How do you convert angular frequency to real Frequency (Hz)?

Question

How do you convert angular frequency to real Frequency (Hz)?

Answer 1

Convert Frequency To Angular Frequency

Answer 2

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Apologies for repeating my answer to another of your questions, but a complex number is just that - a number. It doesn't contain a frequency, and so there is no conversion between the two. From your other questions I'd hazard a guess that you're learning Fourier transforms (and DFTs, FFTs etc.). Maybe I can answer your question best from that angle. That makes this a long answer, so if I've guessed wrong then you may not want to bother reading further. Oh, and apologies if this all sounds patronising... A DFT is used to convert a set of data from one domain (e.g. time samples) into a set of data in another domain (e.g. frequencies). These "sets of data" are sets of numbers (which may be complex). The important thing is that the frequency domain is given by the _set_ of numbers, and not by any single number (complex or not). The DFT is usually written out in text books for a single frequency (e.g. S(w) = sum[s(t) * exp(-jwt)], where the sum is over all t and * is "times"). This is a comparison (technically the "correlation") of your input s(t) with a SINGLE (complex) sinewave of frequency w. However, to get a full spectrum you need to repeat this for all w (giving you one value of S for each w). The FFT does this very efficiently. The magnitude of S that you get from one application of the DFT (i.e. one w) will tell you how similar s(t) is to sin(w) (well, actually exp(jwt)). This would be (a^2 + b^2) if S = a + jb. There will also be a angle component (arctan(b/a)) which tells you the phase-difference between this reference sinewave and the component of your signal which has frequency "w". So, the closest I can get to an answer is this: given a SET of complex numbers (each one computed with a different value of w) find the one with the maximum magnitude (using (a^2 + b^2) for each one). The value of "w" that you used to compute this number is the frequency (assuming your input was a pure sinewave). If you used something like an FFT, things are slightly trickier since "w" is hidden from you, but the frequencies are evenly spread between 0Hz and half the sampling rate - so if you have N values in your input, you'll also have N values in your output, and the nth value will be n/N times the distance between 0 and Fs/2... so frequency = (n/N)*(Fs/2) = (n*Fs)/(2*N) (Fs = sampling frequency).

Answer 3

Multiply Hz by 2 pi and you'll get omega.

Answer 4

divide angular frequency in radians per second by (2*pi) to get frequency in cycles per second (Hz).

Answer 5

An angle measuring 1 radian subtends an arc equal in length to the radius of the circle. 1 radian = 360/2pi = 57.295 degrees.



There are 2π (approximately 6.28318531) radians in a complete circle.



Angular velocity is equal to 2π times the rotational frequency.

Answer 6

w= 2* pi *f



I like to use the unit approach when my memory fails



w (rad/sec) = 2 * Pi ( rad/cycle) * F ( Cyc/sec)