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Unformatted text preview: 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) 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. 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. CM0268 MATLAB DSP GRAPHICS 1 264 JJ II J I Back Close An 8 Hz Sine Wave (Cont.) 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. 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. 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 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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This note was uploaded on 01/24/2012 for the course CM 0268 taught by Professor Davidmarshall during the Winter '11 term at Cardiff University.
 Winter '11
 DavidMarshall

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