Wave Walker DSP

DSP Algorithms for RF Systems

DSP: Fundamentals

Figure 1: The unit circle with an example complex vector e(j pi/3).

The Unit Circle: The Field of Play for the Game of DSP

October 23, 2021

Figure 4: The time-domain plot of e(j2 pi n/8) for n=0 to n=31.

Phase, Frequency and Negative Frequency in Complex Sinusoids

October 19, 2021

Figure 8: The upconverted BPF is the summation of two complex-upconverted LPFs which interfere with one another when summed. The BPF upconversion in Figure 8 is the result of the summation of these two responses.

Designing an FIR Band Pass Filter with Remez

September 24, 2021

Figure 4: The impulse responses of the LPF and HPF filters.

Designing an FIR High Pass Filter with Remez

September 23, 2021

FIR Low Pass Filter Design with Remez

September 22, 2021

Why are Sinusoids used in DSP and RF?

September 18, 2021

Figure 5: An example of angles between 0 and 2pi.

Basic Rules for Complex Numbers

September 17, 2021

Figure 3: Sine waves have three parameters: amplitude, frequency and phase.

How Euler’s Formula Relates Triangles, the Unit Circle and Complex Sinusoids

September 16, 2021

Figure 3: An example of a time invariant IIR filter. Note that an IIR filter can be transformed into an FIR filter by setting all feedback coefficients to zero.

Time Invariant and Time Varying Filters

September 3, 2021

Figure 1: A moving average filter is implemented by delaying the input signal x[n] and then scaling by 1/3 and summing all results.

Digital Signal Processing through the Lens of the FIR Filter

September 1, 2021

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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