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

Started by 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.

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.
>
>
>
>cheers
>jahangir
>
>
>

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?

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
```