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Periodogram of a sinusoid + spike

Periodogram of a sinusoid + spike. Single high value is sum of sine curves all in phase at time t 0 :. 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.

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Periodogram of a sinusoid + spike

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  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. S() Amplitude modulation Phase modulation C() Phase relations for sidelobes • Combined amplitude & phase modulation: • Frequency spectra:

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