On 23.01.2016 1:07, Evgeny Filatov wrote:> On 22.01.2016 13:04, b2508 wrote: > >> Not really :-) I am asked to provide both without knowing why :-) >> My intention is to do this in FPGA. >> --------------------------------------- >> Posted through http://www.DSPRelated.com >> > > Oops! I'm sorry then. > > Perhaps you could _imitate_ real conversion by (1) doing complex > conversion then (2) doing low-pass filtering and (3) filtering out > negative frequencies (which could involve a Hilbert transform filter), > (4) then just leaving the real part of your output. > > Then you could pretend it's just a tricky implementation of real > conversion for the case of signals with BW > fs/4. > > It's just a sketch of an idea. Hope it helps. > > Evgeny. >No, that was REALLY stupid. A case of typing ahead of thinking. :) Just center the desired image of your signal at 0 with the use of complex mixer, then run a low-pass filter, then (if your manager wants you to do it) move the signal elsewhere with another complex mixer and take the real part of it. Regards, Evgeny.
Undersampling with inverted spectrum
Started by ●January 18, 2016
Reply by ●January 22, 20162016-01-22
Reply by ●January 23, 20162016-01-23
On 1/22/2016 5:07 AM, b2508 wrote:>> On 1/19/2016 9:00 AM, b2508 wrote: > >> >> Your spectrum is not between 0 and fs/4. After the complex >> down-conversion it is complex and between -fs/4 and fs/4 or if you >> haven't done the complex down-conversion it is real and between fs/2 and > >> fs. No need to do both conversions. Start with the real representation > >> and convert it to where you want it. >> >> You need to multiply the signal by fs/2 which will, as you say, move the > >> signal to the region between fs/2 and fs. However that is exactly what >> you want as the image of this signal will be frequency inverted again >> and lie between 0 and fs/2 restoring it to the original orientation. >> The images are always there at all multiples of fs/2 with every other >> one having an inverted spectrum. You can use them as you wish. >> >> -- >> >> Rick > > > I did not mean to do downconversion twice. I meant that when I do > undersampling of real signal and it was initially in second Nyquist zone, > it ends up between 0 and fs/4 or fs/4 and fs/2. After that I want to > perform real downconversion and make spectrum oriented in the right way.Hmmm... Perhaps a typo? If you are down converting a real signal by under-sampling, it is in the range of 0 to fs/2 and is inverted or not (in your case it is inverted because it was in the range of the odd multiple of fs/2 to an even multiple of fs/2). To get the real non-inverted image you need to shift frequency by fs/2 so it is between -fs/2 and 0 which will show up as inverted in the range of 0 to fs/2. That would be very easily done by multiplying by a sequence of 1, -1, 1, -1... No filtering is required because all images in the result reflect to the same frequencies in the range of 0 to fs/2. -- Rick
Reply by ●January 25, 20162016-01-25
>On 1/22/2016 5:07 AM, b2508 wrote: >>> On 1/19/2016 9:00 AM, b2508 wrote: >> >>> >>> Your spectrum is not between 0 and fs/4. After the complex >>> down-conversion it is complex and between -fs/4 and fs/4 or if you >>> haven't done the complex down-conversion it is real and between fs/2and>> >>> fs. No need to do both conversions. Start with the realrepresentation>> >>> and convert it to where you want it. >>> >>> You need to multiply the signal by fs/2 which will, as you say, movethe>> >>> signal to the region between fs/2 and fs. However that is exactlywhat>>> you want as the image of this signal will be frequency inverted again >>> and lie between 0 and fs/2 restoring it to the original orientation. >>> The images are always there at all multiples of fs/2 with every other >>> one having an inverted spectrum. You can use them as you wish. >>> >>> -- >>> >>> Rick >> >> >> I did not mean to do downconversion twice. I meant that when I do >> undersampling of real signal and it was initially in second Nyquistzone,>> it ends up between 0 and fs/4 or fs/4 and fs/2. After that I want to >> perform real downconversion and make spectrum oriented in the rightway.> >Hmmm... Perhaps a typo? If you are down converting a real signal by >under-sampling, it is in the range of 0 to fs/2 and is inverted or not >(in your case it is inverted because it was in the range of the odd >multiple of fs/2 to an even multiple of fs/2). To get the real >non-inverted image you need to shift frequency by fs/2 so it is between >-fs/2 and 0 which will show up as inverted in the range of 0 to fs/2. >That would be very easily done by multiplying by a sequence of 1, -1, 1,>-1... No filtering is required because all images in the result reflect>to the same frequencies in the range of 0 to fs/2. > >-- > >RickMy conclusion (and after some simulations as well) is that I can first do what you are proposing - multiply with 1,-1... then my spectrum will be inverted around fs/4 (or what was between -fs/2 and 0 will appear between 0 and fs/2 and vice versa) and in the "original" order of frequencies. After that I can just multiply it with sine in such way that it is moved to frequency = BW/2. Images will appear now but not in the place where my content is (0 to BW). After this I have downsampling by factor of 2 which includes filtering before decimation and that can clear all the unnecessary images. --------------------------------------- Posted through http://www.DSPRelated.com
Reply by ●January 25, 20162016-01-25
On 1/25/2016 4:14 AM, b2508 wrote:>> On 1/22/2016 5:07 AM, b2508 wrote: >>>> On 1/19/2016 9:00 AM, b2508 wrote: >>> >>>> >>>> Your spectrum is not between 0 and fs/4. After the complex >>>> down-conversion it is complex and between -fs/4 and fs/4 or if you >>>> haven't done the complex down-conversion it is real and between fs/2 > and >>> >>>> fs. No need to do both conversions. Start with the real > representation >>> >>>> and convert it to where you want it. >>>> >>>> You need to multiply the signal by fs/2 which will, as you say, move > the >>> >>>> signal to the region between fs/2 and fs. However that is exactly > what >>>> you want as the image of this signal will be frequency inverted again >>>> and lie between 0 and fs/2 restoring it to the original orientation. >>>> The images are always there at all multiples of fs/2 with every other >>>> one having an inverted spectrum. You can use them as you wish. >>>> >>>> -- >>>> >>>> Rick >>> >>> >>> I did not mean to do downconversion twice. I meant that when I do >>> undersampling of real signal and it was initially in second Nyquist > zone, >>> it ends up between 0 and fs/4 or fs/4 and fs/2. After that I want to >>> perform real downconversion and make spectrum oriented in the right > way. >> >> Hmmm... Perhaps a typo? If you are down converting a real signal by >> under-sampling, it is in the range of 0 to fs/2 and is inverted or not >> (in your case it is inverted because it was in the range of the odd >> multiple of fs/2 to an even multiple of fs/2). To get the real >> non-inverted image you need to shift frequency by fs/2 so it is between >> -fs/2 and 0 which will show up as inverted in the range of 0 to fs/2. >> That would be very easily done by multiplying by a sequence of 1, -1, 1, > >> -1... No filtering is required because all images in the result reflect > >> to the same frequencies in the range of 0 to fs/2. >> >> -- >> >> Rick > My conclusion (and after some simulations as well) is that I can first do > what you are proposing - multiply with 1,-1... then my spectrum will be > inverted around fs/4 (or what was between -fs/2 and 0 will appear between > 0 and fs/2 and vice versa) and in the "original" order of frequencies. > > After that I can just multiply it with sine in such way that it is moved > to frequency = BW/2. Images will appear now but not in the place where my > content is (0 to BW). After this I have downsampling by factor of 2 which > includes filtering before decimation and that can clear all the > unnecessary images.I don't follow this last part at all. What is BW exactly? There is no need to worry about the images of the in band signal as they do not interfere with receiving your signal. Maybe it would be good to work with real frequencies rather then symbolic. -- Rick
Reply by ●January 25, 20162016-01-25
>On 1/25/2016 4:14 AM, b2508 wrote: >>> On 1/22/2016 5:07 AM, b2508 wrote: >>>>> On 1/19/2016 9:00 AM, b2508 wrote: >>>> >>>>> >>>>> Your spectrum is not between 0 and fs/4. After the complex >>>>> down-conversion it is complex and between -fs/4 and fs/4 or if you >>>>> haven't done the complex down-conversion it is real and betweenfs/2>> and >>>> >>>>> fs. No need to do both conversions. Start with the real >> representation >>>> >>>>> and convert it to where you want it. >>>>> >>>>> You need to multiply the signal by fs/2 which will, as you say,move>> the >>>> >>>>> signal to the region between fs/2 and fs. However that is exactly >> what >>>>> you want as the image of this signal will be frequency invertedagain>>>>> and lie between 0 and fs/2 restoring it to the originalorientation.>>>>> The images are always there at all multiples of fs/2 with everyother>>>>> one having an inverted spectrum. You can use them as you wish. >>>>> >>>>> -- >>>>> >>>>> Rick >>>> >>>> >>>> I did not mean to do downconversion twice. I meant that when I do >>>> undersampling of real signal and it was initially in second Nyquist >> zone, >>>> it ends up between 0 and fs/4 or fs/4 and fs/2. After that I want to >>>> perform real downconversion and make spectrum oriented in the right >> way. >>> >>> Hmmm... Perhaps a typo? If you are down converting a real signal by >>> under-sampling, it is in the range of 0 to fs/2 and is inverted ornot>>> (in your case it is inverted because it was in the range of the odd >>> multiple of fs/2 to an even multiple of fs/2). To get the real >>> non-inverted image you need to shift frequency by fs/2 so it isbetween>>> -fs/2 and 0 which will show up as inverted in the range of 0 to fs/2. >>> That would be very easily done by multiplying by a sequence of 1, -1,1,>> >>> -1... No filtering is required because all images in the resultreflect>> >>> to the same frequencies in the range of 0 to fs/2. >>> >>> -- >>> >>> Rick >> My conclusion (and after some simulations as well) is that I can firstdo>> what you are proposing - multiply with 1,-1... then my spectrum willbe>> inverted around fs/4 (or what was between -fs/2 and 0 will appearbetween>> 0 and fs/2 and vice versa) and in the "original" order of frequencies. >> >> After that I can just multiply it with sine in such way that it ismoved>> to frequency = BW/2. Images will appear now but not in the place wheremy>> content is (0 to BW). After this I have downsampling by factor of 2which>> includes filtering before decimation and that can clear all the >> unnecessary images. > >I don't follow this last part at all. What is BW exactly? There is no >need to worry about the images of the in band signal as they do not >interfere with receiving your signal. > >Maybe it would be good to work with real frequencies rather thensymbolic.> >-- > >RickBW is bandwidth of my signal. Lets say i have original analog signal centered at 150MHz and bandwidth of signal of interest is 40 MHz. If I undersample it with 200MHz, signal of interest will move to the center of 50 MHz and it will be spread from 30 MHz to 70 MHz but with reversed spectrum. When I multiply it with 1, -1, what was at 30MHz will end up at 70MHz and what was at 70 MHz will go to 30 MHz, in other words I will have spectrum in the "right frequency order" or not inverted any more. Now I want to move it closer to 0Hz or downconvert it but with real downconversion. If I use real LO with frequency of 30 MHz, I will move the content that was at 30-70MHz to 0-40MHz (and replica will be from -40MHz to 0) but I will also get images at 60-100MHz, right? These must be filtered out, am I right? I anyway want to downsample signal afterwards because sample rate of 100MHz should be enough for signal of this bandwidth. Therefore I will filter these components before decimation. --------------------------------------- Posted through http://www.DSPRelated.com
Reply by ●January 25, 20162016-01-25
On 25.1.16 17:13, b2508 wrote:>> On 1/25/2016 4:14 AM, b2508 wrote: >>>> On 1/22/2016 5:07 AM, b2508 wrote: >>>>>> On 1/19/2016 9:00 AM, b2508 wrote: >>>>> >>>>>> >>>>>> Your spectrum is not between 0 and fs/4. After the complex >>>>>> down-conversion it is complex and between -fs/4 and fs/4 or if you >>>>>> haven't done the complex down-conversion it is real and between > fs/2 >>> and >>>>> >>>>>> fs. No need to do both conversions. Start with the real >>> representation >>>>> >>>>>> and convert it to where you want it. >>>>>> >>>>>> You need to multiply the signal by fs/2 which will, as you say, > move >>> the >>>>> >>>>>> signal to the region between fs/2 and fs. However that is exactly >>> what >>>>>> you want as the image of this signal will be frequency inverted > again >>>>>> and lie between 0 and fs/2 restoring it to the original > orientation. >>>>>> The images are always there at all multiples of fs/2 with every > other >>>>>> one having an inverted spectrum. You can use them as you wish. >>>>>> >>>>>> -- >>>>>> >>>>>> Rick >>>>> >>>>> >>>>> I did not mean to do downconversion twice. I meant that when I do >>>>> undersampling of real signal and it was initially in second Nyquist >>> zone, >>>>> it ends up between 0 and fs/4 or fs/4 and fs/2. After that I want to >>>>> perform real downconversion and make spectrum oriented in the right >>> way. >>>> >>>> Hmmm... Perhaps a typo? If you are down converting a real signal by >>>> under-sampling, it is in the range of 0 to fs/2 and is inverted or > not >>>> (in your case it is inverted because it was in the range of the odd >>>> multiple of fs/2 to an even multiple of fs/2). To get the real >>>> non-inverted image you need to shift frequency by fs/2 so it is > between >>>> -fs/2 and 0 which will show up as inverted in the range of 0 to fs/2. >>>> That would be very easily done by multiplying by a sequence of 1, -1, > 1, >>> >>>> -1... No filtering is required because all images in the result > reflect >>> >>>> to the same frequencies in the range of 0 to fs/2. >>>> >>>> -- >>>> >>>> Rick >>> My conclusion (and after some simulations as well) is that I can first > do >>> what you are proposing - multiply with 1,-1... then my spectrum will > be >>> inverted around fs/4 (or what was between -fs/2 and 0 will appear > between >>> 0 and fs/2 and vice versa) and in the "original" order of frequencies. >>> >>> After that I can just multiply it with sine in such way that it is > moved >>> to frequency = BW/2. Images will appear now but not in the place where > my >>> content is (0 to BW). After this I have downsampling by factor of 2 > which >>> includes filtering before decimation and that can clear all the >>> unnecessary images. >> >> I don't follow this last part at all. What is BW exactly? There is no >> need to worry about the images of the in band signal as they do not >> interfere with receiving your signal. >> >> Maybe it would be good to work with real frequencies rather then > symbolic. >> >> -- >> >> Rick > > BW is bandwidth of my signal. > > Lets say i have original analog signal centered at 150MHz and bandwidth of > signal of interest is 40 MHz. If I undersample it with 200MHz, signal of > interest will move to the center of 50 MHz and it will be spread from 30 > MHz to 70 MHz but with reversed spectrum. When I multiply it with 1, -1, > what was at 30MHz will end up at 70MHz and what was at 70 MHz will go to > 30 MHz, in other words I will have spectrum in the "right frequency order" > or not inverted any more. > Now I want to move it closer to 0Hz or downconvert it but with real > downconversion. If I use real LO with frequency of 30 MHz, I will move the > content that was at 30-70MHz to 0-40MHz (and replica will be from -40MHz > to 0) but I will also get images at 60-100MHz, right? > These must be filtered out, am I right? > I anyway want to downsample signal afterwards because sample rate of > 100MHz should be enough for signal of this bandwidth. Therefore I will > filter these components before decimation.Do you have a good pre-sampling filter passing only 130 to 170 MHz, suppressing 30-70 MHz, 230-270 MHz etc? There are images in the input spectrum which must not be ignored. -- -TV
Reply by ●January 25, 20162016-01-25
On 1/25/2016 10:13 AM, b2508 wrote:>> On 1/25/2016 4:14 AM, b2508 wrote: >>>> On 1/22/2016 5:07 AM, b2508 wrote: >>>>>> On 1/19/2016 9:00 AM, b2508 wrote: >>>>> >>>>>> >>>>>> Your spectrum is not between 0 and fs/4. After the complex >>>>>> down-conversion it is complex and between -fs/4 and fs/4 or if you >>>>>> haven't done the complex down-conversion it is real and between > fs/2 >>> and >>>>> >>>>>> fs. No need to do both conversions. Start with the real >>> representation >>>>> >>>>>> and convert it to where you want it. >>>>>> >>>>>> You need to multiply the signal by fs/2 which will, as you say, > move >>> the >>>>> >>>>>> signal to the region between fs/2 and fs. However that is exactly >>> what >>>>>> you want as the image of this signal will be frequency inverted > again >>>>>> and lie between 0 and fs/2 restoring it to the original > orientation. >>>>>> The images are always there at all multiples of fs/2 with every > other >>>>>> one having an inverted spectrum. You can use them as you wish. >>>>>> >>>>>> -- >>>>>> >>>>>> Rick >>>>> >>>>> >>>>> I did not mean to do downconversion twice. I meant that when I do >>>>> undersampling of real signal and it was initially in second Nyquist >>> zone, >>>>> it ends up between 0 and fs/4 or fs/4 and fs/2. After that I want to >>>>> perform real downconversion and make spectrum oriented in the right >>> way. >>>> >>>> Hmmm... Perhaps a typo? If you are down converting a real signal by >>>> under-sampling, it is in the range of 0 to fs/2 and is inverted or > not >>>> (in your case it is inverted because it was in the range of the odd >>>> multiple of fs/2 to an even multiple of fs/2). To get the real >>>> non-inverted image you need to shift frequency by fs/2 so it is > between >>>> -fs/2 and 0 which will show up as inverted in the range of 0 to fs/2. >>>> That would be very easily done by multiplying by a sequence of 1, -1, > 1, >>> >>>> -1... No filtering is required because all images in the result > reflect >>> >>>> to the same frequencies in the range of 0 to fs/2. >>>> >>>> -- >>>> >>>> Rick >>> My conclusion (and after some simulations as well) is that I can first > do >>> what you are proposing - multiply with 1,-1... then my spectrum will > be >>> inverted around fs/4 (or what was between -fs/2 and 0 will appear > between >>> 0 and fs/2 and vice versa) and in the "original" order of frequencies. >>> >>> After that I can just multiply it with sine in such way that it is > moved >>> to frequency = BW/2. Images will appear now but not in the place where > my >>> content is (0 to BW). After this I have downsampling by factor of 2 > which >>> includes filtering before decimation and that can clear all the >>> unnecessary images. >> >> I don't follow this last part at all. What is BW exactly? There is no >> need to worry about the images of the in band signal as they do not >> interfere with receiving your signal. >> >> Maybe it would be good to work with real frequencies rather then > symbolic. >> >> -- >> >> Rick > > BW is bandwidth of my signal. > > Lets say i have original analog signal centered at 150MHz and bandwidth of > signal of interest is 40 MHz. If I undersample it with 200MHz, signal of > interest will move to the center of 50 MHz and it will be spread from 30 > MHz to 70 MHz but with reversed spectrum. When I multiply it with 1, -1, > what was at 30MHz will end up at 70MHz and what was at 70 MHz will go to > 30 MHz, in other words I will have spectrum in the "right frequency order" > or not inverted any more. > Now I want to move it closer to 0Hz or downconvert it but with real > downconversion. If I use real LO with frequency of 30 MHz, I will move the > content that was at 30-70MHz to 0-40MHz (and replica will be from -40MHz > to 0) but I will also get images at 60-100MHz, right? > These must be filtered out, am I right? > I anyway want to downsample signal afterwards because sample rate of > 100MHz should be enough for signal of this bandwidth. Therefore I will > filter these components before decimation.You will have "replicas" at multiples of fs/2 because of the nature of sampling. You do not need to filter out anything. In many ways these images are "imaginary". If there was anything to filter out it would be better done before sampling or at least make sure after aliasing it ends up at a frequency outside of your BW where it can be filtered post sampling. The reflections (images) are impossible to avoid. They are only a problem when you have something out of band that you don't want reflected in band. -- Rick
