Magnitude and Phase of a Complex Number

As a follow-up to the post about the STFT, here are two functions that will come in handy if you are looking to get magnitude or phase information from the complex-valued FFT output. These are similar to the abs() and angle() functions in MATLAB. Note that MATLAB uses the atan2() function as opposed to simply the atan() routine.

Remember that a complex number specifies a vector in the complex plane, so the overloaded nature of abs() in MATLAB can be slightly confusing. What you really want is the magnitude, or length of the vector, which you can get with Pythagoras' theorem.

Check out this link for a nice primer on complex numbers.

// Computes the magnitude of a complex number/vector in the complex plane (similar to abs() in MATLAB)

float computeMag(fftw_complex num) {

double real = num[0];

double imag = num[1];

return sqrt((real * real) + (imag * imag));

}

// Computes the phase of a complex number/vector in the complex plane (similar to angle() in MATLAB)

float computePhase(fftw_complex num) {

double real = num[0];

double imag = num[1];

//SOHCAHTOA

// Tan(@) = imag/real

return atan2(imag, real);

}