## A Fixed-Point Introduction by Example

●6 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...

## Discrete Wavelet Transform Filter Bank Implementation (part 2)

●1 commentFollowing the previous blog entry: http://www.dsprelated.com/showarticle/115.php Difference between DWT and DWPT Before getting to the equivalent filter obtention, I first want to talk about the difference between DWT(Discrete Wavelet...

## Discrete Wavelet Transform Filter Bank Implementation (part 1)

●1 commentUPDATE: Added graphs and code to explain the frequency division of the branches The focus of this article is to briefly explain an implementation of this transform and several filter bank forms. Theoretical information about DWT can be found...

## Music/Audio Signal Processing

●4 commentsGreetings,This is my blog from the point of view of a music/audio DSP research engineer / educator. It is informal and largely nontechnical because nearly everything I have to say about signal processing is (or will be) somewhere in my four-book...

## Frequency Dependence in Free Space Propagation

●1 commentIntroductionIt seems to be fairly common knowledge, even among practicing professionals, that the efficiency of propagation of wireless signals is frequency dependent. Generally it is believed that lower frequencies are desirable since pathloss...

## Pulse Shaping in Single-Carrier Communication Systems

●2 commentsSome common conceptual hurdles for beginning communications engineers have to do with "Pulse Shaping" or the closely-related, even synonymous, topics of "matched filtering", "Nyquist filtering", "Nyquist pulse", "pulse filtering", "spectral...

## Linear-phase DC Removal Filter

●1 commentThis 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...

## Free DSP Books on the Internet

●2 commentsWhile surfing the "net" I have occasionally encountered signal processing books whose chapters could be downloaded to my computer. I started keeping a list of those books and, over the years, that list has grown to over forty books. Perhaps the...

## 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...

## 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...

## Analytic Signal

In communication theory and modulation theory we always deal with two phases: In-phase (I) and Quadrature-phase (Q). The question that I will discuss in this blog is that why we use two phases and not more.

## Some Thoughts on Sampling

●1 commentSome 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...

## DFT Bin Value Formulas for Pure Complex Tones

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...

## Python number crunching faster? Part I

Everyone has their favorite computing platform, regardless if it is Matlab, Octave, Scilab, Mathematica, Mathcad, etc. I have been using Python and the common numerical and scientific packages available. Personally, I have found this...

## An s-Plane to z-Plane Mapping Example

While surfing around the Internet recently I encountered the 's-plane to z-plane mapping' diagram shown in Figure 1. At first I thought the diagram was neat because it's a good example of the old English idiom: "A picture is worth a thousand...

## Should DSP Undergraduate Students Study Z-transform Regions of Convergence?

●2 commentsNot long ago I presented my 3-day DSP class to a group of engineers at Tektronix Inc. in Beaverton Oregon [1]. After I finished covering my material on IIR filters' z-plane pole locations and filter stability, one of the Tektronix engineers asked...

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

●1 commentIntroduction 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...

## 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...

## The Real Star of Star Trek

Unless you've been living under a rock recently, you're probably aware that this month is the 50-year anniversary of the original Star Trek show on American television. It's an anniversary worth noting, as did Time Magazine with their special...

## 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...