EE200_Weber_10-14

# EE200_Weber_10-14 - EE 200 Spatial Frequency Frequency can...

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8 EE 200 Spatial Frequency Frequency can be associated with space rather than with time. An image is a form of a signal. It has a domain (x and y coordinates), and a range of intensity (brightness) values that create the image. Image:VerticalSpace × HorizontalSpace Intensity The intensity values vary as a function of x or y or both. The output of the function only varies with the position in the image, not with time.

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9 EE 200 Spatial Frequency Example: An image of a brick wall contains different spatial frequencies in different parts of the image. Higher spatial frequencies Lower spatial frequencies At left: 35 cycles for 600 pixels = 0.058 cycles/pixel At right: 13 cycles for 600 pixels = 0.022 cycles/pixel
10 EE 200 Periodic Signals A periodic signal is one that repeats after a certain amount of time. x(t) = x(t + p ) + x(t + 2 p ) + x(t + 3 p ) + … The signal repeats after t p = k p for all positive integer values of k. Example: x(t) = sin( ω 0 t) x(t) is periodic with period 2 π / ω 0 since sin( ω 0 (t + 2 π / ω 0 )) = sin( ω 0 t + 2 π ) = sin( ω 0 t)

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11 EE 200 Periodic Signals The period of the signal is defined as the smallest value of p over which x(t) = x(t + k p ) is true. X(t) is periodic with period τ but also repeats every 2 τ (and 3 τ , and 4 τ , etc.). For x(t), p = τ since it is the smallest value over which x(t) = x(t + k p ) is true. The fundamental frequency, f 0 , of a periodic signal is 1/ p , or in radians/second ω 0 = 2 π / p . τ t x(t) 2 τ 3 τ 4 τ 5 τ
12 EE 200 Periodic Signals Example 1: what is the period of the signal The greatest common divisor of the three frequencies (440, 550 and 660) is 110 Hz. Therefore the period is p = 1/f = 1/110 Hz = 9.1 msec

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## EE200_Weber_10-14 - EE 200 Spatial Frequency Frequency can...

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