# Fourier Transform vs. Sum of single sines

I have a table of frequencies ($f$) and corresponding Amplitude ($A$) as well as phase ($p$) values.

Unfortunately the result of performing an iFFT on these data,

$$s_1(t) = \operatorname{iFFT}(\dots)$$

is not the same as when summing up single sine waves at instances of time t_n with appropriate frequency, amplitude and phase,

$$s_2(t) = \sum A\sin(2\pi ft_n+p) \, .$$

But both should output the same result, shouldn't it?

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Did you use MATLAB? Or C? –  Gautam Shenoy Nov 20 '12 at 14:33
python ........ –  Mike Nov 20 '12 at 14:34
Were your answers complex numbers? –  Gautam Shenoy Nov 20 '12 at 14:34
after iFFT I have a purely real valued signal (samples). The same is true for a sum of sine-samples. –  Mike Nov 20 '12 at 14:35
What was your exact input to the IFFT function? –  Gautam Shenoy Nov 20 '12 at 14:38