## Canonic Signed Digit (CSD) Representation of Integers

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

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

●3 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...

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

●1 commentToday’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

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

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

●1 commentIn 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...

## The Power Spectrum

●2 commentsOften, when calculating the spectrum of a sampled signal, we are interested in relative powers, and we don't care about the absolute accuracy of the y axis. However, when the sampled signal represents an analog signal, we sometimes need an accurate picture of the analog signal's power in the frequency domain. This post shows how to calculate an accurate power spectrum.

## New Comments System (please help me test it)

I thought it would take me a day or two to implement, it took almost two weeks...But here it is, the new comments systems for blogs, heavily inspired by the forum system I developed earlier this year. Which means that:You can easily add...

## Wavelets I - From Filter Banks to the Dilation Equation

This is the first in what I hope will be a series of posts about wavelets, particularly about the Fast Wavelet Transform (FWT). The FWT is extremely useful in practice and also very interesting from a theoretical point of view. Of course there...

## 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...

## Minimum Shift Keying (MSK) - A Tutorial

●3 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...

## A Fixed-Point Introduction by Example

●2 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...

## Matlab Code to Synthesize Multiplierless FIR Filters

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,...

## Polyphase Filters and Filterbanks

●1 commentALONG 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...

## The Power Spectrum

●2 commentsOften, when calculating the spectrum of a sampled signal, we are interested in relative powers, and we don't care about the absolute accuracy of the y axis. However, when the sampled signal represents an analog signal, we sometimes need an accurate picture of the analog signal's power in the frequency domain. This post shows how to calculate an accurate power spectrum.

## An Interesting Fourier Transform - 1/f Noise

●2 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...

## Understanding and Implementing the Sliding DFT

●2 commentsIntroduction In many applications the detection or processing of signals in the frequency domain offers an advantage over performing the same task in the time-domain. Sometimes the advantage is just a simpler or more conceptually...

## Linear-phase DC Removal Filter

This blog describes several DC removal networks that might be of interest to the dsprelated.com readers. Back in August 2007 there was a thread on the comp.dsp newsgroup concerning the process of removing the DC (zero Hz) component from a...

## Handling Spectral Inversion in Baseband Processing

●1 commentThe 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...