## 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 to be very useful in my work.  Lately there has been some chatter on speeding up Python.

From another project I follow, MyHDL, I was introduced to the Python JIT compiler,

## Bank-switched Farrow resampler

Bank-switched Farrow resampler Summary

A modification of the Farrow structure with reduced computational complexity.Compared to a conventional design, the impulse response is broken into a higher number of segments. Interpolation accuracy is achieved with a lower polynomial order, requiring fewer multiplications per output sample at the expense of a higher overall number of coefficients.

Example code

This code snippet provides a Matlab / Octave implementation.And

## 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 extends our finite-word length from a finite set of integers to a finite set of rational real numbers [1].  A fixed-point representation of a number consists of integer and fractional components.  The bit length is defined...

## Implementing a full-duplex UART using the TMS320VC33 serial port

Although the TMS320VC33 serial port was designed to be used as a synchronous port, it can also be used as an asynchronous port under software control. This post describes the hardware and software needed to use a TMS320VC33 serial port as a full-duplex UART port. A schematic diagram and a lengthy code listing are provided to illustrate the solution. This note discusses the implementation of an interrupt-driven, full-duplex, asynchronous serial interface, 9600-baud UART with 8 data bits, 1...

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

Following 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 Transform) and DWPT (Discrete Wavelet Packet Transform). The latter is used mostly for image processing.

While DWT has a single "high-pass" branch that filters the signal with the h1 filter, the DWPT separates branches symmetricaly: this means that one...

## State Space Representation and the State of Engineering Thinking

Most, if not all, textbooks in signal processing (SP) thoroughly covers the frequency analysis of signals and systems alike, including the Fourier and the Z-transform that produce the well known Transfer Function. Another way of signal analysis, not as popular in signal processing though, is State Space representation. State space models describes the internal signals of the system or the process and how it affect the output, in contrast to the frequency representation that only describe the...

## Matlab Programming Contest

November 10, 2010

Every 6 months Mathworks hosts an online Matlab programming contest.  If you love or hate Matlab check out the contest.  The group does a really good job putting together the puzzles.  The contest runs for a week and starts today at noon EST (10 Nov 2010).

If you are an experienced Matlab programmer or new to Matlab it is worth checking out.  Even if you do not intend on submitting solutions.  Also, the problems / puzzles only require the base Matlab...

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

October 27, 20101 comment

UPDATE: Added graphs and code to explain the frequency division of the branches

First of all, a 'quick and dirty' simplified explanation of the differences between DFT and DWT:

The DWT (Discrete Wavelet Transform), simply put, is an operation that receives a signal as an input (a vector of data) and...

## Least-squares magic bullets? The Moore-Penrose Pseudoinverse

Hello,

the topic of this brief article is a tool that can be applied to a variety of problems: The Moore-Penrose Pseudoinverse.While maybe not exactly a magic bullet, it gives us least-squares optimal solutions, and that is under many circumstances the best we can reasonably expect.

I'll demonstrate its use on a short example. More details can be found for example on Wikipedia, or the Matlab documentation...

Overview

The topic of this article are the effects of radio frequency distortions on a baseband signal, and how to model them at baseband. Typical applications are use as a simulation model or in digital predistortion algorithms.

Introduction

Transmitting and receiving wireless signals usually involves analog radio frequency circuits, such as power amplifiers in a transmitter or low-noise amplifiers in a receiver.Signal distortion in those circuits deteriorates the link quality. When...

## Matlab Programming Contest

November 10, 2010

Every 6 months Mathworks hosts an online Matlab programming contest.  If you love or hate Matlab check out the contest.  The group does a really good job putting together the puzzles.  The contest runs for a week and starts today at noon EST (10 Nov 2010).

If you are an experienced Matlab programmer or new to Matlab it is worth checking out.  Even if you do not intend on submitting solutions.  Also, the problems / puzzles only require the base Matlab...

## Two Bin Exact Frequency Formulas for a Pure Real Tone in a DFT

Introduction

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving exact formulas for the frequency of a real tone in a DFT. This time it is a two bin version. The approach taken is a vector based one similar to the approach used in "Three Bin Exact Frequency Formulas for a Pure Complex Tone in a DFT"[1]. The real valued formula presented in this article actually preceded, and was the basis for the complex three bin...

## DFT Bin Value Formulas for Pure Complex Tones

March 17, 2017
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 treatment to the real case given in DFT Bin Value Formulas for Pure Real Tones. In order to understand how a multiple tone signal acts in a DFT it is necessary to first understand how a single pure tone acts. Since a DFT is a linear transform, the...

## Determination of the transfer function of passive networks with MATLAB Functions

With MATLAB functions, the transfer function of passive networks can be determined relatively easily. The method is explained using the example of a passive low-pass filter of the sixth order, which is shown in Fig.1

Fig.1 Passive low-pass filter of the sixth order

If one tried, as would be logical, to calculate the transfer function starting from the input, it would be quite complicated. On the other hand, if you start from the output, the determination of this function is simple...

## Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 1)

May 12, 2017
Introduction

This is an article that is a another digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). Although it is not as far off as the last blog article.

A new family of formulas for calculating the frequency of a single pure tone in a short interval in the time domain is presented. They are a generalization of Equation (1) from Rick Lyons' recent blog article titled "Sinusoidal Frequency Estimation Based on Time-Domain Samples"[1]. ...

## Compressive Sensing - Recovery of Sparse Signals (Part 1)

November 28, 2015

The amount of data that is generated has been increasing at a substantial rate since the beginning of the digital revolution. The constraints on the sampling and reconstruction of digital signals are derived from the well-known Nyquist-Shannon sampling theorem. To review, the theorem states that a band-limited signal, with the highest frequency of $f_{max}$, can be completely reconstructed from its samples if the sampling rate, $f_{s}$, is at least twice the signal bandwidth. If the...

June 13, 20211 comment
≥≥≥ Simulink-Simulation of SSB demodulation or modulation from the article “Understanding the ‘Phasing Method’ of Single Sideband Demodulation” by Richard Lyons Josef Hoffmann

The article “Understanding the ‘Phasing Method’ of Single Sideband Demodulation” by Richard Lyons is a very good description of this topic. The block representation from the figures are clear and easy to understand. They are predestined for a simulation in Simulink. The simulation can help...

## Phase and Amplitude Calculation for a Pure Complex Tone in a DFT using Multiple Bins

March 14, 2018
Introduction

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving exact formulas to calculate the phase and amplitude of a pure complex tone from several DFT bin values and knowing the frequency. This article is functionally an extension of my prior article "Phase and Amplitude Calculation for a Pure Complex Tone in a DFT"[1] which used only one bin for a complex tone, but it is actually much more similar to my approach for real...