Question

Find Modulus and amplitude of -1+√3i​

Answer 1

Answer:

here's your answer

Step-by-step explanation:

It's not really a programming question, and is not specific to numpy. Briefly, the absolute value of the complex number (sqrt(x.real**2 + x.imag**2), or numpy.abs()) is the amplitude.

More detailed, when you apply FFT to an array X (which, say, contains a number of samples of a function X(t) at different values of t), you try to represent it as a sum of "plane waves" exp(i w t) (where i is an imaginary unit, and w is a real-valued frequency) with different values of w. That is, you want something like

X = A exp(i w1 t) + B exp(i w2 t) + ...

An FFT returns you these coefficients A, B etc corresponding to some fixed frequencies w1, w2 etc (in numpy, you can get their values from fftfreq()).

Now, these coefficients are, in general, complex. A complex number A can be represented as a combination of "amplitude" and "phase" as:

A = r exp(i p)

where r (== numpy.abs(A)) is the amplitude, and p (== numpy.angle(A)) is the phase, both real values. If you substitute it into the term in the FFT expansion, you get

r exp(i p) exp(i w t) == r exp(i (w t + p))

So, the amplitude r changes the absolute value of the term, and the phase p, well, shifts the phase. Therefore, in order to get the array of amplitudes from the result of an FFT, you need to apply numpy.abs to it