## Add a Power Marker to a Power Spectral Density (PSD) Plot

Perhaps we should call most Power Spectral Density (PSD) calculations relative PSD, because usually we don’t have to worry about absolute power levels. However, for cases (e.g., measurements or simulations) where we are concerned with...

## A Simpler Goertzel Algorithm

In this blog I propose a Goertzel algorithm that is simpler than the version of the Goertzel algorithm that is traditionally presented DSP textbooks. Below I very briefly describe the DSP textbook version of the Goertzel algorithm followed by a...

## 60-Hz Noise and Baseline Drift Reduction in ECG Signal Processing

Electrocardiogram (ECG) signals are obtained by monitoring the electrical activity of the human heart for medical diagnostic purposes [1]. This blog describes a very efficient digital filter used to reduce both 60 Hz AC powerline noise and...

## Find Aliased ADC or DAC Harmonics (with animation)

When a sinewave is applied to a data converter (ADC or DAC), device nonlinearities produce harmonics. If a harmonic frequency is greater than the Nyquist frequency, the harmonic appears as an alias. In this case, it is not at once...

## Adaptive Beamforming is like Squeezing a Water Balloon

Adaptive beamforming was first developed in the 1960s for radar and sonar applications. The main idea is that signals can be captured using multiple sensors and the sensor outputs can be combined to enhance the signals propagating from...

## Compute Images/Aliases of CIC Interpolators/Decimators

Cascade-Integrator-Comb (CIC) filters are efficient fixed-point interpolators or decimators. For these filters, all coefficients are equal to 1, and there are no multipliers. They are typically used when a large change in sample...

## Exploring Human Hearing Range

Human Hearing Range In this post, I'll look at an interesting aspect of Audacity – using it to explore the threshold of human hearing. In my book Digital Signal Processing: A Gentle Introduction with Audio Examples, I go into this topic...

## The Zeroing Sine Family of Window Functions

Introduction This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by introducing a class of well behaved window functions that the author believes to be previously unrecognized. The definition...

## Design Square-Root Nyquist Filters

In his book on multirate signal processing, harris presents a nifty technique for designing square-root Nyquist FIR filters with good stopband attenuation [1]. In this post, I describe the method and provide a Matlab function for designing the filters. You can find a Matlab function by harris for designing the filters at [2].

## Make Hardware Great Again

By now you're aware of the collective angst in the US about 5G. Why is the US not a leader in 5G ? Could that also happen -- indeed, is it happening -- in AI ? If we lead in other areas, why not 5G ? What makes it so hard ? This...

## Add the Hilbert Transformer to Your DSP Toolkit, Part 1

In some previous articles, I made use of the Hilbert transformer, but did not explain its theory in any detail. In this article, I’ll dig a little deeper into how the Hilbert Transformer works. Understanding the Hilbert Transformer...

## PID Without a PhD

I both consult and teach in the area of digital control. Through both of these efforts, I have found that while there certainly are control problems that require all the expertise I can bring to bear, there are a great number of control problems...

## Understanding and Preventing Overflow (I Had Too Much to Add Last Night)

Happy Thanksgiving! Maybe the memory of eating too much turkey is fresh in your mind. If so, this would be a good time to talk about overflow. In the world of floating-point arithmetic, overflow is possible but not particularly common. You can...

## 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 snippet This article relates to the Matlab / Octave code snippet: Delay estimation with...

## Pulse Shaping in Single-Carrier Communication Systems

Some common conceptual hurdles for beginning communications engineers have to do with "Pulse Shaping" or the closely-related, even synonymous, topics of "matched filtering", "Nyquist filtering", "Nyquist pulse", "pulse filtering", "spectral...

## 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...

## Decimators Using Cascaded Multiplierless Half-band Filters

In my last post, I provided coefficients for several multiplierless half-band FIR filters. In the comment section, Rick Lyons mentioned that such filters would be useful in a multi-stage decimator. For such an application, any subsequent multipliers save on resources, since they operate at a fraction of the maximum sample frequency. We’ll examine the frequency response and aliasing of a multiplierless decimate-by-8 cascade in this article, and we’ll also discuss an interpolator cascade using the same half-band filters.

## Return of the Delta-Sigma Modulators, Part 1: Modulation

About a decade ago, I wrote two articles: Modulation Alternatives for the Software Engineer (November 2011) Isolated Sigma-Delta Modulators, Rah Rah Rah! (April 2013) Each of these are about delta-sigma modulation, but they’re...

## Evaluate Window Functions for the Discrete Fourier Transform

The Discrete Fourier Transform (DFT) operates on a finite length time sequence to compute its spectrum. For a continuous signal like a sinewave, you need to capture a segment of the signal in order to perform the DFT. Usually, you...