Inverse FFT

I have taken 'ifft' of a column matrix in frequency domain, containing complex numbers.Though I was expecting absolute values as answer in time domain,to my surprise the out put has also come as a set of complex numbers.Now I want to plot this output values vs time.Wether I have to take 'abs(OUTPUT) and then plot or as it is?.Presently when I plot as it is the max value is coming 6.8 against the expected max value of 44.6.Kindly help me .Shrinivas

[Sean de Wolski]

Could you show us a small set of sample data?

[Shrinivas Gombi]

FORCE=[27018.0205405475 + 0.00000000000000i

-1154.62563594004 - 1154.93974246692i

-712.513475418666 + 672.923373056472i

2232.51355792485 - 3749.20240402260i

258.652202486357 + 80.4639451616814i

1187.61909318472 + 3158.64023861326i

-704.167340674255 - 899.888518006497i

-17.3813698383540 - 1400.06891720823i

943.659476653797 + 550.186353344297i

-934.496786601128 - 47.2380026438227i];

This is part of a large matrix of 30000x1 sizei frequency domain.

force= ifft(FORCE)is expected to be a matrix in time domain of non complex nombers which will be a time history of force which is to be plotted for compairing with the time history of force measured.Pl help me to identify the mistake. Shrinivas

[Shrinivas Gombi]

Dear Sir,

I just observed that The ratio of expected answer and actual value is exactly 2*PI!.If I multiply by 2*pi and plot is perfectly coming.But I am unable justify the reason!.Kindly help me. Shrinivas

Answer 1

[Rick Rosson]

The difference in what you have and what you want is a constant scaling factor of 2*pi. That means the shape of your result is correct regardless of the actual scale or gain. One could argue (and some often do) that a constant scale factor is generally irrelevant in most situations.

But, if you really are concerned about the actual values (instead of the shape alone), the fact that the scale factor is exactly 2*pi suggests that the ratio is a units of measure conversion. The number 2*pi is not a pure number, but rather it has units of measure: radians per cycle. If we assume that the time domain signal is in units of newtons and time itself is seconds, then the Fourier domain is in units of either newtons per hertz OR newton-seconds per radian. Since hertz is cycles per second, the conversion factor is exactly 2*pi radians per cycle.

The bottom-line really is whether you are using standard frequency (in cycles per second or hertz), or angular frequency (in radians per second) as the unit of measure for the frequency domain.

[Shrinivas Gombi]

Respected Mr.Rick Rosson,

Thanq u very much for reply.This strengthens my justification of using multiplier 2*pi.