had of that to spare for cut off/aliases, meaning that you can have a transition width of of your bandwidth. Best regards, Marcus ¹ it is, it would just be infinitely long, so it's not useful to us mere mortals.
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