09_CM0268_Frequence_Space

09_CM0268_Frequence_Space - Moving into the Frequency...

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CM0268 MATLAB DSP GRAPHICS 1 261 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 Fourier Transform (FT) Fourier Transform (FT) MPEG Audio Related Discrete Cosine Transform (DCT) — Heart of JPEG and MPEG Video , (alt.) MPEG Audio. Not Studied here — CM0340 Multimedia (YEAR 3)
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CM0268 MATLAB DSP GRAPHICS 1 262 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.
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CM0268 MATLAB DSP GRAPHICS 1 263 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.
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CM0268 MATLAB DSP GRAPHICS 1 264 JJ II J I Back Close An 8 Hz Sine Wave (Cont.)
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CM0268 MATLAB DSP GRAPHICS 1 265 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.
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CM0268 MATLAB DSP GRAPHICS 1 266 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.
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CM0268 MATLAB DSP GRAPHICS 1 267 JJ II J I Back Close How to Filter? Low pass filter — Ignore high frequency noise components — make zero or a very low value. Only store lower frequency components
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CM0268 MATLAB DSP GRAPHICS 1 268 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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