# Will the spectra of the transmitted and received signal be different?

chipmunk22
Will the spectra of the transmitted and received signal be different as a result of multipath reflection and noise?

MedievalMan
I'm no expert in communications, but the answer is, yes.

If the distortion affects the signal in the time domain - ie. distortion, noise, this will show up in the frequency domain (spectra.)

chipmunk22
If multipath reflection and noise distorts the spectra of the received signal, such that it is different from the orginally transmitted signal, how then does the reciever 'decipher' the originally transmitted signal?

MedievalMan
Well...

For starters, if the frequency range of the noise is not that of your signal, you can just filter it out (low pass, bandpass.)

As to the other distortions.. well, that's what communication systems are all about. You'd have to do some reading. :)

If you know the approximate "transformation" the distortion causes to the original signal, you can apply the reverse transformation at the receiver end.

Those are the 2 most basic techniques, that I bet rarely work in practice without other advanced communication techniques.

antoker
There are two types of distortion: 1. Linear 2. Non-Linear

1. Linear distortion (additive noise) is an additive contribution to the source, so it can be easily avoided via some well-known techniques such as spread-spectrum etc. Linear does not change the signal the only thing it does is suppress some frequencies and amplify others. Linear distortion never introduces any new harmonics to the existing signal.

2. Non-linear distortion: Occurs within the active devices (such as bjt's etc) since an active device can't be perfectly linear (transfer characteristic) thus additional harmonics will be produced.

So the answer to your first question will be yes, multi path reflections and noise will suppress the spectra of your signal, may bee even distort the phase of the original signal , but it won't create any new harmonics.

The answer to the second question comes directly from the first one, since the transmitted signal is received at the same frequency (quite obvious ;)) the receiver wont have any trouble amplifying (using Automatic Gain Control or equivalent ) the received signal to an acceptable (usually done by a special type of LNA amplifiers with very high SNR values) value and reading the envelope to produce sound waves or whatever.

P.S Sometimes you apply some extreme filtering techniques, such as noise predictive algorithms in order to be able do decipher heavily corrupted signal, but those algorithms are beyond normal electronics and can only be done using a uC or some other processing device.

If you're interested in diverse filtering techniques you should read up or take courses such as: Digital Image Processing (heavy emphasis on filtering using statistics ) and Statistical Signal Theory

MedievalMan
Thanks for the better explanation.

Indeed, Image Processing was a fun class. By the end of the class, you made a program in C++ that was a mini-photoshop, with your own custom filtering routines! :)

antoker
Thanks for the better explanation.

Indeed, Image Processing was a fun class. By the end of the class, you made a program in C++ that was a mini-photoshop, with your own custom filtering routines! :)

LoL, man! Were we in the same class?!?!? We did the same thing, just in matlab (since it was easier to import the images), I was truly amazed when i developed my first low-pass filter in time domain (using moving kernel technique), the most amazing thing about that was that i could do every thing photoshop could just using my own skills ;) Same thing goes for Wiener filtering, i just could not believe that reasonably easy calculations could provide us with such an amazing result! :surprised

MedievalMan
Heh, yeah.

For our "project" we had to implement a recent paper in image processing or machine vision (which is inferring information from image processing data).

I did a "fuzzy" filter.

Fuzzy logic is great like that: with just some basic vague rule based knowledge, you can make some neat, effective and practical filters.

chipmunk22
Thanks for the explanation!

Another qn, which of the following is the best technique to measure the response of an audio equalizer?
a. input known sinusoid, measure output, change freq and repeat
b. input impules, measure output, change freq and repeat
c. input unit step, measure output, change freq and repeat
d. all gives the same result

Mentor

Chipmunk, welcome to the PF, but homework and coursework questions need to be posted in the homework help forums, not in the general forums like the EE forum.

On your original question, no, multipath does not alter the spectrum.

On your new question, you are required to show your own work and thoughts in order for us to help you. We do not supply answers to homework questions here on the PF. We are very willing to help tutor you, as long as you show us that you are trying your best on the problem

chipmunk22
For measuring the response, my ans is (d). I feel that it shd be ok to input either sinusoids, impulses or even unit step. although the best approach will be to use a sinusoid, bcos using impulses may have a tendency to spoil the loudspeaker. correct me if i'm wrong.

As for the qn on multipath, am i right to say that since multipath distorts the phase spectrum, but do no changes to the amplitude spectrum?

antoker
Thanks for the explanation!

Another qn, which of the following is the best technique to measure the response of an audio equalizer?
a. input known sinusoid, measure output, change freq and repeat
b. input impules, measure output, change freq and repeat
c. input unit step, measure output, change freq and repeat
d. all gives the same result

a. sine will give you are response at a specified frequency => no good.
b. input impules. Hmm I need more info on what kind of impulses? If you're talking about dirac-delta impulse, then the rest of sentence is absurd ;) Since a frequency responce of an impulse will be spectra from -infinity to +infinity ;)
c. input unit step => good idea, but not as good as b)

When analyzing circuits, black box modeling, reverse engineering or whatever, on would probably use s-domain. Normally one would connect a signal-gen to a circuit and send in 101010101010, measure output, from the output develop a transfer function and transform it to jw-domain.

d) is not correct since: sine contain only one frequency, but step and impulse contains, by definition an infinite number of harmonics.

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Mentor
For measuring the response, my ans is (d). I feel that it shd be ok to input either sinusoids, impulses or even unit step. although the best approach will be to use a sinusoid, bcos using impulses may have a tendency to spoil the loudspeaker. correct me if i'm wrong.

As for the qn on multipath, am i right to say that since multipath distorts the phase spectrum, but do no changes to the amplitude spectrum?

In the real world, to measure the transfer function of the equalizer, you would use the Gain-Phase side of an analyzer like the HP 4194. Maybe check out how the Gain-Phase measurement is done on this type of insrument. (Hint -- it does not use impulses.)

As for phase spectrum, I don't really understand what you mean. Think of the simple case of one extra path to the measuring antenna. The length of the 2nd path can vary so that you add the two receive signals with a phase offset anywhere from 0 to 2PI? How does the amplitude of the resultant vary as the 2nd path length changes to vary the 2nd signal phase delta from zero to 2PI. And what do you get if there is a different level of attenuation for each of the two paths from source antenna to receive antenna? What does that difference in attenuation do to the depth of the null that you can get at the receive antenna from the multipath?