A Quadrature Signals Tutorial: Complex, But Not Complicated

Rick Lyons April 12, 201365 comments

Introduction Quadrature signals are based on the notion of complex numbers and perhaps no other topic causes more heartache for newcomers to DSP than these numbers and their strange terminology of j operator, complex, imaginary, real, and orthogonal. If you're a little unsure of the physical meaning of complex numbers and the j = √-1 operator, don't feel bad because you're in good company. Why even Karl Gauss, one the world's greatest mathematicians, called the j-operator the "shadow of...


FIR sideways (interpolator polyphase decomposition)

Markus Nentwig September 12, 20129 comments

An efficient implementation of a symmetric-FIR polyphase 1:3 interpolator that doesn't follow the usual tapped delay line-paradigm. The example exploits the impulse response symmetry and avoids four multiplications out of 10. keywords: symmetric polyphase FIR filter implementation ASIC Matlab / Octave implementation

Introduction

An interpolating FIR filter can be implemented with a single tapped delay line, possibly going forwards and backwards for a symmetric impulse response. To...


Design of an anti-aliasing filter for a DAC

Markus Nentwig August 18, 2012
Overview
  • Octaveforge / Matlab design script. Download: here
  • weighted numerical optimization of Laplace-domain transfer function
  • linear-phase design, optimizes vector error (magnitude and phase)
  • design process calculates and corrects group delay internally
  • includes sinc() response of the sample-and-hold stage in the ADC
  • optionally includes multiplierless FIR filter
Problem Figure 1: Typical FIR-DAC-analog lowpass line-up

Digital-to-analog conversion connects digital...


Understanding the 'Phasing Method' of Single Sideband Demodulation

Rick Lyons August 8, 201230 comments

There are four ways to demodulate a transmitted single sideband (SSB) signal. Those four methods are:

  • synchronous detection,
  • phasing method,
  • Weaver method, and
  • filtering method.

Here we review synchronous detection in preparation for explaining, in detail, how the phasing method works. This blog contains lots of preliminary information, so if you're already familiar with SSB signals you might want to scroll down to the 'SSB DEMODULATION BY SYNCHRONOUS DETECTION'...


Python scipy.signal IIR Filter Design Cont.

Christopher Felton June 19, 20127 comments

In the previous post the Python scipy.signal iirdesign function was disected.  We reviewed the basics of filter specification and reviewed how to use the iirdesign function to design IIR filters.  The previous post I only demonstrated low pass filter designs.  The following are examples how to use the iirdesign function for highpass, bandpass, and stopband filters designs.

Highpass Filter

The following is a highpass filter design for the different filter...


Python scipy.signal IIR Filter Design

Christopher Felton May 13, 20124 comments
Introduction

The following is an introduction on how to design an infinite impulse response (IIR) filters using the Python scipy.signal package.  This post, mainly, covers how to use the scipy.signal package and is not a thorough introduction to IIR filter design.  For complete coverage of IIR filter design and structure see one of the references.

Filter Specification

Before providing some examples lets review the specifications for a filter design.  A filter...


Instant CIC

Markus Nentwig May 8, 20124 comments

Summary:

A floating point model for a CIC decimator, including the frequency response.

Description:

A CIC filter relies on a peculiarity of its fixed-point implementation: Normal operation involves repeated internal overflows that have no effect to the output signal, as they cancel in the following stage.

One way to put it intuitively is that only the speed (and rate of change) of every little "wheel" in the clockworks carries information, but its absolute position is...


Curse you, iPython Notebook!

Christopher Felton May 1, 20124 comments

 

First, I think ipython is great. I use it daily and always have an ipython terminal open.  But just recently, I was showing off the ipython 0.12 notebook and in the process created a lengthy example while demonstrating the cool features of the ipython notebook.  The example included LaTeX equations, plots, etc.  Since the notebook session was on something of relevance I decided to clean up the session and use it for the beginning of a report.


[Book Review] Numpy 1.5 Beginner's Guide

Christopher Felton January 7, 2012

Full Disclosure: The publisher of this book, PACKT, was soliciting reviewers.  I volunteered to review the book and the publisher sent me an e-version of the book.

Introduction

The following is a review of "Numpy 1.5 Beginner's Guide", "Learn by doing: less theory, more results" by Ivan Idris.  As the title suggests this book is for a beginner.  Either someone who is new to numerical computing with high-level languages (HLL) or someone who is new to the Python...


Design study: 1:64 interpolating pulse shaping FIR

Markus Nentwig December 26, 20115 comments

This article is the documentation to a code snippet that originated from a discussion on comp.dsp.

The task is to design a root-raised cosine filter with a rolloff of a=0.15 that interpolates to 64x the symbol rate at the input.

The code snippet shows a solution that is relatively straightforward to design and achieves reasonably good efficiency using only FIR filters.

Motivation: “simple solutions?”

Least-squares magic bullets? The Moore-Penrose Pseudoinverse

Markus Nentwig October 24, 20109 comments

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...


Approximating the area of a chirp by fitting a polynomial

Alexandre de Siqueira November 15, 20158 comments

Once in a while we need to estimate the area of a dataset in which we are interested. This area could give us, for example, force (mass vs acceleration) or electric power (electric current vs charge).

One way to do that is fitting a curve on our data, and let's face it: this is not that easy. In this post we will work on this issue using Python and its packages. If you do not have Python installed on your system, check here how to...


Compute Images/Aliases of CIC Interpolators/Decimators

Neil Robertson November 1, 20202 comments

Cascade-Integrator-Comb (CIC) filters are efficient fixed-point interpolators or decimators.  For these filters, all coefficients are equal to 1, and there are no multipliers.  They are typically used when a large change in sample rate is needed.  This article provides two very simple Matlab functions that can be used to compute the spectral images of CIC interpolators and the aliases of CIC decimators.

1.  CIC Interpolators

Figure 1 shows three interpolate-by-M...


The Zeroing Sine Family of Window Functions

Cedron Dawg August 16, 20202 comments
Introduction

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by introducing a class of well behaved window functions that the author believes to be previously unrecognized. The definition and some characteristics are displayed. The heavy math will come in later articles. This is an introduction to the family, and a very special member of it.

This is one of my longer articles. The bulk of the material is in the front half. The...


Exploring Human Hearing Range

Stephen Morris October 31, 20204 comments
Human Hearing Range

In this post, I'll look at an interesting aspect of Audacity – using it to explore the threshold of human hearing. In my book Digital Signal Processing: A Gentle Introduction with Audio Examples, I go into this topic and I include a side note on the amazing hearing range of our canine companions.

Creating a Test Audio File

Audacity allows for the generation of a variety of test signals. If you click the Generate->Tone menu, it looks something like...


Polar Coding Notes: Channel Combining and Channel Splitting

Lyons Zhang October 19, 20181 comment

Channel Combining  

Channel combining is a step that combines copies of a given B-DMC $W$ in a recursive manner to produce a vector channel $W_N : {\cal X}^N \to {\cal Y}^N$, where $N$ can be any power of two, $N=2^n, n\le0^{[1]}$.  

The notation $u_1^N$ as shorthand for denoting a row vector $(u_1, \dots , u_N)$.  

The vector channel $W_N$ is the virtual channel between the input sequence $u_1^N$ to a linear encoder and the output sequence $y^N_1$ of $N$...


[Book Review] Numpy 1.5 Beginner's Guide

Christopher Felton January 7, 2012

Full Disclosure: The publisher of this book, PACKT, was soliciting reviewers.  I volunteered to review the book and the publisher sent me an e-version of the book.

Introduction

The following is a review of "Numpy 1.5 Beginner's Guide", "Learn by doing: less theory, more results" by Ivan Idris.  As the title suggests this book is for a beginner.  Either someone who is new to numerical computing with high-level languages (HLL) or someone who is new to the Python...


Unit Testing for Embedded Algorithms

Anthony Ricke December 21, 2009

Happy Holidays! For my premier article, I am writing about my favorite technique to use when designing and developing software- unit testing. Unit testing is a best practice when designing software. It allows the designer to verify the behavior of the software units before the entire system is complete, and it facilitates the change and growth of the software system because the developer can verify that the changes will not affect the behavior of other parts of the system. I have used...


Implementing a full-duplex UART using the TMS320VC33 serial port

Manuel Herrera March 16, 20112 comments

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...


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

Cedron Dawg March 20, 20179 comments
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 given in Exact Frequency Formula for a Pure Real Tone in a DFT. Since a real signal is the sum of two complex signals, the frequency formula for a single complex tone signal is a lot less complicated than for the real case.

Theoretical...