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Peak to Average Power Ratio and CCDF

Neil Robertson ● May 17, 2016●2 comments

Peak to Average Power Ratio (PAPR) is often used to characterize digitally modulated signals.  One example application is setting the level of the signal in a digital modulator.  Knowing PAPR allows setting the average power to a level that is just low enough to minimize clipping.

However, for a random signal, PAPR is a statistical quantity.  We have to ask, what is the probability of a given peak power?  Then we can decide where to set the average...

Filter a Rectangular Pulse with no Ringing

Neil Robertson ● May 12, 2016●10 comments

To filter a rectangular pulse without any ringing, there is only one requirement on the filter coefficients:  they must all be positive.  However, if we want the leading and trailing edge of the pulse to be symmetrical, then the coefficients must be symmetrical.  What we are describing is basically a window function.

Consider a rectangular pulse 32 samples long with fs = 1 kHz.  Here is the Matlab code to generate the pulse:

N= 64; fs= 1000; % Hz sample...

Digital Envelope Detection: The Good, the Bad, and the Ugly

Rick Lyons ● April 3, 2016●11 comments

Recently I've been thinking about the process of envelope detection. Tutorial information on this topic is readily available but that information is spread out over a number of DSP textbooks and many Internet web sites. The purpose of this blog is to summarize various digital envelope detection methods in one place.

Here I focus on envelope detection as it is applied to an amplitude-fluctuating sinusoidal signal where the positive-amplitude fluctuations (the sinusoid's envelope)...

Exponential Smoothing with a Wrinkle

Cedron Dawg ● December 17, 2015
Introduction

This is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by providing a set of preprocessing filters to improve the resolution of the DFT. Because of the exponential nature of sinusoidal functions, they have special mathematical properties when exponential smoothing is applied to them. These properties are derived and explained in this blog article.

Basic Exponential Smoothing

Exponential smoothing is also known as...

Discrete-Time PLLs, Part 1: Basics

Reza Ameli ● December 1, 2015●9 comments

Design Files: Part1.slx

Hi everyone,

In this series of tutorials on discrete-time PLLs we will be focusing on Phase-Locked Loops that can be implemented in discrete-time signal proessors such as FPGAs, DSPs and of course, MATLAB.

In the first part of the series, we will be reviewing the basics of continuous-time baseband PLLs and we will see some useful mathematics that will give us insight into the inners working of PLLs. In the second part, we will focus on...

Multilayer Perceptrons and Event Classification with data from CODEC using Scilab and Weka

David E Norwood ● November 25, 2015

For my first blog, I thought I would introduce the reader to Scilab [1] and Weka [2].  In order to illustrate how they work, I will put together a script in Scilab that will sample using the microphone and CODEC on your PC and save the waveform as a CSV file.  Then, we can take the CSV file and open it in Weka.  Once in Weka, we have a lot of paths to consider in order to classify it.  I use the term classify loosely since there are many things you can do with data sets...

Multimedia Processing with FFMPEG

Karthick Kumaran A S V ● November 16, 2015

FFMPEG is a set of libraries and a command line tool for encoding and decoding audio and video in many different formats. It is a free software project for manipulating/processing multimedia data. Many open source media players are based on FFMPEG libraries.

FFMPEG is developed under Linux but it can be compiled under most operating systems including Mac OS, Microsoft Windows. For more details about FFMPEG please refer

Approximating the area of a chirp by fitting a polynomial

Alexandre de Siqueira ● November 15, 2015●8 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...

GPS - some terminology!

Vivek Sankaravadivel ● October 30, 2015●3 comments

Hi!

For my first post, I will share some information about GPS - Global Positioning System. I will delve one step deeper than a basic explanation of how a GPS system works and introduce some terminology.

GPS, like we all know is the system useful for identifying one's position, velocity, & time using signals from satellites (referred to as SV or space vehicle in literature). It uses the principle of trilateration  (not triangulation which is misused frequently) for...

The Most Interesting FIR Filter Equation in the World: Why FIR Filters Can Be Linear Phase

Rick Lyons ● August 18, 2015●16 comments

This blog discusses a little-known filter characteristic that enables real- and complex-coefficient tapped-delay line FIR filters to exhibit linear phase behavior. That is, this blog answers the question:

What is the constraint on real- and complex-valued FIR filters that guarantee linear phase behavior in the frequency domain?

I'll declare two things to convince you to continue reading.

Declaration# 1: "That the coefficients must be symmetrical" is not a correct

Exponential Smoothing with a Wrinkle

Cedron Dawg ● December 17, 2015
Introduction

This is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by providing a set of preprocessing filters to improve the resolution of the DFT. Because of the exponential nature of sinusoidal functions, they have special mathematical properties when exponential smoothing is applied to them. These properties are derived and explained in this blog article.

Basic Exponential Smoothing

Exponential smoothing is also known as...

Coefficients of Cascaded Discrete-Time Systems

Neil Robertson ● March 4, 2018

In this article, we’ll show how to compute the coefficients that result when you cascade discrete-time systems.  With the coefficients in hand, it’s then easy to compute the time or frequency response.  The computation presented here can also be used to find coefficients of mixed discrete-time and continuous-time systems, by using a discrete time model of the continuous-time portion [1].

This article is available in PDF format for...

Generating Partially Correlated Random Variables

Harry Commin ● March 23, 2019●10 comments
IntroductionIt is often useful to be able to generate two or more signals with specific cross-correlations. Or, more generally, we would like to specify an $\left(N \times N\right)$ covariance matrix, $\mathbf{R}_{xx}$, and generate $N$ signals which will produce this covariance matrix.

There are many applications in which this technique is useful. I discovered a version of this method while analysing radar systems, but the same approach can be used in a very wide range of...

A Two Bin Solution

Cedron Dawg ● July 12, 2019
Introduction

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by showing an implementation of how the parameters of a real pure tone can be calculated from just two DFT bin values. The equations from previous articles are used in tandem to first calculate the frequency, and then calculate the amplitude and phase of the tone. The approach works best when the tone is between the two DFT bins in terms of frequency.

The Coding...

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

Cedron Dawg ● 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]. ...

Exact Near Instantaneous Frequency Formulas Best at Zero Crossings

Cedron Dawg ● July 20, 2017
Introduction

This is an article that is the last of my digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). It is along the lines of the last two.

In those articles, I presented exact formulas for calculating the frequency of a pure tone signal as instantaneously as possible in the time domain. Although the formulas work for both real and complex signals (something that does not happen with frequency domain formulas), for real signals they...

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

Cedron Dawg ● October 4, 2017●9 comments
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...

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

Cedron Dawg ● March 20, 2017●9 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...

DFT Bin Value Formulas for Pure Complex Tones

Cedron Dawg ● 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...

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

Cedron Dawg ● 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...