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Unformatted text preview: 97 JJ II J I Back Close Moving into the Frequency Domain Frequency domains can be obtained through the transformation from one ( Time or Spatial ) domain to the other ( Frequency ) via Discrete Cosine Transform (DCT) Heart of JPEG and MPEG Video , (alt.) MPEG Audio. ( New ) Fourier Transform (FT) MPEG Audio ( Recap From CM0268 ) Note : We mention some image (and video) example in this section as DCT (in particular) but also the FT is commonly applied to filter multimedia data. 98 JJ II J I Back Close 1D Example Lets consider a 1D (e.g. Audio) example to see what the different domains mean: Consider a complicated sound such as the noise of a car horn. We can describe this sound in two related ways: Sample the amplitude of the sound many times a second, which gives an approximation to the sound as a function of time. Analyse the sound in terms of the pitches of the notes, or frequencies, which make the sound up, recording the amplitude of each frequency. 99 JJ II J I Back Close An 8 Hz Sine Wave In the example (next slide): A signal that consists of a sinusoidal wave at 8 Hz. 8 Hz means that wave is completing 8 cycles in 1 second The frequency of that wave (8 Hz). From the frequency domain we can see that the composition of our signal is one wave (one peak) occurring with a frequency of 8 Hz with a magnitude/fraction of 1.0 i.e. it is the whole signal. 100 JJ II J I Back Close An 8 Hz Sine Wave (Cont.) 101 JJ II J I Back Close 2D Image Example Now images are no more complex really: Brightness along a line can be recorded as a set of values measured at equally spaced distances apart, Or equivalently, at a set of spatial frequency values. Each of these frequency values is a frequency component . An image is a 2D array of pixel measurements. We form a 2D grid of spatial frequencies. A given frequency component now specifies what contribution is made by data which is changing with specified x and y direction spatial frequencies. 102 JJ II J I Back Close What do frequencies mean in an image? Large values at high frequency components then the data is changing rapidly on a short distance scale. e.g. a page of text Large low frequency components then the large scale features of the picture are more important. e.g. a single fairly simple object which occupies most of the image. 103 JJ II J I Back Close The Road to Compression How do we achieve compression? Low pass filter ignore high frequency noise components Only store lower frequency components High Pass Filter Spot Gradual Changes If changes to low Eye does not respond so ignore? 104 JJ II J I Back Close Visualising Frequency Domain Transforms Any function (signal) can be decomposed into purely sinusoidal components (sine waves of different size/shape) When added together make up our original signal....
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 Fall '09
 DavidMarshall

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