## Interpolation Basics

This article covers interpolation basics, and provides a numerical example of interpolation of a time signal. Figure 1 illustrates what we mean by interpolation. The top plot shows a continuous time signal, and the middle plot shows a sampled version with sample time Ts. The goal of interpolation is to increase the sample rate such that the new (interpolated) sample values are close to the values of the continuous signal at the sample times [1]. For example, if we increase the sample rate by the integer factor of four, the interpolated signal is as shown in the bottom plot. The time between samples has been decreased from Ts to Ts/4.

## Round-robin or RTOS for my embedded system

First of all, I would like to introduce myself. I am Manuel Herrera. I am starting to write blogs about the situations that I have faced over the years of my career and discussed with colleagues.To begin, I would like to open a conversation...

## Somewhat Off Topic: Deciphering Transistor Terminology

I recently learned something mildly interesting about transistors, so I thought I'd share my new knowledge with you folks. Figure 1 shows a p-n-p transistor comprising a small block of n-type semiconductor sandwiched between two blocks of p-type...

## DSP Jobs Soaring | Ready Your Interview Skills

Digital Signal Processing (DSP) technology is the cornerstone of most cutting edge technology today. For example, digital signal processing drives much of machine learning in artificial intelligence (AI). It also steers eyesight and movement...

## Generating Partially Correlated Random Variables

IntroductionIt is often useful to be able to generate two or more signals with specific cross-correlations. Or, more generally, we would like to specify an $\left(N \times N\right)$ covariance matrix, $\mathbf{R}_{xx}$, and generate $N$ signals...

## Stereophonic Amplitude-Panning: A Derivation of the "Tangent Law"

This article presents a derivation of the "Tangent Law"

## A Brief Introduction To Romberg Integration

This article briefly describes a remarkable integration algorithm, called "Romberg integration." The algorithm is used in the field of numerical analysis but it's not so well-known in the world of DSP.

## 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...

## Feedback Controllers - Making Hardware with Firmware. Part 10. DSP/FPGAs Behaving Irrationally

This article will look at a design approach for feedback controllers featuring low-latency "irrational" characteristics to enable the creation of physical components such as transmission lines. Some thought will also be given as to...

## An IIR 'DC Removal' Filter

It seems to me that DC removal filters (also called "DC blocking filters") have been of some moderate interest recently on the dsprelated.com Forum web page. With that notion in mind I thought I'd post a little information, from Chapter 13 of my "Understanding DSP" book, regarding infinite impulse response (IIR) DC removal filters.

## Polyphase filter / Farrows interpolation

Hello, this article is meant to give a quick overview over polyphase filtering and Farrows interpolation. A good reference with more depth is for example Fred Harris' paper: http://www.signumconcepts.com/IP_center/paper018.pdf The task is as...

## Music/Audio Signal Processing

Greetings,This is my blog from the point of view of a music/audio DSP research engineer / educator. It is informal and largely nontechnical because nearly everything I have to say about signal processing is (or will be) somewhere in my four-book...

## Spectral Flipping Around Signal Center Frequency

Most of us are familiar with the process of flipping the spectrum (spectral inversion) of a real signal by multiplying that signal's time samples by (-1)n. In that process the center of spectral rotation is fs/4, where fs is the signal's sample...

## 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.

## A New Contender in the Quadrature Oscillator Race

There have been times when I wanted to determine the z-domain transfer function of some discrete network, but my algebra skills failed me. Some time ago I learned Mason's Rule, which helped me solve my problems. If you're willing to learn the...

## Two Easy Ways To Test Multistage CIC Decimation Filters

This article presents two very easy ways to test the performance of multistage cascaded integrator-comb (CIC) decimation filters. Anyone implementing CIC filters should take note of the following proposed CIC filter test methods.

## Sinusoidal Frequency Estimation Based on Time-Domain Samples

The topic of estimating a noise-free real or complex sinusoid's frequency, based on fast Fourier transform (FFT) samples, has been presented in recent blogs here on dsprelated.com. For completeness, it's worth knowing that simple frequency estimation algorithms exist that do not require FFTs to be performed . Below I present three frequency estimation algorithms that use time-domain samples, and illustrate a very important principle regarding so called "exact" mathematically-derived DSP algorithms.

## The Number 9, Not So Magic After All

This blog is not about signal processing. Rather, it discusses an interesting topic in number theory, the magic of the number 9. As such, this blog is for people who are charmed by the behavior and properties of numbers. For decades I've thought...

## Frequency Translation by Way of Lowpass FIR Filtering

Some weeks ago a question appeared on the dsp.related Forum regarding the notion of translating a signal down in frequency and lowpass filtering in a single operation [1]. It is possible to implement such a process by embedding a discrete cosine...

## Python scipy.signal IIR Filter Design

Introduction The following is an introduction on how to design an infinite impulse response (IIR) filters using the Python scipy.signal package. This post, mainly, covers how to use the scipy.signal package and is not a thorough...