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DSP Algorithms for RF Systems
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Stop Using Too Many Commas to be a Better Writer

March 30, 2022

Too many commas destroys the flow of a sentence. I know because I use too many commas. Each comma acts as a pause and too many commas makes good writing sound sluggish and boring.

The problem arises because I write as I’m thinking (I almost put a comma here!) and I put a comma when I need to take a thought break in the middle of sentence. However, you don’t want your reader to have a thought break. You want your reader to flow through your thoughts without a break in concentration. Using too many commas is an easy way to hamper otherwise excellent writing.

In writing the two paragraphs above I removed, or stopped myself from writing, 4-5 commas alone!

Figure 3: The complex sinusoid e(j2 pi (2/4) n) only contains energy at X[2].

DFT Frequency Resolution Explained

March 16, 2022

Frequency resolution is defined as the ability to perfectly distinguish one frequency from another. The DFT frequency resolution is improved by increasing the signal length, not increasing the DFT size. The frequency resolution \omega_{res} in radians of the DFT is

(1)   \begin{equation*}\omega_{res} = \frac{2\pi}{N}\end{equation*}

where N is the length of the input signal.

In this blog I demonstrate graphically and mathematically why and how increasing the signal length improves the frequency resolution, and why simply increasing the DFT size does not.

Is the Nyquist Sampling Rate Satisfied? (Homework Problem)

March 2, 2022

In this blog I answer a question I received about how to apply Nyquist’s sampling rate mathematically and thought it’s worth sharing. One of the difficult parts about getting started in DSP is the concepts are not intuitive which is further compounded by the requirement that the early work must done mathematically, rather than by building or simulating. Take heart if you feel this way, you are not alone! I hope this blog is useful in helping to understand the mathematics of DSP. Please leave a comment below with other questions you have.

Figure 4: The impulse response and frequency response of the LPF before the FIR filter gain is normalized.

Designing FIR Filter Gain

February 23, 2022

This blog describes how to design the FIR filter gain through normalization and then applying a gain. Applying filter gain may be desirable to setting the proper amplitude level or power level needed for follow on processing based on threshold values or other reference levels.

Filter design methods may create different gains for the resulting filters such as with Remez, using windowed sinc functions or as specially designed pulse shaping filters. Normalizing the magnitude response of an FIR filter makes the gain 1, or 0 dB, at a desired frequency. A gain factor can then be applied by scaling each of the filter weights.

Wave Walker DSP YouTube Channel Video

Wave Walker DSP YouTube Channel

February 9, 2022

I started a YouTube channel! My first video is a lecture I gave as a PhD student at Virginia Tech. Be on the lookout for

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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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