I have a time domain signal.I want to calculate energy of my signal......

Suppose my signal is X(t) then I want to get Fourier Transform >>> X(f) and then I want to calculate energy of my signal...

Can anyone help me? Thank you so much

[panchami Rhk]

How to get time domain signal from .wav file

Answer 1

[SK]

Use the fft() function to calculate fourier transform. Then take the of squares of the coefficients:

F = fft(X); 
pow = F.*conj(F);

This gives the power at each frequency. You can sum it (using the sum() fumction) to get the total power.

[vahid torabi]

Thank you so much sir for your answer.Actually I have my time domain signal in workspace in matlab(.mat data... time & value) in this case>>

what would be the code to calculate energy of signal??

[SK]

Are the time points uniformly spaced? If so, you can use fft() just as above:

F = fft(values);
pow = F.*conj(F);
total_pow = sum(pow);

Note: fft() is taken along the columns so ensure that values is a column vector. For a matrix with multiple columns, fft() returns a matrix whose each column has the discrete fourier transform for the corresponding input column. Check the documentation for fft().

For non uniformly spaced points, you could interpolate first to get uniformly spaced points and then use the procedure above.

[vahid torabi]

I've attached my signal for you sir.Please place that in workspace in your matlab program. I want to calculate its energy in frequency domain. How much is its energy if you want to calculate that??? Let me know your result sir. Thank you very much sir.

Answer 2

[SK]

Your time values are more or less uniformly spaced with some slight variation but that shouldn't matter. Just type in the exact same code as above. I get as my answer:

total_pow =

     4.7414e+03

[vahid torabi]

Your result is same as mine.plz have a look at this pdf. I really appreciate your help.

[SK]

You have to normalize by the frequency step:

Frequency step is approximately 1/20000 in your pdf example (freq goes from 0 to 1 over 20000 steps). Multiply the answer by 1/20000 and the result is the same.

[vahid torabi]

You're right sir.plz have a look at my file again. I can't write formula in here,So I have to attach pdf file. Thank you very much sir.

Answer 3

[SK]

I'm not sure what your question is, but if you want to understand how it works, you will have to study the "Discrete Time Fourier Trasform" (DTFT) and "Discrete Fourier Transform" (DFT). This is the discrete time, discrete frequency version of the continuous Fourier transform. "Fast Fourier Transfrom" (FFT) is a fast algorithm to compute the DFT. You can easily find many tutorials online on these topics.

Mathematically there is an elegant theory for Fourier transforms and if you are an engineer it will be worth it to invest the time to know the theory. The equivalence of the variance and the sum of squares of the fourier coefficients comes from there and is known as Parseval's theorem. Another way to say it is that the fourier transform maps the space of square summable sequences (square integrable functions in the continuous case) onto the same space and preserves distance in that space (this is called isometry).

The naive implementation of dft is simple. fft is more involved so this is not the place to describe it, but you can find the implementation in some textbooks. A good textbook is "Linear Algebra and its applications" by Gilbert Strang.

[vahid torabi]

Thanks a lot for your complete explanation sir.Your tips really helped me. I wish you all the best.

[SK]

Thank you. You too.