Digital Filters. Part A characterization and analysis.
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Digital Filters
Part A characterization and analysis
If mask is centered about origin, (x,y) in image:
If origin, (x,y), in image is aligned with (0,0) in mask:
Example of a lowpass filter (passes low frequencies, attenuates high frequencies)
y[n] = 1/3 x[n-1] + 1/3 x[n]
+ 1/3 x[n+1]
More generally,
y[n] = h[-1] x[n-1] + h[0] x[n]
+ h[1] x[n+1]
Lowpass filters
X
Input: (before)
x(t) = 0.5*sin(t) + sin(3*t+pi/3) + sin(5*t+pi/8)
Output: (after)
y(t) = 0.5*sin(t) + sin(3*t+pi/3)
h[-1] = h[0] = h[1] = 1/3.
h[-5]=h[-4]=h[-3] =h[-3] =h[-2] =h[-1] =h[0] =h[1] =h[2] =h[3] =h[4] =h[5]=1/11.
“The decibel (dB) is used to measure sound level, but it is also widely used in electronics, signals and communication. The dB is a logarithmic way of describing a ratio. The ratio may be power, sound pressure, voltage or intensity or several other things.”
“One decibel is close to the Just Noticeable Difference (JND) for sound level.
Experimentally it was found that a 10 dB increase in sound level corresponds approximately to a perceived doubling of loudness.”
Ex. lowpass box highpass
(more efficient implementation)
(more efficient implementation)