Spectrum of *PSK

[jimon]

It's hard for me to get it : in BPSK (or any other PSK) when phase shift happens, we get transition on much higher frequency then the carrier (I mean it's vertical line vs sinusoidal signal in some cases). I assume to filter it there should be a passband filter afterwards because PSK is a passband modulation.

So how does BPSK spectrum looks like before the filter ?
How does 90 and 180 degrees phase shifts looks in frequency domain ? I guess they don't even appear there ?
And how does BPSK signal looks like in time domain after a passband filter ?

My educated guess is that all of this somehow relates to phase spectrum, but haven't seen any phase filters in PSK transmission diagrams

[coppice]

Too many comms books show the graphs you showed, and fail to immediately follow up with reality . In a real system you don't apply square pulse to the modulator, because if you did you'd splurge over many other people's channels. You pulse shape with something like an RRC (root raised cosine) filter at the transmit end, and then RRC filter again as the signal is recovered at the receiver. 2 root raised cosine filters gives you a raised cosine filter, and a raised cosine filter is one which gives no ISI when its bang on. There are several filter types which have this no ISI quality, but most are very sensitive, and give horrible ISI if they are not spot on. Raised cosine filters are somewhat relaxed, and generally the most practical.

When you design your RRC filter one of the input parameters is excess bandwidth (often called alpha). This allows you adjust how much the final signal will spread spectrally. Of course, asking for very little spreading has important downsides. These are left as an exercise for the reader. 

[T3sl4co1l]

The spectrum goes from a carrier (delta(f +/- f0), to a modulated carrier.  The spectrum around the carrier looks just like the modulation, i.e., if it's a square wave, then it has odd harmonics; if it's PRBS, it's pretty flat in the center, has a first zero around the bitrate (or is it half the bitrate, I forget), and looks like a sinc(f) spectrum beyond that (i.e., zeroes at harmonics of the bitrate, and humps inbetween).

QPSK has asymmetrical sidebands.  This can be seen by interpreting it as the superposition of two (orthogonal) BPSK signals in quadrature; each one can be isolated independently, and each will have a BPSK spectrum.  The sum will have harmonics above and below the carrier adding or subtracting, depending on the signal content, hence both sidebands must be retained.

QPSK can also be viewed as the superposition of several AM signals.  The previous case is if the constellation diagram is aligned to 45 degree axes: amplitude in either the I or Q direction is constant for every symbol.  If the constellations are aligned to the I/Q axes, then the phases are either the presence or absence of one or the other component, and therefore the sidebands of each I/Q component are identical to an AM signal of the same modulation (DSB-SC, to be precise).

So it shouldn't be surprising that all these modes (AM, PM, BPSK, QPSK) have similar spectra (i.e., all the signal energy within Fc +/- Fs, and repeating sidebands beyond there, which can be filtered off), with more subtle differences due to their nature.

Tim