Editing Pulse-width modulation (section)

==== Spectrum ====
The resulting [[spectrum|spectra]] (of the three alignments) are similar. Each contains a [[DC component]], a base sideband containing the modulating signal, and phase modulated [[Carrier signal|carriers]] at each [[harmonic]] of the frequency of the pulse. The amplitudes of the harmonic groups are restricted by a <math>\sin x / x</math> envelope ([[sinc function]]) and extend to infinity. The infinite bandwidth is caused by the nonlinear operation of the pulse-width modulator. In consequence, a digital PWM suffers from [[aliasing]] distortion that significantly reduce its applicability for modern [[communication system]]s. By limiting the bandwidth of the PWM kernel, aliasing effects can be avoided.<ref>{{cite journal |last=Hausmair |first=Katharina |author2=Shuli Chi |author3=Peter Singerl |author4=Christian Vogel |date=February 2013 |title=Aliasing-Free Digital Pulse-Width Modulation for Burst-Mode RF Transmitters |journal=IEEE Transactions on Circuits and Systems I: Regular Papers |volume=60 |issue=2 |pages=415–427 |citeseerx=10.1.1.454.9157 |doi=10.1109/TCSI.2012.2215776 |s2cid=21795841}}</ref>

On the contrary, [[delta modulation]] and [[delta-sigma modulation]] are random processes{{Clarification needed|reason=What exactly is meant by "random" here?|date=February 2024}} that produces a continuous spectrum without distinct harmonics. While intersective PWM uses a fixed period but a varying duty cycle, the period of delta and delta-sigma modulated PWMs varies in addition to their duty cycle.