# Does phase shift introduce high frequencies?

In PSK phase modulation scheme, the signal phase is shifted, hence it looks something like this:

I cannot understand why this doesn't introduce a set of unwanted high-frequencies, as the steep changes are supposed to reflect as so in the frequency domain.

• Sorry for my silly comment, but to me, it's a difficult question to answer without the details of where you got the information 'PSK doesn't introduce a set of unwanted high-frequencies' - was this from observing a diagram somewhere that you can link to ? Or did you do some experimentation that you could share? Sep 18 at 14:12
• It does introduce high frequency components! Take a look at the wikipedia article describing variants of PSK that use less bandwidth. Sep 18 at 15:05
• For me, it would be good to know where OP got this information from so it/they can be named/blamed for misinformation or perhaps OP misread something lost in translation! Sep 18 at 15:10
• "In every *-PSK phase modulation scheme..." well, no. Could you edit your question with the source of this claim? Certainly when PSK schemes are introduced, they are described as having this character to make the math easy -- but then, as you go on to develop a real system, some scheme is introduced that reduces bandwidth. Sep 18 at 21:15

## 1 Answer

The steps in the time domain for unshaped PSK refer to a rectangular baseband modulation waveform. The frequency response of this is a Sinc function which does indeed contain high frequency components, compared to a pulse shaped version where the time domain transitions are tapered rather than stepped.

When modulated to a carrier, the spectrum at baseband is simply frequency translated to the carrier frequency. Thus at a carrier the spectrum associated with the unshaped BPSK waveform will have wider occupied bandwidth, due to those higher frequency components.

It is typical to shape the PSK waveform such as with root-raised cosine pulse shaping, to limit the occupied bandwidth and therefore improve the spectral efficiency. The resulting waveform the OP is seeing is not shaped. To see the significance of this, I added a plot showing the frequency spectrum for PSK waveform without pulse-shaping (blue) and with pulse-shaping (red). The step in phase shift introduces significant high frequency components that can be significantly reduced if stepping is not allowed.

And here is a portion of the modulation waveform in the time domain with and without pulse shaping. It's rather straightforward: A slow change in time corresponds to lower frequencies, a rapid change in time corresponds to high frequencies:

• Thanks Dan for this very clear answer!
– matt
Sep 21 at 14:06