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Introduction to DSP - frequency: frequency spectra II

Using the Fourier transform, any signal can be analysed into its frequency components.

Every signal has a frequency spectrum.

  • the signal defines the spectrum
  • the spectrum defines the signal

We can move back and forth between the time domain and the frequency domain without losing information.

The above statement is true mathematically, but is quite incorrect in any practical sense - since we will lose information due to errors in the calculation, or due to deliberately missing out some information that we can't measure or can't compute. But the basic idea is a good one when visualising time signals and their frequency spectra.

signals and their frequency spectra

The diagram shows a number of signals and their frequency spectra.

Understanding the relation between time and frequency domains is useful:

  • some signals are easier to visualise in the frequency domain
  • some signals are easier to visualise in the time domain
  • some signals take less information to define in the time domain
  • some signals take less information to define in the frequency domain

For example a sine wave takes a lot of information to define accurately in the time domain: but in the frequency domain we only need three data - the frequency, amplitude and phase.

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