## Second Order Discrete-Time System Demonstration

Discrete-time systems are remarkable: the time response can be computed from mere difference equations, and the coefficients ai, bi of these equations are also the coefficients of H(z). Here, I try to illustrate this remarkableness by converting a continuous-time second-order system to an approximately equivalent discrete-time system. With a discrete-time model, we can then easily compute the time response to any input. But note that the goal here is as much to understand the discrete-time model as it is to find the response.

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

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

## 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.

## An IIR 'DC Removal' Filter

●2 commentsIt 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.

## Two Easy Ways To Test Multistage CIC Decimation Filters

●2 commentsThis 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.

## 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.

## An Efficient Linear Interpolation Scheme

●4 commentsThis article presents a computationally-efficient linear interpolation trick that requires at most one multiply per output sample.

## Sinusoidal Frequency Estimation Based on Time-Domain Samples

●6 commentsThe 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.

## Launch of Youtube Channel: My First Videos - Embedded World 2017

I went to Embedded World 2017 in Nuremberg with an ambitious plan; I would make video highlights of several exhibits (booths) to be presented to the *Related sites audience. I would try to make the vendors focus their pitch on the essential...

## 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...

## 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...

## 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.

## Minimum Shift Keying (MSK) - A Tutorial

●7 commentsMinimum 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...

## 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...

## Polyphase filter / Farrows interpolation

●6 commentsHello, 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...

## Handling Spectral Inversion in Baseband Processing

●3 commentsThe problem of "spectral inversion" comes up fairly frequently in the context of signal processing for communication systems. In short, "spectral inversion" is the reversal of the orientation of the signal bandwidth with...

## Two Easy Ways To Test Multistage CIC Decimation Filters

●2 commentsThis 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.

## 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...