# Wave Walker DSP

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DSP for Beginners: Simple Explanations for Complex Numbers! The second edition includes a new chapter on complex sinusoids.

Signal and Noise: The Vocabulary of RF
August 31, 2021

#### Introduction

All DSP scenarios will include a signal and noise. But what are they? Using a common set of clearly defined terms is important to properly understand what information is trying to be conveyed.

#### Time-Series

A time-series is a collection of data measured over time. That can be the Dow Jones Industrial Average every day at the closing bell, the temperature every hour or samples from an analog to digital converter (ADC). A time-series might be represented through an array,

(1)

or through an equation,

(2)

#### Signal and Noise

I consider a signal to be a time-series which is information bearing. An example of a signal might be your height if you were able to measure it with infinite precision. I consider noise to be a time-series of randomness. Noise can come from many places, including measurement error or environmental variables. Figure 1 is an example of how a height measurement might be effected by noise.

A height estimate could have noise or error coming from one or multiple sources:

• How fine of resolution is your ruler?
• How accurately was your ruler constructed?
• Did you forget to take off your shoes?
• Are you slouching or leaning?

Note that both signals and noise are time-series and their labels are used to represent the expectation about the content of the time-series.

Frequently the term signal is used loosely and acts as a catch-all for any time-series. Consider that a transmit signal is a signal with information while a receive signal is a signal with information and noise. Figure 2 is a simplified version of how a receive signal relates to a transmit signal and noise and Figure 3 is an example of how noise corrupts a receive signal.

#### Interference

Interference is a signal which is undesired, sometimes referred to as signal not of interest (SNOI). Conversely a signal with information that is desired may be referred to as a signal of interest (SOI) or desired signal.

#### Signal Processing

The goal of signal processing is to apply effects to a receive signal in order to:

• Enhance the information within the signal of interest
• Minimize the impact of noise
• Minimize the impact of interference

#### Conclusion

The terms signal and noise are only labels used to express the expectation about the content within a time-series. Noise corrupts a signal through measurement error or other uncontrollable environmental errors.

The Explaining Why category is a good place to start if you are interested in or new to DSP and looking for some answers about common questions.

God, the Lord, is my strength; He makes my feet like the deer's; He makes me tread on my high places. Habakkuk 3:19
For everything there is a season, and a time for every matter under heaven. A time to cast away stones, and a time to gather stones together. A time to embrace, and a time to refrain from embracing. Ecclesiastes 3:1,5
The earth was without form and void, and darkness was over the face of the deep. And the Spirit of God was hovering over the face of the waters. Genesis 1:2
Behold, I am toward God as you are; I too was pinched off from a piece of clay. Job 33:6
Enter His gates with thanksgiving, and His courts with praise! Give thanks to Him; bless His name! Psalm 100:4
Lift up your hands to the holy place and bless the Lord! Psalm 134:2
Blessed is the man who trusts in the Lord, whose trust is the Lord. He is like a tree planted by water, that sends out its roots by the stream, and does not fear when heat comes, for its leaves remain green, and is not anxious in the year of drought, for it does not cease to bear fruit. Jeremiah 17:7-8
He said to him, “You shall love the Lord your God with all your heart and with all your soul and with all your mind. This is the great and first commandment. And a second is like it: You shall love your neighbor as yourself. On these two commandments depend all the Law and the Prophets.” Matthew 22:37-39
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Riches do not profit in the day of wrath, but righteousness delivers from death. Proverbs 11:4
The angel of the Lord appeared to him in a flame of fire out of the midst of a bush. He looked, and behold, the bush was burning, yet it was not consumed. And Moses said, “I will turn aside to see this great sight, why the bush is not burned.” When the Lord saw that he turned aside to see, God called to him out of the bush, “Moses, Moses!” And he said, “Here I am.” Exodus 3:2-3
Daniel answered and said: “Blessed be the name of God forever and ever, to whom belong wisdom and might. He changes times and seasons; He removes kings and sets up kings; He gives wisdom to the wise and knowledge to those who have understanding." Daniel 2:20-21
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