Show 3 simple plots (sine wave, square wave, noisy signal).
Then: Which one would be hardest to analyze automatically—and why?
ENTRYTASK
From Analog...
...to Digital
Distortions
Sampling Limitations
Noise
Sampling
Analog
Sampling Rate
Samples per second [1/s]
Hertz [Hz]
Analog Signal
2 Samples per second
0
1
time [s]
6 Samples per second
10 Samples per second
6 Hz
10 Hz
2 Hz
Aliasing
Original Signal
Sampled Points
Reconstructed Signal
Sampling Rate too low
A higher sampling rate is better
?
2 Floats
6 Floats
10 Floats
It's a trade-off!
Nyquist-Shannon Theorem
sampling frequency > 2x signal frequency
guarantees perfect reconstruction
What does that mean? And how do we get the signal frequency?
Fourier Analysis
In the US: 60 Hz
In Europe: 50 Hz
From Analog...
...to Digital
Distortions
Sampling Limitations
Noise
What is the sampling rate here?
19/6000s = 0.0032 Hz
[104, 104, 104, 103, 103, 102, 101, 101, 100, 100, 99, 99, 98, 98, 98, 99, 99, 100, 100]How to represent the data?
Show 3 simple plots (sine wave, square wave, noisy signal).
Then: Which one would be hardest to analyze automatically, and why?
Fourier Analysis
Fourier Analysis
any signal can be decomposed into harmonic signal components
complex
with circular frequency
Power Spectrum (S_t ** 2)
s_t
Frequency in images ~ level of detail
0
0
low pass filter
high pass filter
usually high frequency noise
60 Hz noise: electric humming around transformers
Low-pass == High-cut
High-pass == Low-cut
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