The inverse Fourier transform

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[mavinicesumaljag]

at least i know what my dog hears when my talking to him.

[kkgt]

Are there circuits which can do this or we need to sample signals and take it in digital domain

[chansonjoy]

To invert FFT, it is not use a single Fourier coefficient to times the complex signal wave conjugate, in stead it loops all the Fourier coefficients, times the complex signal wave conjugate, sum the result then divided by N

[emmanuelasante]

Thanks for this video. Infact, inverse Fourier Transform is explicitly explained

[AudeSapere-]

The mind is represented perfectly by eulers formula, the complex circle is equal to 0, through Fourier mathematics we as eternal minds, can and do create everything around us, this is a shared dream, sin and cosine waves are the most basic mathematical component of space time, they are non orthogonal waves, while purely mental unextended waves are interaxial. We as minds are equal to 0, and 0 also contains every possible value, from imaginary numbers to real numbers.

[leagoo]

I have a question regarding correctness of explained theory. You explain inverse Fourier transform as this: create goniometric wave (sine, cosine) and multiply it with one Fourier coefficient that is part of input data. This will give you one intermediate wave. Then create another goniometric wave of different frequency and multiply it with another Fourier coefficient to obtain another intermediate wave. And so on. At the end sum all intermediate waves together to obtain original wave (obtain time domain signal).

Publicly available source code does it differently. It generates just one point of goniometric wave and multiples it with one Fourier coefficient. Then generate second point of goniometric wave and multiply it with second Fourier coefficient and so on. Sum all results into one number which is one point of original signal (obviously unscaled). Then continue the same procedure with goniometric wave of different frequency.

Could you please comment on both approaches if they are the same?

Here is publicly available code for dft:

static void dft(double[] inreal, double[] inimag,
double[] outreal, double[] outimag) {
int n = inreal.length;
for (int k = 0; k < n; k++) { // For each output element
double sumreal = 0;
double sumimag = 0;
for (int t = 0; t < n; t++) { // For each input element
double angle = 2 * Math.PI * t * k / n;
sumreal += inreal[t] * Math.cos(angle) + inimag[t] * Math.sin(angle);
sumimag += -inreal[t] * Math.sin(angle) + inimag[t] * Math.cos(angle);
}
outreal[k] = sumreal;
outimag[k] = sumimag;
}
}

[arash]

Hi,
What about the phaze? None of the sine or cosine waves have phase?

[FranziskaKirsch-do]

Thanks for the video! I have a somewhat complex problem and would appreciate some help: I would like to subtract the baseline activity of a control task from the main trials, trial-by-trial, not averaged. Is this possible? After that I want to use a toolbox for single-trial regression where I need the data in the time domain. Does the correction have to be done in the TF domain or is the time domain sufficient? If it has to be done in the tf domain, can I then bring the data back into the time domain via an inverse transformation for the toolbox I want to use? Thanks for your help!

[STKeTcH]

i have no idea how to apply these ideas to my exact math course (no calculator)

[jangky]

Thank you for this video, Mike X Cohen. It really helped me a lot, though I have some questions in mind. If you multiply complex sine wave to matching fourier coefficient, aren't the outputs in the form of complex numbers? And if that is true, how do you sum them up to get the original time domain signal? Again, thanks for good quality lecture!

[douggale]

I was watching the whole time to see how you converted the imaginary part to a phase angle. Did I miss it? Is it already radians or something?

[susmitapanda]

Sir please upload videos on IFFT in matlab conversion from frequency to time domain. I am stucked at a point and would like to learn from you.