Continuous Signal

Analog

Infinite Accuracy and Infinite Measurements

Discrete Signal

Digital

Limited Accuracy and Limited Measurements

From Analog...

...to Digital

Distortions

Sampling Limitations

Noise

Analog Signal

2 Samples per second

0

1

time [s]

6 Samples per second

10 Samples per second

6 Hz

10 Hz

2 Hz

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

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?

Fourier Analysis

any signal can be decomposed into harmonic signal components

complex

with circular frequency

many different waves combined

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

Next time

Electrocardiogram

By Daniel Haehn

# CS480 Lecture 04

Slides for CS80 Biomedical Signal and Image Processing at UMass Boston. See https://cs480.org!

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