## A Differentiator With a Difference

Some time ago I was studying various digital differentiating networks, i.e., networks that approximate the process of taking the derivative of a discrete time-domain sequence. By "studying" I mean that I was experimenting with various differentiating filter coefficients, and I discovered a computationally-efficient digital differentiator. A differentiator that, for low fequency signals, has the power of George Foreman's right hand! Before I describe this differentiator, let's review a few...

## A brief look at multipath radio channels

Summary: Discussion of multipath propagation and fading in radio links

Radio channels, their effects on communications links and how to model them are a popular topic on comp.dsp. Unfortunately, for many of us there is little or no opportunity to get any "hands-on" experience with radio-related issues, because the required RF measurement equipment is not that easily available.This article gives a very simple example of a radio link that shows multipath propagation and...

## Delay estimation by FFT

Given x=sig(t) and y=ref(t), returns [c, ref(t+delta), delta)] = fitSignal(y, x);:Estimates and corrects delay and scaling factor between two signals Code snippetThis article relates to the Matlab / Octave code snippet: Delay estimation with subsample resolution It explains the algorithm and the design decisions behind it.

IntroductionThere are many DSP-related problems, where an unknown timing between two signals needs to be determined and corrected, for example, radar, sonar,...

## Unit Testing for Embedded Algorithms

Happy Holidays! For my premier article, I am writing about my favorite technique to use when designing and developing software- unit testing. Unit testing is a best practice when designing software. It allows the designer to verify the behavior of the software units before the entire system is complete, and it facilitates the change and growth of the software system because the developer can verify that the changes will not affect the behavior of other parts of the system. I have used...

## A Complex Variable Detective Story – A Disconnect Between Theory and Implementation

Recently I was in the middle of a pencil-and-paper analysis of a digital 5-tap FIR filter having complex-valued coefficients and I encountered a surprising and thought-provoking problem. So that you can avoid the algebra difficulty I encountered, please read on.

A Surprising Algebra Puzzle

I wanted to derive the H(ω) equation for the frequency response of my FIR digital filter whose complex coefficients were h0, h1, h2, h3, and h4. I could then test the validity of my H(ω)...

## Fibonacci trick

I'm working on a video, tying the Fibonacci sequence into the general subject of difference equations.

Here's a fun trick: take any two consecutive numbers in the Fibonacci sequence, say 34 and 55. Now negate one and use them as the seed for the Fibonacci sequence, larger magnitude first, i.e.

$-55, 34, \cdots$

Carry it out, and you'll eventually get the Fibonacci sequence, or it's negative:

$-55, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0, 1, 1 \cdots$

This is NOT a general property of difference...

## Exact Near Instantaneous Frequency Formulas Best at Zero Crossings

IntroductionThis is an article that is the last of my digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). It is along the lines of the last two.

In those articles, I presented exact formulas for calculating the frequency of a pure tone signal as instantaneously as possible in the time domain. Although the formulas work for both real and complex signals (something that does not happen with frequency domain formulas), for real signals they...

## Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 1)

IntroductionThis is an article that is a another digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). Although it is not as far off as the last blog article.

A new family of formulas for calculating the frequency of a single pure tone in a short interval in the time domain is presented. They are a generalization of Equation (1) from Rick Lyons' recent blog article titled "Sinusoidal Frequency Estimation Based on Time-Domain Samples"[1]. ...

## Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 2)

IntroductionThis is an article that is a continuation of a digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). It is recommended that my previous article "Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 1)"[1] be read first as many sections of this article are directly dependent upon it.

A second family of formulas for calculating the frequency of a single pure tone in a short interval in the time domain is presented. It...