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While we are decomposing a signal using Wavelets into levels why do we call our high frequency components as Detail and Low Frequency Components as Approximation ?

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Intuitively speaking, anything that is 'high frequency' is something that is 'rapidly changing in time'. Anything that is 'low frequency' is something that is 'slowly changing in time'.

If you think about it, any time you have 'detail' in a signal or image, it means that you have, very quick, rapid variations in time or space. This then becomes the 'detail' of your signal/image.

In contrast, if you just care about how something changes generally, you care about long-term trends - you dont care about how things change with every sample, you just care about how things change over a long time, or over long space. In this case, you just want to 'approximate' your signal.

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Another metaphor to complete Mohammad's answer: think of zooming in/out on your signal.

  • Zooming out makes details of the signal / image disappear, and it is a low pass operation such as the one used to recover the low frequency components.
  • Zooming in on the other hand will reveal things that were lost (or hidden) in the low frequency part. The difference between the zoomed-in and the zoomed-out images can be intuitively called details.
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