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what's the different between a frequency shifted signal band and a normal signal?

Started by jcseruet July 13, 2009
Hi,

I am facing some confusion about frequency shifting. I have sampled a
random noise signal at 48K . Now I have taken 5K to 11K signal band from
the main signal and shift this band at zero to 6K. I have done it 
multiplying the  5K to 11K band signal   by 2*cos(2.pi.5000.t). After
multiplying there is two band : one from 0 to 6K and another from 10K to
16K. Then using a a low pass filter I have taken the 0 to 6K band signal.
Then downsampled the signal by a factor of 4 to make the sampling rate 12K
. Now resultant signal seems to be smapled at 12K  and it's band is 0 to
6K. (Is there anything wrong about my thought?)


Now if I sample the random noise signal at 12K then is there any
difference between this signal and the signal after frequency shifting  and
downsampling. 


Thanks in advace for your time.

cheers
jahangir


On 13 Jul, 17:06, "jcseruet" <jahangir01326...@yahoo.com> wrote:
> Hi, > > I am facing some confusion about frequency shifting. I have sampled a > random noise signal at 48K . Now I have taken 5K to 11K signal band from > the main signal and shift this band at zero to 6K. I have done it > multiplying the &#2013266080;5K to 11K band signal &#2013266080; by 2*cos(2.pi.5000.t). After > multiplying there is two band : one from 0 to 6K and another from 10K to > 16K. Then using a a low pass filter I have taken the 0 to 6K band signal. > Then downsampled the signal by a factor of 4 to make the sampling rate 12K > . Now resultant signal seems to be smapled at 12K &#2013266080;and it's band is 0 to > 6K. (Is there anything wrong about my thought?)
You don't mention a band-limiting filter before the first mixer. I am not sure if the mixer shifts the frequency band up or down in frequeny. If it works as intended and shifts the signal down in frequency, you might get into trouble with aliasing if you don't use a band-limiting filter first.
> Now if I sample the random noise signal at 12K then is there any > difference between this signal and the signal after frequency shifting &#2013266080;and > downsampling.
Assuming you have done everything right - why would there be? If the signal is random noise, as you said above, the result of all this should also be random noise. Band-limited and down-sampled, but still random noise. I can't see any reason why you would see any significant difference between the original and the end result. Rune
>Hi, > >I am facing some confusion about frequency shifting. I have sampled a >random noise signal at 48K . Now I have taken 5K to 11K signal band from >the main signal and shift this band at zero to 6K. I have done it >multiplying the 5K to 11K band signal by 2*cos(2.pi.5000.t). After >multiplying there is two band : one from 0 to 6K and another from 10K to >16K. Then using a a low pass filter I have taken the 0 to 6K band
signal.
>Then downsampled the signal by a factor of 4 to make the sampling rate
12K
>. Now resultant signal seems to be smapled at 12K and it's band is 0 to >6K. (Is there anything wrong about my thought?) > > >Now if I sample the random noise signal at 12K then is there any >difference between this signal and the signal after frequency shifting
and
>downsampling. > > >Thanks in advace for your time. > >cheers >jahangir > > >
Thanks Rune for your reply.. I am trying to make things clear. I have applied a band pass filter to take 5k to 11k signal from main signal. Then shifted this band. As after shifting two resultant signal is 0 to 6k and 10k to 16k , so is there any possibility of causing aliasing because sampling rate is 48k. Can you please make it clear to me? Again before downsampling I have applied a low pass filter with cutoff frequency 6k where downsampled frequency is 12 k. So it's also safe from aliasing. I know it doesn't matter what's the sampling rate I am using because of randomness. All that I have done to understand frequency shifting. Random noise does not matter to me. My main intention is to know after frequency shifting whether only the frequency is shifted or there is any other effect on the shifted signal. Now suppose we have two signal . 1. sampled at 12k. 2. sampled at 48k. I think that -- downshifted and downsampled signal of signal (2) is same as signal (1) if there is no more effect other than just frequency shifting. Is my thought correct? thanks in advance..... cheers jahangir
What shifting operation is
in Fourier transformation?

What is modulation, what are
e^jw,
e^-jw,
sin,
cos
for a Fourier transformation?

What do they do
to a signal in freq. domain.

Look at equations. Find properties of this transformation.


-- 
Mikolaj