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Figure 2: The periodicity of a complex sinusoid can be seen easier in three dimensions.

Why Does the DFT Need Windowing Functions?

September 1, 2023

Introduction The blog describes why windowing functions are needed in spectral analysis! This blog uses the Fourier Transform as a Cross-Correlation as a foundation and

The Value of Internships

June 1, 2023

Introduction Internships are an incredible way to gain experience and insight into industry while you are still in school. Read on to discover why internships

Figure 3: Increasing the delay M increases the number of teeth in the comb filter and reduces their width. Note that the magnitude has been normalized to 0 dB gain at omega=0.

Comb Filter Introduction and Analysis

March 1, 2023

Introduction A comb filter is a multiplier-less filter, meaning it only uses additions when computing the impulse response. The comb filter is one of the

Figure 1: Magnitude of the frequency response for the band pass single pole IIR filter.

Band Pass Single Pole IIR Filter Design

February 1, 2023

Introduction A low-pass single pole infinite impulse response (IIR) filter is transformed into a band pass filter using simple mathematics! A previous blog described the

Figure 2: Complex frequency shifting can result in aliasing if the frequency response overlaps the half sampling rate.

Complex Frequency Shifting in Discrete Time

January 1, 2023

Introduction Complex frequency shifting is the process of shifting a signal’s frequency response in the frequency domain. This blog describes how to apply complex frequency

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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
Then He said to me, “Prophesy over these bones, and say to them, O dry bones, hear the word of the Lord. Thus says the Lord God to these bones: Behold, I will cause breath to enter you, and you shall live." Ezekiel 37:4-5
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
Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom. 2 Corinthians 3:17
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