# up conversion using multirate technique from DC

Started by July 13, 2016
```This is something I thought I would be able to do, but seems that I am runn=
ing through issues.

I have a CPM spectrum signal that I want to convert to an IF of 600MHz.

The source is an IQ pair converted at a DAC rate of 400 MHz. (2nd DAC Zone)
I thought why not=20
a ) put the complex signal pair at Fs/4 sampled at 100MHz

b) get the bandpass signal (Re{. }  =3D> I - Q)

c) downsample by 4  (copy of spectrum @ 0 =3D> DC =3D > 600MHz in DAC repli=
ca image eventually)

d) upsample by 4 digitally (reach @ 100MHz)

e) upsample by 4 (2 steps of 2x within the DAC =3D> image @ 600MHz).

-- What I am getting is more confusing that what I experienced below. I am =
willing to accept that I am not understanding fundamentally something about=
bandpass and baseband signals and the relationship with analog frequency c=
onversion. It looks like the spectrum actually is aliased when I look at it=
. Has anybody tried the above method to convert a complex signal from baseb=
and to an IF? the more important question is, considering i failed misreabl=
y as described below, what am I not understanding about multirate spectra i=
mages and their relationship to one another at baseband vs passband?

I came up with the above scheme after making a MAJOR mistake of destroying =
the phase information of CPM spectrum thinking I could just convert the IQ =
pair while at baseband to a passband (real-world signal).=20
Of course the PSD was ok, but the scatter plot definitively told me I was d=
estroying the phase content of the signal. So I thought, why not try to do =
it the way I described above.=20

Question is, why am I not getting the spectrum I thought I was seeing in my=
matlab simulation I modeled?=20
Just FYI, the spectrum prior to downsampling is adequately squeezed (10x). =
So, there was no need for me to filter the signal prior. (and even if it we=
re so, I doubt it makes a difference)

Would greatly appreciate to be able to learn from this nightmare I am going=
through.

sam
```
```A couple of first principles:

* When viewed in the frequency domain discrete time sequences are periodica=
lly extended with period equal to the sampling frequency, fs.

* Downsampling (decimation in time) by a factor D modifies the period of th=
e spectral replicas to the new sampling frequency of fs/D.

* Upsampling (zero-stuffing) by L "uncovers" spectral replicas which were a=
lways there but now visible when viewing the Fourier transform say over the=
range +/-L*fs/2.

So the Fourier transform of your original baseband signal contains spectral=
replicas at +/-400*n MHz with n being any integer.  After decimation by D=
=3D4 spectral replicas occur at +/-400/D*n MHz or every 100 MHz.  Your last=
2 upsampling by 4 steps are equivalent to 1 step of upsampling by 16.  Bec=
ause the final fs=3D1600 MHz, when viewing the Fourier transform over the r=
ange +/-800 MHz you'll see spectral replicas every 100 MHz out to +/-800 MH=
z.

But what it sounds like you're after is the original baseband signal hetrod=
yned to center at 600 MHz.  If you want to use multi-rate techniques then y=
ou 'll need filtering to remove unwanted spectral replicas.

```
```> So the Fourier transform of your original baseband signal contains spectr=
al replicas at +/-400*n MHz with n being any integer.  After decimation by =
D=3D4 spectral replicas occur at +/-400/D*n MHz or every 100 MHz.  Your las=
t 2 upsampling by 4 steps are equivalent to 1 step of upsampling by 16.  Be=
cause the final fs=3D1600 MHz,=20

The final Fs =3D 400MHz. Sorry if I didn't make that clear. The downsample =
by 4 takes it to 25MHz then by 4 to 100MHz and the DAC 4x interpolation to =
400MHz.
> But what it sounds like you're after is the original baseband signal hetr=
odyned to center at 600 MHz.  If you want to use multi-rate techniques then=
you 'll need filtering to remove unwanted spectral replicas.
i am pretty sure that I have used proper filtering for suppression of the i=
mages. The one filter that I did need, I was not worried about since the si=
gnal is properly "squeezed" prior to down sampling it by 4.

I have come to the conclusion that when I down sampled the signal, or even =
the original up conversion i was doing, I can't do anything at baseband or =
near baseband because of the negative side spectrum lying right on top of t=
he spectrum from the right side at the moment I down sampled by 4 or I trie=
d to get the "passband" version of the signal from the digital spectrum at =
DC in the case of my original method. (the problem is that I have 1 DAC to =
use and not an IQ path in the analog chain).=20
Would be good if someone can confirm this thought for me, as I guess this i=
s the stereo typical dual of the RF image rejection problem, and hence I gu=
ess why SAWs are practically the filters used after DACs.
```
```On Thursday, July 14, 2016 at 12:38:20 PM UTC-4, samberhanu wrote:
> Would be good if someone can confirm this thought for me, as I guess this is the stereo typical dual of the RF image rejection problem, and hence I guess why SAWs are practically the filters used after DACs.

Perhaps you could post a signal flow diagram of your processing chain and include spectral plots of your signal after each rate conversion stage.  Be sure to include all filter blocks as well as any decimation or interpolation stages in your diagram.

A carefully annotated drawing will not only help me or others on this board to figure out what may be happening but also may lead to an aha moment for yourself.
```
```> On Thursday, July 14, 2016 at 12:38:20 PM UTC-4, samberhanu wrote:
> Would be good if someone can confirm this thought for me, as I guess this=
is the stereo typical dual of the RF image rejection problem, and hence I =
guess why SAWs are practically the filters used after DACs.

I can confirm there is a minimum center frequency requirement to avoid self=
-interference caused by analytic to real-valued passband conversion.  Speci=
fically an analytic signal of bandwidth B must be centered at a frequency f=
c no less than B/2 to avoid self interference due to passband conversion.
```