I know by theory that the energy spectrum of a given signal is the sum of the squared fourier coefficient.
What if I have the real and imaginary part of the corresponding fourier coefficient, can I say that energy spectrum of a given signal is equal to sum of (real part + imaginary part)^2
I hope that is straightforward what Im trying to say?!
best regards
ben
Not quite. You want:
sum of fft_result_magnitudes^2
which is:
sum of (sqrt(real_part^2 + imaginary_part^2)^2
which is:
sum of (real_part^2 + imaginary_part^2)
to get the sum of the squared magnitude of a complex FFT's results.
As for a fuller statement of Parseval's theorem, see:
http://en.wikipedia.org/wiki/Parseval%27s_theorem
If result is a column vector with N elements,
the energy spectrum is also a vector with N elements.
powerSpec = abs(result).^2;
The total energy can be calculated by
totalPower = sum(powerSpec);
or
totalPower = result' * result;
If result is a row vector you have to use
totalPower = result * result';