Real Fourier Transformation: confusing phase spectrum

[sowatt]

When setting sample rate and block size both to 1024, the Real Fourier Transformation of a sin-wave with Frequency=1 and PhaseAngel=0 calculates the phase spectrum as displayed in the left part of the image.

Setting sample rate and block size both to 512, results in the phase spectrum as displayed in the right part of the image.

There are a few things I don't understand:

*) Why is the phase of frequency 1 equals -90, when I set the phase angel of the input signal to 0?
My explanation is that the phases are calculated relative to a cos-signal. Is that true?

*) Why does the phase spectrum contain more than one value, when the input signal just contains one single frequency?

*) Why do the phase spectra (is this the plural of "spectrum"?) look different for different sample rates / block sizes?

Maybe someone is able to answer these questions

Thanks!

Roman

[CJ_Butler__DASYLab_Pro]

This is not my area of expertise, so, I went to one of the experts, and he gave me this. I hope that it helps.

*) Why is the phase of frequency 1 equals -90, when I set the phase angel of the input signal to 0?
My explanation is that the phases are calculated relative to a cos-signal. Is that true?

The important information of the phase spectrum is how the different sine waves forming a signal are shifted in relation to each other.

In a typical signal analysis you cannot force your analysis interval to be in phase with a specific sine wave,  so the offset of the phase spectrum is arbitrary.

If you try to analyse the composite signal of several sine waves with different frequencies, you will see that  they all have the same offset.  I would also have expected an phase offset of 0 in this ananlysis, but it does not make a difference.

*) Why does the phase spectrum contain more than one value, when the input signal just contains one single frequency

At all other frequencies the amplitude value (and also the complex frequency value) should be 0. But 0 does not have a defined phase.   The values come from rounding errors and it cannot be determined by software whether there is a meaningful information.

Typically you should only take those phase values into account where the corresponding amplitude value is larger than 0.  The software cannot determine whether this is inherent to the signal ar an artifact of the rounding errors.

*) Why do the phase spectra (is this the plural of "spectrum"?) look different for different sample rates / block sizes?

Same reason as above, different settings yield different rounding errors.

[sowatt]

> The important information of the phase spectrum is how the different sine waves forming a signal are shifted in relation to each other.

> In a typical signal analysis you cannot force your analysis interval to be in phase with a specific sine wave,  so the offset of the phase spectrum is arbitrary.

> If you try to analyse the composite signal of several sine waves with different frequencies, you will see that  they all have the same offset.  I would also have expected an
> phase offset of 0 in this ananlysis, but it does not make a difference.

Thanks!! This was a great explanation!