RE: Physics chalange in signal processing

[Damian Harty]

Wavelets are your friend under these circumstances...

Damian Harty 
Director - Vehicle & System Dynamics Group
Coventry University
+44(0)24 7688 8924
+44(0)7799 414832

-----Original Message-----
From: address@hidden [mailto:address@hidden On Behalf Of Juan Pablo Carbajal
Sent: 11 February 2013 19:01
To: sloopools
Cc: address@hidden
Subject: Re: Physics chalange in signal processing

On Mon, Feb 11, 2013 at 7:10 PM, sloopools <address@hidden> wrote:
> Hi Doug!
>
> I am sorry, maybe I went too straight forward without explaing well.
> By modulating, I realy mean to modulate it in terms of signal ad 
> processing, meaning, to describe the amlitude and frequency for each 
> time point. This would be the main goal but of course impossible or 
> very hard to do it, because my original signal O is never stationary 
> and many more variables can also for noise...
>
> My idea was to try to make it simple and get a hint from you about 
> where and how to look for an answer. I dont even know what kind of 
> matematical problem I am dealing with...
>
> So, to be realistic and simple, lets say I have a signal that is 
> represented by the Fourrier Transform (FFT) ploted in Black (see 
> figure I have attached on original post). I want to change that signal 
> in terms of amplitude and frequencies shifts (everything that is 
> necessary) in order to generate a different signal witch FFT is given 
> by te RED line. In short words, I want to be able to artificially generate my 
> red line FFT signal tweeking my data.
>
> Let me try to brainstorm here for a second:
> I read that in order to make a frequency shift to a signal, we can 
> multiply the raw signal by a cousin, like this:
> raw_data_signal.*cos(2*pi*1000*t) --> This would cause a w=1000 Hz 
> shift of frequency.
> Then if do some adjustments in the amplitude of the raw signal in some 
> frequency bands, I might be able to get a very similar curve as my red 
> FFT one. Would you agree?
> Is this the typically way that people do it or am I beeing naive?
> Keywords?
>
> Sloopools
>
> On 11 February 2013 17:29, Doug Stewart-4 [via Octave] <[hidden 
> email]>
> wrote:
>>
>>
>>
>>
>> On Mon, Feb 11, 2013 at 10:38 AM, sloopools <[hidden email]> wrote:
>>>
>>> Hey guys!
>>> I have a chalange for you guys:
>>>
>>> *Scenario 1:* /This is a scenario of Frequency_Shift - 
>>> Same_Amplitude/ Lets say you have an ambulance car passing by you 
>>> and you are standing still in a sidewalk. The sirenes sound as the 
>>> car is approximating to you is different from the sound of the same 
>>> sirenes as the car moves away from you.
>>> This fenomena is obviously because of the sound propagation velocity 
>>> that is added or subtracted from the car velocity as it passwer by 
>>> you.
>>> Now if you record the sound of that sirene, you would see a higher 
>>> speed *signal A *(higher frequencies) as the car approximates and a 
>>> lower speed *signal B *(lower freqs) as the car distances from you. So far, 
>>> no news.
>>> If you have an original recording of the sirenes without the 
>>> ambulance moving, lets call it *signal O*, and compare it with 
>>> signal A, you would see that signal A has higher frequencies for the 
>>> whole spectra and Signal B would have lower frequencies than signal 
>>> O for the whole spectra as well.
>>> Moreover, it the ambulance moves at constant speed, the shift of 
>>> frequencies between O-A and 0-B should be the same. Note that the 
>>> although the frequencies of those sounds are different, the power of 
>>> those sounds A and B would be the same and equal to signal 0.
>>>
>>> *Scenario 2:* /This is a scenario of Constant_Frequency - 
>>> Amplitude_Decrease/I have a sound that propagates trough a wall. 
>>> This means that some frequencies will pass more easily than others. 
>>> Lets say that lower frequencies can propagate easier than higher 
>>> freqs, so the sound after going trough that wall will have less 
>>> AMPLITUDE (power) in the higher frequencies.
>>>
>>> /*Now the big question:*/ /Scenario 1 + scenario 2/ I have a signal 
>>> that travels at a certain speed (like in scenario 1) and I am 
>>> measuring it after going trough a wall (like in scenario 2). I have 
>>> the original signal (signal O) for comparison purposes.
>>> I am trying to quantify the captured signal after going trough that wall.
>>> I see a decrease of amplitude(power) for certain frequency bands 
>>> that are due to that wall, but I also see a frequency shift because 
>>> the source of noise moves at considerable speed.
>>>
>>> How can I modulate this problem?
>>> To put it simple, how can I artificially generate the sound wave 
>>> after crossing that wall, tweeking the velocity(shifting the 
>>> frequency bands
>>> linearly) and amplitude.
>>>
>>> I am not an expert on sound or signal processing. Most of the work I 
>>> do goes in Matlab.
>>> I have plotted my original signal FFT (in black) and the recorded 
>>> signal (in red). Frequency goes in the xx and amplitude (db) in the 
>>> yy axes.
>>> Looks like tis wave hit a truck and all the frequencies shifted a 
>>> little bit to lower freqs and alsoe there was some power 
>>> diminuishing...
>>>
>>> <http://octave.1599824.n4.nabble.com/file/n4649745/zscore_raw_data.j
>>> pg>
>>>
>>> Note that the peak on the 20Hz was lowered to 15 Hz and also lowered 
>>> in amplitude.
>>> the frequncies up to 10 Hz (inclusively the minima at 10 Hz) didnt 
>>> suffer any frequency shift BUT AMAZINGLY has more POWER. I think 
>>> this is because as there is a shift of the 20Hz curve and that the 
>>> power of that frequency band must go somewere...
>>>
>>> Eitherway, not so much for the details, what I really want is to 
>>> know how to modulate these signals?
>>> What is the relation between them?
>>> Multiplication in power, change if fase, shift if frequency.
>>>
>>> By the way, do you think is ok to make an FFT of and FFT, meaning, 
>>> to do an FFT of those curves (that are acctually already the FFT 
>>> signals of my
>>> sound)
>>> what is the meaning of the FFT of and FFT?
>>>
>>> I am available to answer your questions... and I will be fast :) 
>>> Thank you for now
>>>
>>>
>>>
>>>
>>>
>>
>> "Eitherway, not so much for the details, what I really want is to 
>> know how to modulate these signals?"
>>
>>
>> What do you mean by   modulate ?????
>>
>> Do you mean alter them or to model them????
>>
>>
>> --
>> DAS
>>
>> https://linuxcounter.net/user/206392.html
>>
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>
>
>
>
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If you want to model the phenomena with linear tools, you can try to model the 
transfer function. You already did the first step, get the FFT of input and 
output and look at the ratio.
You can go more advance and run "system identification" on the transfer 
function of your process (wall + motion).
I recommend you to check the book "System identification: theory for the user" 
by Lennart Ljung to get a grip of the basics... it is indeed quite simple.
http://books.google.be/books/about/System_identification.html?id=M_hQAAAAMAAJ&redir_esc=y

A first approach would be to see how a delta input (a very loud very short 
pulse of sound) and a square input (a sustanied loud sound that goes on and off 
very rapidly) go through your system. With those signals you can use the 
"control" package to estimate transfers functions. Once you have your transfer 
function you can use it the other way around to guess what was the input for a 
give output.

I hope this helps.

Cheers
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