Hm, I'd call that /spectrum/, simply :) In any case, I don't fully
understand, then, how you'd circumvent the need for a real and imaginary
part. Your $X_k$ is complex!
Cheers,
Marcus
On 04/26/2017 03:46 PM, Fernando wrote:
> Hi!.
>
> I think the amplitude spectrum is the DFT:
> {\displaystyle {\begin{aligned}X_{k}&=\sum _{n=0}^{N-1}x_{n}\cdot
> e^{-i2\pi kn/N}\\&=\sum _{n=0}^{N-1}x_{n}\cdot [\cos(2\pi kn/N)-i\cdot
> \sin(2\pi kn/N)],\end{aligned}}}
>
> So, it has sign. The power spectrum is the absolute value so it has no
> sign.
>
>
> I wish to be able to see the difference in the spectrum between this
> two signals below. If the signal generators are A and B, A+B and A-B
> are different signals, but in the power spectrum we see them as the
> same signal, so I woul like to be able to difference one from the
> other from their spectrum.
>
>
>
>
> regards
>
>
>
>
> El 26/04/17 a las 09:52, Marcus Müller escribió:
>>
>> Hey Fernando,
>>
>> not quite sure I get what you need; I'd say the Amplitude Spectrum
>> you'd be looking for is
>>
>> $$A_{|\cdot|}[f]=|X[f]| = \left\lvert\sum_{n=0}^{N-1} x[n]\cdot
>> e^{j2\pi \frac {nf}N}\right\rvert $$
>>
>> or, rather, the decibel representation of that. There's no way to get
>> a negative number out of the absolute of something – it's by
>> definition a positive real number.
>>
>> Now, we could also use our freedoms to define our amplitude spectrum
>> to take the shape
>>
>> $$A_\text{signed} = s(X[f]) |X[f]|\text{ with }
>> s(X[f])=\begin{cases}1&\text{for } -\pi \le \angle X[f] < \pi \\ 0
>> &\text{else.} \end{cases}$$
>>
>> But: that's really only useful if you have phase-coherent reception –
>> as an analytic tool for an unsynchronized observation of the
>> spectrum, it doesn't help you much, since you have a random $\angle$
>> due to having random relative phase.
>>
>> So, maybe it'd be a good idea to formulate what purpose you're doing
>> this for :) You can, indeed, tell 180° out-of-phase signals apart by
>> this, but I'd argue that being 180° out-of-phase, for the most things
>> I can think of, is only meaningful on one and the same frequency –
>> and hence, I'm not quite sure this is what you're looking for!
>>
>> Best regards,
>>
>> Marcus
>>
>>
>> On 25.04.2017 12:01, Fernando wrote:
>>> Hello.
>>>
>>> Yes, with Time sink I can see the difference, but if the signal is
>>> compound of some other signals (for instance signal=1K/amplitude +1
>>> +2K/amplitude -1 +3K/qamplitude +1 +4K/amplitude +1 ) i would like
>>> to see the 2k signal as -1 amplitude, but in the power spectrum it
>>> will appear as possitive and in the QT time sink it is very
>>> difficult to see the signal as it is a complex one.
>>>
>>> regards
>>>
>>>
>>> El 25/04/17 a las 10:57, Jinyang Lee escribió:
>>>> Hello Fernando,
>>>>
>>>> I think the QT GUI time sink displays the relationship between time
>>>> and amplitude. You can see the signal through it. But when I use
>>>> the channel model block,the QT2 can see the signal which is zero.
>>>> Enclose is running result with channel model and with channel model.
>>>>
>>>> Regards,
>>>> Lee
>>>>
>>>> 2017-04-25 15:45 GMT+08:00 Fernando <ferna...@samara.com.es
>>>> <mailto:ferna...@samara.com.es>>:
>>>>
>>>> Hi.
>>>>
>>>>
>>>> Is there a way of visualizing ampitude spectrum (with + and -
>>>> signals)
>>>> instead of power spectrum?
>>>>
>>>>
>>>> regards
>>>>
>>>>
>>>>
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>>>>
>>>
>>>
>>>
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