IFFT time-interval units

If I do an inverse-FFT of an amplitude and phase vs frequency plot (where there are 2000 points for a range of 0 to 2 GHz frequency at 1 MHz sampling intervals) , what is the time units X-axis of the resulting inverse-FFT value? Is the inverse-FFT data reported for every 1 ns (ie 1 GHz) , 0.5 ns ( 2 GHz) or 0.25 ns (ie 4 GHz) intervals?

example : For inverse-FFT Generation, I use matlab command x=ifft(complex number in reactangular form) . Will result "x" be generated with data (in time domain) at double the sample rate of max-frequancy (2GHz) in frequency domain? This would be 2x2 GHz ie 4GHz intervals ( ie 0.25ns each in time scale)?

Answer 1

[Star Strider]

My calculations would indicate 0.25 ns.

Derivation:

Fn = 2E+9;                                          % Nyquist Frequency
Fs = Fn*2;                                          % Sampling Frequency
Ts = 1/Fs                                           % Sampling Interval

producing:

Ts =
   2.5000e-10

This is a one-sided Fourier transform (also assuming that it is calculated and reported correctly, and the frequency axis is not artificially truncated). Since 2 GHz is the Nyquist frequency (½ the sampling frequency), multiplying it by 2 to yields the sampling frequency, Fs. The sampling interval is the inverse of that, 2.5E-10 s or 0.25E-9 s = 0.25 ns.

[vk]

Could you please clarify this statement : "the frequency axis is not artificially truncated" ? Though in this case I donot truncate the frequence axis, why is it incorrect to truncate the frequency axis say from 2GHz to 250MHz. In doing so, the one-sided IFFT will be generated at 500MHz sampling interval. Why will the one-sided IFFT be incorrect because of truncation?

[Star Strider]

By that I mean that the frequency axis (x-axis) is displayed from d-c (0 Hz) to the Nyquist frequency, and not artificially shortened.

It is not incorrect to truncate the frequency axis, however if that has been done (so the maximum displayed value of the frequency axis is not the Nyquist frequency), then my calculations are not valid.

[vk]

Thanks for the quick response.

The frequency profile in this case is generated from ADS tool used for impedance analysis. ADS can generate any frequency span user specifies (in this case the user specifed freq span till 2GHz) and has nothing to do with transient simulation.

1) With this information is it still accurate to assume nyquist is 2GHz?

2) Now, if I truncate the frequency axis from 2GHz to 250 MHz , does IFFT still produce data-points at every 0.25ns sampling interval (assuming nyquist is 2GHz). If not, how will your calculations change?

[Star Strider]

I have no experience with ADS tools. If what it does conforms to my assumptions, my analysis would hold. If it does not, then my analysis is not applicable to it.

Since I now have no idea what you are doing, I will delete my Answer in a few minutes.