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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

The response of time invariant filters is independent of time and have filter weights which do not change over time. Time invariance (TI) is a nice quality for filters to have when analyzing them mathematically and have many applications in which adaptation is not needed. Time-varying filters (TV) are common in radio receivers such as equalizers, automatic gain control and polyphase filters. For example an equalizer is time-varying because the filter weights are dependent on previous input samples. Understanding TI filters is necessary for having a proper DSP foundation before moving onto TV filters.

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

Digital signal processing has two components: signals and filters.

A signal is a time-series which has information (RF vocabulary) and filters are useful in applying a desired affect to a signal. These affects can be:

  • enhancing information elements of a signal,
  • attenuating or minimizing noise,
  • or some other modification.

Figure 3: Environmental noise corrupts the receive signal. The difference between the transmit signal and receive signal is the error.

Signal and Noise: The Vocabulary of RF

August 31, 2021

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.

Richard Hamming

Richard Hamming, Acorns and the Engineering Mindset

August 31, 2021

Richard Hamming was a pioneer in the fields of electrical engineering, computer engineering and computer science. You might not know he has also had a positive and significant impact on engineering culture with his talk “You and Your Research”.

Figure 3: Filtered BPSK symbols have a distribution that has both continuous and discrete elements.

Central Limit Theorem: Fact or Fiction?

August 30, 2021

Where were you when you first heard about the Central Limit Theorem (CLT)?

If you are like me, you heard of the CLT in the classroom as a justification for the assumption of Gaussian noise in the RF environment. The CLT states that the summation of independent random variables (RV) approaches a Gaussian distribution with an increasing number of random variables.

The CLT is convenient in simplifying mathematics, but when and how should it be used? Under what circumstances is it valid?

Let’s take a brief look at how well three different random variables follow the CLT.

Welcome to Wave Walker DSP!

August 28, 2021

Thanks for coming to Wave Walker DSP! I plan to bridge the gap between academic knowledge found in the classroom with the intuition of the

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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
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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
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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
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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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