Periodogram of a sinusoid spike

1
Periodogram of a sinusoid spike

• Single high value is sum of sine curves all in
  phase at time t0

2
Periodogram of a sinusoid white noise

• White noise is sum of sine curves with equal
  amplitude but random phases
• NOTE THAT BOTH FLAT NOISE AND A SPIKE HAVE FLAT
  PERIODOGRAMS

3
Amplitude modulation

• Suppose the amplitude of the oscillation changes
  sinusoidally with time
• This produces sidelobes at ???.

4
Phase modulation

• Suppose the phase increases at a rate that has a
  sine variation superposed
• This also gives sidelobes at ????but with
  different phases relative to those produced by
  amplitude modulation.

5
Phase relations for sidelobes

• Combined amplitude phase modulation
• Frequency spectra