A Two Bin Exact Frequency Formula for a Pure Complex Tone in a DFT

Cedron Dawg

Introduction This is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by deriving an exact formula for the frequency of a complex tone in a DFT. It is basically a parallel treatment to the real case...

DFT Bin Value Formulas for Pure Complex Tones

Cedron Dawg

Introduction This is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by deriving an analytical formula for the DFT of pure complex tones and an alternative variation. It is basically a parallel...

Multi-Decimation Stage Filtering: Design and Optimization


During my research on digital FIR decimation filters I have been developing various Matlab scripts and functions. In which I have decided later on to consolidate it in a form of a toolbox. I have developed this toolbox to assist and...

Canonic Signed Digit (CSD) Representation of Integers

Neil Robertson

In my last post I presented Matlab code to synthesize multiplierless FIR filters using Canonic Signed Digit (CSD) coefficients.  I included a function dec2csd1.m (repeated here in Appendix A) to convert decimal integers to binary CSD...

Frequency Translation by Way of Lowpass FIR Filtering

Rick Lyons

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...

Minimum Shift Keying (MSK) - A Tutorial

Qasim Chaudhari

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...

Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine

Jason Sachs
1 comment

Today’s topic is rounding in embedded systems, or more specifically, why you don’t need to worry about it in many cases.One of the issues faced in computer arithmetic is that exact arithmetic requires an ever-increasing bit length to...

Some Thoughts on Sampling

Qasim Chaudhari
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Some time ago, I came across an interesting problem. In the explanation of sampling process, a representation of impulse sampling shown in Figure 1 below is illustrated in almost every textbook on DSP and communications. The question is: how is...

Matlab Code to Synthesize Multiplierless FIR Filters

Neil Robertson

This article presents Matlab code to synthesize multiplierless Finite Impulse Response (FIR) lowpass filters. A filter coefficient can be represented as a sum of powers of 2.  For example, if a coefficient = decimal 5 multiplies input x,...

Wavelets II - Vanishing Moments and Spectral Factorization

Vincent Herrmann
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In the previous blog post I described the workings of the Fast Wavelet Transform (FWT) and how wavelets and filters are related. As promised, in this article we will see how to construct useful filters. Concretely, we will find a way to calculate...