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...
Simulink-Simulation of SSB demodulation
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...
Polynomial calculations on an FIR filter engine, part 1
Polynomial evaluation is structurally akin to FIR filtering and fits dedicated filtering engines quite well, with certain caveats. It’s a technique that has wide applicability. This two-part note discusses transducer and amplifier non-linearity...
Make Hardware Great Again
By now you're aware of the collective angst in the US about 5G. Why is the US not a leader in 5G ? Could that also happen -- indeed, is it happening -- in AI ? If we lead in other areas, why not 5G ? What makes it so hard ? This...
Plotting Discrete-Time Signals
A discrete-time sinusoid can have frequency up to just shy of half the sample frequency. But if you try to plot the sinusoid, the result is not always recognizable. For example, if you plot a 9 Hz sinusoid sampled at 100 Hz, you get the result shown in the top of Figure 1, which looks like a sine. But if you plot a 35 Hz sinusoid sampled at 100 Hz, you get the bottom graph, which does not look like a sine when you connect the dots. We typically want the plot of a sampled sinusoid to resemble its continuous-time version. To achieve this, we need to interpolate.
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...
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...
Adventures in Signal Processing with Python
Author’s note: This article was originally called Adventures in Signal Processing with Python (MATLAB? We don’t need no stinkin' MATLAB!) — the allusion to The Treasure of the Sierra Madre has been removed, in deference to being...
Off-Topic: A Fluidic Model of the Universe
Introduction This article is a followup to my previous article "Off Topic: Refraction in a Varying Medium"[1]. Many of the concepts should be quite familiar and of interest to the readership of this site. In the "Speculations" section of my...
Add a Power Marker to a Power Spectral Density (PSD) Plot
Perhaps we should call most Power Spectral Density (PSD) calculations relative PSD, because usually we don’t have to worry about absolute power levels. However, for cases (e.g., measurements or simulations) where we are concerned with...
Compute Images/Aliases of CIC Interpolators/Decimators
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...
