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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.

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