Prev: magnitude response of IdQ-QdI
Next: AQuA Powered Voice Quality Monitoring Solution
From: gct on 24 May 2010 15:48
So I'm reading this paper, and they're deriving a formula for the
correlation between a received signal (r(n) a superposition of multipath
copies) and a known copy s(n). The formula can be seen here:
http://img20.imageshack.us/img20/4129/formulab.jpg

I get they're substituting the definition of r(n) back into the summation
and then carrying s(n) inside the second summation, but then it looks like
they're doing some DFT/IDFT stuff that I don't understand how they justify.
Can anyone help to decipher?
From: Dilip Warrier on 24 May 2010 22:16
On May 24, 3:48 pm, "gct" <smcallis(a)n_o_s_p_a_m.gmail.com> wrote:
> So I'm reading this paper, and they're deriving a formula for the
> correlation between a received signal (r(n) a superposition of multipath
> copies) and a known copy s(n).  The formula can be seen here:http://img20.imageshack.us/img20/4129/formulab.jpg
>
> I get they're substituting the definition of r(n) back into the summation
> and then carrying s(n) inside the second summation, but then it looks like
> they're doing some DFT/IDFT stuff that I don't understand how they justify.
>  Can anyone help to decipher?

Yes, in the second step, they are using the result that a circular
convolution in time is equivalent to multiplication in the frequency
domain. It's a result that's derived in most DSP textbooks. See for
instance Oppenheim & Schafer, Discrete-time Signal Processing.

Dilip.
From: Jerry Avins on 24 May 2010 22:39
On 5/24/2010 10:16 PM, Dilip Warrier wrote:
> On May 24, 3:48 pm, "gct"<smcallis(a)n_o_s_p_a_m.gmail.com> wrote:
>> So I'm reading this paper, and they're deriving a formula for the
>> correlation between a received signal (r(n) a superposition of multipath
>> copies) and a known copy s(n). The formula can be seen here:http://img20.imageshack.us/img20/4129/formulab.jpg
>>
>> I get they're substituting the definition of r(n) back into the summation
>> and then carrying s(n) inside the second summation, but then it looks like
>> they're doing some DFT/IDFT stuff that I don't understand how they justify.
>> Can anyone help to decipher?
>
> Yes, in the second step, they are using the result that a circular
> convolution in time is equivalent to multiplication in the frequency
> domain. It's a result that's derived in most DSP textbooks. See for
> instance Oppenheim& Schafer, Discrete-time Signal Processing.

Circular?

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
From: robert bristow-johnson on 24 May 2010 23:43
On May 24, 10:39 pm, Jerry Avins <j...(a)ieee.org> wrote:
> On 5/24/2010 10:16 PM, Dilip Warrier wrote:
>
> > On May 24, 3:48 pm, "gct"<smcallis(a)n_o_s_p_a_m.gmail.com>  wrote:
> >> So I'm reading this paper, and they're deriving a formula for the
> >> correlation between a received signal (r(n) a superposition of multipath
> >> copies) and a known copy s(n).  The formula can be seen here:http://img20.imageshack.us/img20/4129/formulab.jpg
>
> >> I get they're substituting the definition of r(n) back into the summation
> >> and then carrying s(n) inside the second summation, but then it looks like
> >> they're doing some DFT/IDFT stuff that I don't understand how they justify.
> >>   Can anyone help to decipher?
>
> > Yes, in the second step, they are using the result that a circular
> > convolution in time is equivalent to multiplication in the frequency
> > domain. It's a result that's derived in most DSP textbooks. See for
> > instance Oppenheim&  Schafer, Discrete-time Signal Processing.
>
> Circular?

yeah, if it's the DFTs being multiplied.

r b-j

 | 
Pages: 1
Prev: magnitude response of IdQ-QdI
Next: AQuA Powered Voice Quality Monitoring Solution