# How is the fourier transform applied to signals? and other questions on the fourier transform.

#### abdulwahab.hajar

Joined Jun 14, 2016
93
Hello everyone

I have a bunch of questions regarding the Fourier transform and the frequency domain generally.

1) Firstly, the Fourier transform is used for analytical purposes as far as I know, in other words it's a mathematical operation used to find the constituting frequency components of a signal, am I right? In other words, we don't have to apply a Fourier transform to a signal for it's frequency components to take effect on whatever circuit element they are going through, but we rather use the Fourier transform to understand how it would affect these circuit elements?

2) Secondly, if the fourier transform is applied to a signal in the time domain, we want to see it's corresponding frequency components. However, would the signal in the time domain look different after the application of the fourier transform?

3) I'm assuming that there isn't a circuit used to apply the fourier transform right?

4) Last but not least, thank you very much, I know that many of these questions sound very awkward.

Also, if this post should have been posted in a different section of the forum, kindly tell me!
Best Regards.

#### Yaakov

Joined Jan 27, 2019
1,612
You are correct that FFTs (Fast Fourier Transforms) are used for analysis, and are mathematical operations, not physical processes. They operate on data collected by instruments, whether by manual sampling and tabulation or automatically by instruments with those functions built in.

So, the FFT itself has no impact on the signals against which it is applied, it is purely calculation.

Theorectically, the observations required to collect the data for an FFT could perturb the signal under observation in various ways, but the FFT is only applied to the data, not the signal.

#### abdulwahab.hajar

Joined Jun 14, 2016
93
You are correct that FFTs (Fast Fourier Transforms) are used for analysis, and are mathematical operations, not physical processes. They operate on data collected by instruments, whether by manual sampling and tabulation or automatically by instruments with those functions built in.

So, the FFT itself has no impact on the signals against which it is applied, it is purely calculation.

Theorectically, the observations required to collect the data for an FFT could perturb the signal under observation in various ways, but the FFT is only applied to the data, not the signal.
Thank you.
Would you happen to know how it is used with OFDM, because it is used completely differently... Using the IFFT / FFT for modulation and demodulation or would you happen to know where I could ask, some specialized telecomm forums.. etc?

#### Yaakov

Joined Jan 27, 2019
1,612

You probably know as much as I do, that since OFDM uses subcarriers that are orthogonal to each other, the FFT can be used to separate them efficiently. That's not very helpful, I'm afraid.

#### crutschow

Joined Mar 14, 2008
25,995
I would think the FFT would be useful in analyzing the OFDM signal, but not in any sort of real-time modulation/demodulation of the video signal.

#### Yaakov

Joined Jan 27, 2019
1,612
I would think the FFT would be useful in analyzing the OFDM signal, but not in any sort of real-time modulation/demodulation of the video signal.
It is actually used in the modulation and demodulation. Since the availability of cheapish, fast FFT hardware it became possible to do that. It's very efficient because the subcarriers are orthogonal. It's pretty clever when you think about it.

#### abdulwahab.hajar

Joined Jun 14, 2016
93
It is actually used in the modulation and demodulation. Since the availability of cheapish, fast FFT hardware it became possible to do that. It's very efficient because the subcarriers are orthogonal. It's pretty clever when you think about it.
It is which is what I don't understand, because I mean didn't we say that generally FFT / IFFT is used for analysis. In the case of OFDM however, as I understand it's applied to the actual signal right?

and also you've been very helpful, thank you very much

#### abdulwahab.hajar

Joined Jun 14, 2016
93
I would think the FFT would be useful in analyzing the OFDM signal, but not in any sort of real-time modulation/demodulation of the video signal.
Sir, would you happen to know where I could post such a question in this forum? Given that you're somewhat a senior member

#### ericgibbs

Joined Jan 29, 2010
11,582
hi ab,
Is this a College or Homework assignment.?
E

#### Yaakov

Joined Jan 27, 2019
1,612
It is which is what I don't understand, because I mean didn't we say that generally FFT / IFFT is used for analysis. In the case of OFDM however, as I understand it's applied to the actual signal right?

and also you've been very helpful, thank you very much
I don’t want to explain anything that exceeds my understanding but this is what I know. The inverse FFT is applied to the signal to modulate it. The original signal is carefull composed of orthogonal subcarriers—that is, they are discrete in frequency and cannot affect each other. Each subcarrier is synchronized with the others symbol by symbol.

The resulting signal can be demodulated with a simple FFT on the receiver side ot derive the original subcarriers as separate signals.

In this case, the FFT operation decides what the modulation will look like, but I am not sure that you would say it is somehow directly used to change the signal. The original signals are in the digital domain, so the FFT is used to combine and separate them before the signal is generated and after it is received. It’s not as if there is a signal that is passed through an FFT, it is still data being processed then acted on.

http://www.wirelesscommunication.nl/reference/chaptr05/ofdm/ofdmmath.htm#FFT

#### abdulwahab.hajar

Joined Jun 14, 2016
93
hi ab,
Is this a College or Homework assignment.?
E
I wouldn't say so, I came across it during university work and it stuck to my mind. It's not for the completion of an assignment though.

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#### abdulwahab.hajar

Joined Jun 14, 2016
93
I don’t want to explain anything that exceeds my understanding but this is what I know. The inverse FFT is applied to the signal to modulate it. The original signal is carefull composed of orthogonal subcarriers—that is, they are discrete in frequency and cannot affect each other. Each subcarrier is synchronized with the others symbol by symbol.

The resulting signal can be demodulated with a simple FFT on the receiver side ot derive the original subcarriers as separate signals.

In this case, the FFT operation decides what the modulation will look like, but I am not sure that you would say it is somehow directly used to change the signal. The original signals are in the digital domain, so the FFT is used to combine and separate them before the signal is generated and after it is received. It’s not as if there is a giant that is passed through an FFT, it is still data being processed then acted on.

http://www.wirelesscommunication.nl/reference/chaptr05/ofdm/ofdmmath.htm#FFT
Thank you!

#### nsaspook

Joined Aug 27, 2009
7,868
I don’t want to explain anything that exceeds my understanding but this is what I know. The inverse FFT is applied to the signal to modulate it. The original signal is carefull composed of orthogonal subcarriers—that is, they are discrete in frequency and cannot affect each other. Each subcarrier is synchronized with the others symbol by symbol.

The resulting signal can be demodulated with a simple FFT on the receiver side ot derive the original subcarriers as separate signals.

In this case, the FFT operation decides what the modulation will look like, but I am not sure that you would say it is somehow directly used to change the signal. The original signals are in the digital domain, so the FFT is used to combine and separate them before the signal is generated and after it is received. It’s not as if there is a signal that is passed through an FFT, it is still data being processed then acted on.

http://www.wirelesscommunication.nl/reference/chaptr05/ofdm/ofdmmath.htm#FFT
Nice article.

This method is rather old as we used (and repaired) a crude 16 channel HF radio analog FSK version of ODFM on the UCC-1 at times to increase transmission speed (sending split parts of a message at the same time) and reliability (using several sub-channels at the same time) of RTTY links. The main requirement for full efficiency was a very linear transfer function in the RF analog systems from the transmitter source to receiver demodulator and very precise frequency matching using master clock oscillators that phased-locked all transmitter and receivers

The modulation sound was similar to this.
https://www.sigidwiki.com/wiki/BR-6028
https://www.sigidwiki.com/wiki/CIS-16

The SDR waterfall display shows the channels and spacing of the signals.

Russian ODFM HF voice range modulation signal.
https://www.sigidwiki.com/wiki/CIS-128

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