## 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...

## A Beginner's Guide To Cascaded Integrator-Comb (CIC) Filters

This article discusses the behavior, mathematics, and implementation of cascaded integrator-comb filters.

## A Fixed-Point Introduction by Example

●9 commentsIntroduction The finite-word representation of fractional numbers is known as fixed-point. Fixed-point is an interpretation of a 2's compliment number usually signed but not limited to sign representation. It...

## FFT Interpolation Based on FFT Samples: A Detective Story With a Surprise Ending

●4 commentsThis blog presents several interesting things I recently learned regarding the estimation of a spectral value located at a frequency lying between previously computed FFT spectral samples. My curiosity about this FFT interpolation process was triggered by reading a spectrum analysis paper written by three astronomers.

## A Beginner's Guide to OFDM

In the recent past, high data rate wireless communications is often considered synonymous to an Orthogonal Frequency Division Multiplexing (OFDM) system. OFDM is a special case of multi-carrier communication as opposed to a conventional...

## An Interesting Fourier Transform - 1/f Noise

●4 commentsPower law functions are common in science and engineering. A surprising property is that the Fourier transform of a power law is also a power law. But this is only the start- there are many interesting features that soon become apparent. This may...

## Minimum Shift Keying (MSK) - A Tutorial

Minimum Shift Keying (MSK) is one of the most spectrally efficient modulation schemes available. Due to its constant envelope, it is resilient to non-linear distortion and was therefore chosen as the modulation technique for the GSM cell phone...

## Simplest Calculation of Half-band Filter Coefficients

Half-band filters are lowpass FIR filters with cut-off frequency of one-quarter of sampling frequency fs and odd symmetry about fs/4 [1]*. And it so happens that almost half of the coefficients are zero. The passband and stopband bandwiths are equal, making these filters useful for decimation-by-2 and interpolation-by-2. Since the zero coefficients make them computationally efficient, these filters are ubiquitous in DSP systems. Here we will compute half-band coefficients using the window method. While the window method typically does not yield the fewest taps for a given performance, it is useful for learning about half-band filters. Efficient equiripple half-band filters can be designed using the Matlab function firhalfband [2].

## Understanding and Relating E_{b}/N_{o}, SNR, and other Power Efficiency Metrics

●8 comments Introduction Evaluating the performance of communication systems, and wireless systems in particular, usually involves quantifying some performance metric as a function of Signal-to-Noise-Ratio (SNR) or some similar measurement. Many systems...

## Polyphase Filters and Filterbanks

●2 commentsALONG CAME POLY Polyphase filtering is a computationally efficient structure for applying resampling and filtering to a signal. Most digital filters can be applied in a polyphase format, and it is also possible to create efficient resampling...

## 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...