# Sampling a signal corrupted by AWGN

Started by November 13, 2008
```RIMalhi wrote:
>> RIMalhi wrote:
>>
>>
>>   ...
>>
>>> Hi Jerry,
>>> frequency in the above sequence? I think it can be considered as two
>>> multiplexed streams. But the question is how to determine spectrum of
> the
>>> composite stream?
>> come through the same filters and therefore have the same bandwidth. The
>
>> receiver does generate some internal noise, but that is only significant
>
>> in the input stage and most of the filtering happens after that.
>>
>> Jerry
>> --
>> Engineering is the art of making what you want from things you can get.
>>
>
> Hi Jerry,
> Thanks for your reply. The bandwidth of the filters will be dicatated by
> the spectrum of the useful signal. My question was related to the bandwidth
> of the useful signal. I  restate my question here. Let us forget any
> filters or any receiver. I have an i.i.d. random process s(t). We make a
> new process s'(t) such that we have the following realizations of s'(t)
>
> ....s1 s2 s3 1 s4 s5 s6 1 s7 s8 s9 1....
>
> where s1,s2... are realization from random process s(t). Now if random
> process   s(t) has maximum frequency f_c.
>
> My question is what will be the maximum frequency of
> s'(t)? Can we say something at least qualitatively that the maximum
> frequency in the spectrum of s'(t) is equal to or greater than s(t)?
>
> The above sequence is simply s(t) with 1's multiplexed into it (we can
> consider that way because s(t) is i.i.d.).

The bandwidth of the filters is usually determined by the spectrum of
the useful signal (although sometimes you use what's on hand), but it is
also true that the bandwidth of the actual received signal is determined
by the filters.

The (purely hypothetical) case in which signal and noise are generated
separately is the same as the addition of any two signals. The bandwidth
of the sum is the overlap of the bandwidth of the signals being added.

Jerry
--
Engineering is the art of making what you want from things you can get.
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