Understanding and Preventing Overflow (I Had Too Much to Add Last Night)
Happy Thanksgiving! Maybe the memory of eating too much turkey is fresh in your mind. If so, this would be a good time to talk about overflow. In the world of floating-point arithmetic, overflow is possible but not particularly common. You can...
Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine
Today’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...
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.Fig.1 Passive low-pass filter...
Multi-Decimation Stage Filtering: Design and Optimization
During my research on digital FIR decimation filters I have been developing various Matlab scripts and functions. In which I have decided later on to consolidate it in a form of a toolbox. I have developed this toolbox to assist and...
Learn About Transmission Lines Using a Discrete-Time Model
We don’t often think about signal transmission lines, but we use them every day. Familiar examples are coaxial cable, Ethernet cable, and Universal Serial Bus (USB). Like it or not, high-speed clock and signal traces on...
Signed serial-/parallel multiplication
Keywords: Binary signed multiplication implementation, RTL, Verilog, algorithm Summary A detailed discussion of bit-level trickstery in signed-signed multiplication Algorithm based on Wikipedia example Includes a Verilog implementation with...
Harmonic Notch Filter
My basement is covered with power lines and florescent lights which makes collecting ECG and EEG data rather difficult due to the 60 cycle hum. I found the following notch filter to work very well at eliminating the background signal...
Feedback Controllers - Making Hardware with Firmware. Part 10. DSP/FPGAs Behaving Irrationally
This article will look at a design approach for feedback controllers featuring low-latency "irrational" characteristics to enable the creation of physical components such as transmission lines. Some thought will also be given as to...
A Brief Introduction To Romberg Integration
This article briefly describes a remarkable integration algorithm, called "Romberg integration." The algorithm is used in the field of numerical analysis but it's not so well-known in the world of DSP.
Four Ways to Compute an Inverse FFT Using the Forward FFT Algorithm
If you need to compute inverse fast Fourier transforms (inverse FFTs) but you only have forward FFT software (or forward FFT FPGA cores) available to you, below are four ways to solve your problem. Preliminaries To define what we're...
Handy Online Simulation Tool Models Aliasing With Lowpass and Bandpass Sampling
Analog Devices Inc. has posted a neat software simulation tool on their corporate web site that graphically shows the aliasing effects of both lowpass and bandpass periodic sampling. This is a nice tutorial tool for beginners in DSP. The...
Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter
Other articles in this series: Part 1: Russian Peasant Multiplication Part 2: The Single-Pole Low-Pass Filter Part 3: Welford’s Method (And Friends) Part 4: Topological Sort I’m writing this article in a room with a bunch of...
Understanding and Implementing the Sliding DFT
Introduction In many applications the detection or processing of signals in the frequency domain offers an advantage over performing the same task in the time-domain. Sometimes the advantage is just a simpler or more conceptually...
Why Time-Domain Zero Stuffing Produces Multiple Frequency-Domain Spectral Images
This blog explains why, in the process of time-domain interpolation (sample rate increase), zero stuffing a time sequence with zero-valued samples produces an increased-length time sequence whose spectrum contains replications of the original...
The Exponential Nature of the Complex Unit Circle
Introduction This is an article to hopefully give an understanding to Euler's magnificent equation: $$ e^{i\theta} = cos( \theta ) + i \cdot sin( \theta ) $$ This equation is usually proved using the Taylor series expansion for the given...
The Number 9, Not So Magic After All
This blog is not about signal processing. Rather, it discusses an interesting topic in number theory, the magic of the number 9. As such, this blog is for people who are charmed by the behavior and properties of numbers. For decades I've thought...
Signed serial-/parallel multiplication
Keywords: Binary signed multiplication implementation, RTL, Verilog, algorithm Summary A detailed discussion of bit-level trickstery in signed-signed multiplication Algorithm based on Wikipedia example Includes a Verilog implementation with...
Understanding and Preventing Overflow (I Had Too Much to Add Last Night)
Happy Thanksgiving! Maybe the memory of eating too much turkey is fresh in your mind. If so, this would be a good time to talk about overflow. In the world of floating-point arithmetic, overflow is possible but not particularly common. You can...
Return of the Delta-Sigma Modulators, Part 1: Modulation
About a decade ago, I wrote two articles: Modulation Alternatives for the Software Engineer (November 2011) Isolated Sigma-Delta Modulators, Rah Rah Rah! (April 2013) Each of these are about delta-sigma modulation, but they’re...
Filtering Noise: The Basics (Part 1)
IntroductionFinding signals in the presence of noise is one of the fundamental quests of the discipline of signal processing. Noise is inherently random by nature, so a probability oriented approach is needed to develop a mathematical framework...
ADC Clock Jitter Model, Part 2 – Random Jitter
In Part 1, I presented a Matlab function to model an ADC with jitter on the sample clock, and applied it to examples with deterministic jitter. Now we’ll investigate an ADC with random clock jitter, by using a filtered or unfiltered...
A Two Bin Exact Frequency Formula for a Pure Complex Tone in a DFT
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...
Some Thoughts on Sampling
Some 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...
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...
Signed serial-/parallel multiplication
Keywords: Binary signed multiplication implementation, RTL, Verilog, algorithm Summary A detailed discussion of bit-level trickstery in signed-signed multiplication Algorithm based on Wikipedia example Includes a Verilog implementation with...
DAC Zero-Order Hold Models
This article provides two simple time-domain models of a DAC’s zero-order hold. These models will allow us to find time and frequency domain approximations of DAC outputs, and simulate analog filtering of those outputs. Developing the models is also a good way to learn about the DAC ZOH function.
Evaluate Window Functions for the Discrete Fourier Transform
The Discrete Fourier Transform (DFT) operates on a finite length time sequence to compute its spectrum. For a continuous signal like a sinewave, you need to capture a segment of the signal in order to perform the DFT. Usually, you...
