 ## 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. ## Algebra's Laws of Powers and Roots: Handle With Care ## 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. ## A Fast Guaranteed-Stable Sliding DFT Algorithm ## 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... ## The Discrete Fourier Transform as a Frequency Response

The discrete frequency response H(k) of a Finite Impulse Response (FIR) filter is the Discrete Fourier Transform (DFT) of its impulse response h(n) .  So, if we can find H(k) by whatever method, it should be identical to the DFT of... ## Simple Concepts Explained: Fixed-Point

IntroductionMost signal processing intensive applications on FPGA are still implemented relying on integer or fixed-point arithmetic. It is not easy to find the key ideas on quantization, fixed-point and integer arithmetic. In a series of...