## Model a Sigma-Delta DAC Plus RC Filter

Sigma-delta digital-to-analog converters (SD DAC’s) are often used for discrete-time signals with sample rate much higher than their bandwidth. For the simplest case, the DAC output is a single bit, so the only interface hardware required is a standard digital output buffer. Because of the high sample rate relative to signal bandwidth, a very simple DAC reconstruction filter suffices, often just a one-pole RC lowpass. In this article, I present a simple Matlab function that models the combination of a basic SD DAC and one-pole RC filter. This model allows easy evaluation of the overall performance for a given input signal and choice of sample rate, R, and C.

## DAC Zero-Order Hold Models

This article provides two simple time-domain models of a DAC’s zero-order hold. These models will allow us to find time and frequency domain approximations of DAC outputs, and simulate analog filtering of those outputs. Developing the models is also a good way to learn about the DAC ZOH function.

## 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.

## Pentagon Construction Using Complex Numbers

A method for constructing a pentagon using a straight edge and a ruler is deduced from the complex values of the Fifth Roots of Unity. Analytic values for the points are also derived.

## Multiplierless Half-band Filters and Hilbert Transformers

This article provides coefficients of multiplierless Finite Impulse Response 7-tap, 11-tap, and 15-tap half-band filters and Hilbert Transformers. Since Hilbert transformer coefficients are simply related to half-band coefficients, multiplierless Hilbert transformers are easily derived from multiplierless half-bands.

## Interpolator Design: Get the Stopbands Right

In this article, I present a simple approach for designing interpolators that takes the guesswork out of determining the stopbands.

## 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...

## Simple Discrete-Time Modeling of Lossy LC Filters

There are many software applications that allow modeling LC filters in the frequency domain. But sometimes it is useful to have a time domain model, such as when you need to analyze a mixed analog and DSP system. For example, the...

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

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

## 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...

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

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

This 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

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

## 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...

## Handling Spectral Inversion in Baseband Processing

The 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

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.

## A Fixed-Point Introduction by Example

Introduction 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...

## A Fast Real-Time Trapezoidal Rule Integrator

This article presents a computationally-efficient network for computing real?time discrete integration using the Trapezoidal Rule.