Frequency Dependence in Free Space Propagation
Introduction
It 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 effects will be less than they would be at higher frequencies. As evidence of this, the Friis Transmission Equation[i] is often cited, the general form of which is usually written as:
Pr = Pt Gt Gr ( λ / 4πd )2 (1)
where the...
Pulse Shaping in Single-Carrier Communication Systems
Some 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 shaping", etc. Some of the confusion comes from the use of terms like "matched filter" which has a broader meaning in the more general field of signal processing or detection theory. Likewise "Raised Cosine" has a different meaning or application in this...
Correlation without pre-whitening is often misleading
White Lies
Correlation, as one of the first tools DSP users add to their tool box, can automate locating a known signal within a second (usually larger) signal. The expected result of a correlation is a nice sharp peak at the location of the known signal and few, if any, extraneous peaks.
A little thought will show this to be incorrect: correlating a signal with itself is only guaranteed to give a sharp peak if the signal's samples are uncorrelated --- for example if the signal is composed...
Of Forests and Trees and DSP
When Stephane invited me to write a blog for dsprelated.com I immediately came up with a flood of ideas for highly detailed, technical, narrowly focused articles related to the intersection of DSP and control systems.
Then the USENET groups that I frequent received a spate of posts from people that were either asking about how to implement highly detailed, narrowly focused algorithms in ways that were either fundamental misapplications or were flawed because they were having problems...
Instantaneous Frequency Measurement
I would like to talk about the oft used method of measuring the carrier frequency in the world of Signal Collection and Characterization world. It is an elegant technique because of its simplicity. But, of course, with simplicity, there come drawbacks (sometimes...especially with this one!).
In the world of Radar detection and characterization, one of the key characteristics of interest is the carrier frequency of the signal. If the radar is pulsed, you will have a very wide bandwidth, a...
Resolving 'Can't initialize target CPU' on TI C6000 DSPs - Part 2
Configuration
The previous article discussed CCS configuration. The prerequisite for the following discussion is a valid CCS configuration file. All references will be for CCS 3.3, but they may be used or adapted to other versions of CCS. From the previous discussion, we know that the configuration file is located at 'C:\CCStudio_v3.3\cc\bin\brddat\ccBrd0.dat'.
XDS510 Emulators
Initial discussion will address only XDS510 class emulators that support TI drivers and utilities. This will...
A brief look at multipath radio channels
Summary: Discussion of multipath propagation and fading in radio links
Radio channels, their effects on communications links and how to model them are a popular topic on comp.dsp. Unfortunately, for many of us there is little or no opportunity to get any "hands-on" experience with radio-related issues, because the required RF measurement equipment is not that easily available.This article gives a very simple example of a radio link that shows multipath propagation and...
Resolving 'Can't initialize target CPU' on TI C6000 DSPs - Part 1
Introduction
Today I am going to discuss some of the basics that can help prevent errors that frustrate some users. The information is directed toward TI C6000 family DSPs, but much of it also applies to other TI DSPs. In many cases they represent the user's first involvement with using Code Composer Studio [CCS] and a target board. It has been my experience that the primary cause of the "Can't initialize target CPU" error message and similar messages like "Error connecting to...
Modelling a Noisy Communication Signal in MATLAB for the Analog to Digital Conversion Process
A critical thing to realize while modeling the signal that is going to be digitally processed is the SNR. In a receiver, the noise floor (hence the noise variance and hence its power) are determined by the temperature and the Bandwidth. For a system with a constant bandwidth, relatively constant temperature, the noise power remains relatively constant as well. This implies that the noise variance is a constant.
In MATLAB, the easiest way to create a noisy signal is by using...
Delay estimation by FFT
Given x=sig(t) and y=ref(t), returns [c, ref(t+delta), delta)] = fitSignal(y, x);:Estimates and corrects delay and scaling factor between two signals Code snippetThis article relates to the Matlab / Octave code snippet: Delay estimation with subsample resolution It explains the algorithm and the design decisions behind it.
IntroductionThere are many DSP-related problems, where an unknown timing between two signals needs to be determined and corrected, for example, radar, sonar,...
Implementing Impractical Digital Filters
This blog discusses a problematic situation that can arise when we try to implement certain digital filters. Occasionally in the literature of DSP we encounter impractical digital IIR filter block diagrams, and by impractical I mean block diagrams that cannot be implemented. This blog gives examples of impractical digital IIR filters and what can be done to make them practical.
Implementing an Impractical Filter: Example 1
Reference [1] presented the digital IIR bandpass filter...
An Alternative Form of the Pure Real Tone DFT Bin Value Formula
Introduction
This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving alternative exact formulas for the bin values of a real tone in a DFT. The derivation of the source equations can be found in my earlier blog article titled "DFT Bin Value Formulas for Pure Real Tones"[1]. The new form is slighty more complicated and calculation intensive, but it is more computationally accurate in the vicinity of near integer frequencies. This...
Unit Testing for Embedded Algorithms
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...
[Book Review] Numpy 1.5 Beginner's Guide
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.
IntroductionThe 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...
Fibonacci trick
I'm working on a video, tying the Fibonacci sequence into the general subject of difference equations.
Here's a fun trick: take any two consecutive numbers in the Fibonacci sequence, say 34 and 55. Now negate one and use them as the seed for the Fibonacci sequence, larger magnitude first, i.e.
$-55, 34, \cdots$
Carry it out, and you'll eventually get the Fibonacci sequence, or it's negative:
$-55, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0, 1, 1 \cdots$
This is NOT a general property of difference...
Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 2)
IntroductionThis is an article that is a continuation of a digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). It is recommended that my previous article "Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 1)"[1] be read first as many sections of this article are directly dependent upon it.
A second family of formulas for calculating the frequency of a single pure tone in a short interval in the time domain is presented. It...
Knowledge Mine for Embedded Systems
I stumbled upon a great website (actually I found it on the google ads in gmail!) with comprehensive and deep information on embedded systems. The website talks about four main categories in embedded systems:
1) Embedded Systems Design.
2) Design Life cycle.
3) Design Methods.
4) Design Tools.
What I found special about this website is that when browse through the systems design section, you usually find a...
Matlab Programming Contest
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...
Maximum Likelihood Estimation
Any observation has some degree of noise content that makes our observations uncertain. When we try to make conclusions based on noisy observations, we have to separate the dynamics of a signal from noise.
Candan's Tweaks of Jacobsen's Frequency Approximation
IntroductionThis is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by explaining how a tweak to a well known frequency approximation formula makes it better, and another tweak makes it exact. The first tweak is shown to be the first of a pattern and a novel approximation formula is made from the second. It only requires a few extra calculations beyond the original approximation to come up with an approximation suitable for most...
Smaller DFTs from bigger DFTs
Introduction
Let's consider the following hypothetical situation: You have a sequence $x$ with $N/2$ points and a black box which can compute the DFT (Discrete Fourier Transform) of an $N$ point sequence. How will you use the black box to compute the $N/2$ point DFT of $x$? While the problem may appear to be a bit contrived, the answer(s) shed light on some basic yet insightful and useful properties of the DFT.
On a related note, the reverse problem of computing an $N$...
An Alternative Form of the Pure Real Tone DFT Bin Value Formula
IntroductionThis is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving alternative exact formulas for the bin values of a real tone in a DFT. The derivation of the source equations can be found in my earlier blog article titled "DFT Bin Value Formulas for Pure Real Tones"[1]. The new form is slighty more complicated and calculation intensive, but it is more computationally accurate in the vicinity of near integer frequencies. This...
Of Forests and Trees and DSP
When Stephane invited me to write a blog for dsprelated.com I immediately came up with a flood of ideas for highly detailed, technical, narrowly focused articles related to the intersection of DSP and control systems.
Then the USENET groups that I frequent received a spate of posts from people that were either asking about how to implement highly detailed, narrowly focused algorithms in ways that were either fundamental misapplications or were flawed because they were having problems...
Finding the Best Optimum
When I was in school learning electrical engineering I owned a large mental pot, full of simmering resentment against the curriculum as it was being taught.
It really started in my junior year, when we took Semiconductor Devices, or more accurately "how to build circuits using transistors". I had been seduced by the pure mathematics of sophomore EE courses, where all the circuit elements (resistors, capacitors, coils and -- oh the joy -- dependent sources) are ideally modeled, and the labs...
A Free DSP Laboratory
Getting Started In Audio DSP
Imagine you're starting out studying DSP and your particular interest is audio. Wouldn't it be nice to have access to some audio signals and the tools to analyze and modify them? In the old days, a laboratory like this would most likely have cost a lot of time and money to set up. Nowadays, it doesn't have to be like this. The magic of open source software makes it quite straightforward to build yourself a simple audio DSP laboratory – just use the brilliant...
Knowledge Mine for Embedded Systems
I stumbled upon a great website (actually I found it on the google ads in gmail!) with comprehensive and deep information on embedded systems. The website talks about four main categories in embedded systems:
1) Embedded Systems Design.
2) Design Life cycle.
3) Design Methods.
4) Design Tools.
What I found special about this website is that when browse through the systems design section, you usually find a...
New Video: Parametric Oscillations
I just posted this last night. It's kinda off-topic from the mission of the channel, but I realized that it had been months since I'd posted a video, and having an excuse to build on helped keep me on track.
Maximum Likelihood Estimation
Any observation has some degree of noise content that makes our observations uncertain. When we try to make conclusions based on noisy observations, we have to separate the dynamics of a signal from noise.
