# Spectral properties of QPSK modulation

From what I've read, the spectral properties of the modulation largely depend on the rate of change of the signal phase - "a signal in which the phase changes stepwise has a broad spectrum, well beyond the allocated radio channel". I don't know if I understand this correctly.

An example of the spectrum of QPSK modulation with a random signal causing step changes in the output signal is shown in the figure below:

The book I am using says that "if we assume that the bandwidth of the radio channel allocated to this emission is $$\B_k = 1/T\$$, then a significant portion of the signal power (approximately a quarter) is emitted outside the bandwidth of that channel. The appearance of such strong interference in other radio channels is unacceptable (moreover - the band in which 99% of signal power is transmitted is approximately ten times wider than $$\B_k\$$)"

What does it result from? Why ~1/4 of the signal power is emitted outside the bandwidth of this channel? How do phase spikes affect this? And why is the bandwidth in which 99% of the signal power is transmitted approximately ten times wider than $$\ B_k \$$?

• This is a result of square modulation to the encoder without the use of raised cosine filtering to limit the BW – Tony Stewart EE75 Feb 9 at 0:41
• Thank you, but do you happen to know where these values come from? Why is approximately a quarter of the signal power emitted outside the bandwidth of that channel? Does it have to do with the random modulating sequence and phase jumps? – MagicMan Feb 9 at 1:27
• No it has to do with the power of harmonics in a square wave and it's more efficient to make a sinusoidal filter without jitter or ISI using a "raised cosine filter" on the signals before modulation with sin/cos and 4 phases and 4 amplitudes – Tony Stewart EE75 Feb 9 at 1:37