Setting the 3-dB Cutoff Frequency of an Exponential Averager
This blog discusses two ways to determine an exponential averager's weighting factor so that the averager has a given 3-dB cutoff frequency. Here we assume the reader is familiar with exponential averaging lowpass filters, also called a "leaky integrators", to reduce noise fluctuations that contaminate constant-amplitude signal measurements. Exponential averagers are useful because they allow us to implement lowpass filtering at a low computational workload per output sample.
Figure 1 shows...
'z' as in 'Zorro': Frequency Masking FIR
An efficient way to implement FIR filters. Matlab / Octave example included. Keywords: Frequency masking FIR filter implementation
IntroductionAn "upsampled" FIR filter uses multiple-sample delays between the taps, compared to the unity delays in a conventional FIR filter. The resulting frequency response has steeper edges, but contains periodic images along the frequency axis (Fig. 1). Due to the latter, it is typically not too useful on its own.
Figure 1: Conventional and 'upsampled'...Do you like the new Comments System?
I have just finished implementing a new comments system for the blogs. Do you like it?
Please share your thoughts with me by adding a comment.
I'll wait a few days and make sure it works properly and then I'll port it to the code snippets and papers section.
Thanks!
FIR sideways (interpolator polyphase decomposition)
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
IntroductionAn 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
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
Digital-to-analog conversion connects digital...
Understanding the 'Phasing Method' of Single Sideband Demodulation
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'...
Frequency-Domain Periodicity and the Discrete Fourier Transform
Introduction
Some of the better understood aspects of time-sampled systems are the limitations and requirements imposed by the Nyquist sampling theorem [1]. Somewhat less understood is the periodic nature of the spectra of sampled signals. This article provides some insights into sampling that not only explain the periodic nature of the sampled spectrum, but aliasing, bandlimited sampling, and the so-called "super-Nyquist" or IF sampling. The approaches taken here include both mathematical...
Time-Domain Periodicity and the Discrete Fourier Transform
Introduction
The Discrete Fourier Transform (DFT) and it's fast-algorithm implementation, the Fast Fourier Transform (FFT), are fundamental tools for processing and analysis of digital signals. While the continuous Fourier Transform and its inverse integrate over all time from minus infinity to plus infinity, and all frequencies from minus infinity to plus infinity, practical application of its discrete cousins can only be made over finite time and frequency intervals. The discrete nature...
Python scipy.signal IIR Filter Design Cont.
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 FilterThe following is a highpass filter design for the different filter...
TCP/IP interface (Matlab/Octave)
Communicate with measurement instruments via Ethernet (no-toolbox-Matlab or Octave)
PurposeMeasurement automation is digital signal processing in a wider sense: Getting a digital signal from an analog world usually involves some measurement instruments, for example a spectrum analyzer. Modern instruments, and also many off-the-shelf prototyping boards such as FPGA cards [1] or microcontrollers [2] are able to communicate via Ethernet. Here, I provide some basic mex-functions (compiled C...
Overview of my Articles
Introduction
This article is a summary of all the articles I've written here at DspRelated. The main focus has always been an increased understanding of the Discrete Fourier Transform (DFT). The references are grouped by topic and ordered in a reasonable reading order. All the articles are meant to teach math, or give examples of math, in context within a specific application. Many of the articles also have sample programs which demonstrate the equations derived in the articles. My...
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...
There's No End to It -- Matlab Code Plots Frequency Response above the Unit Circle
Reference [1] has some 3D plots of frequency response magnitude above the unit circle in the Z-plane. I liked them enough that I wrote a Matlab function to plot the response of any digital filter this way. I’m not sure how useful these plots are, but they’re fun to look at. The Matlab code is listed in the Appendix.
This post is available in PDF format for easy...
Two Easy Ways To Test Multistage CIC Decimation Filters
This blog presents two very easy ways to test the performance of multistage cascaded integrator-comb (CIC) decimation filters [1]. Anyone implementing CIC filters should take note of the following proposed CIC filter test methods.
Introduction
Figure 1 presents a multistage decimate by D CIC filter where the number of stages is S = 3. The '↓D' operation represents downsampling by integer D (discard all but every Dth sample), n is the input time index, and m is the output time index.
Implementing a full-duplex UART using the TMS320VC33 serial port
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...
Design Square-Root Nyquist Filters
In his book on multirate signal processing, harris presents a nifty technique for designing square-root Nyquist FIR filters with good stopband attenuation [1]. In this post, I describe the method and provide a Matlab function for designing the filters. You can find a Matlab function by harris for designing the filters at [2].
BackgroundSingle-carrier modulation, such as QAM, uses filters to limit the bandwidth of the signal. Figure 1 shows a simplified QAM system block...
Orfanidis Textbooks are Available Online
I have just learned that Sophocles J. Orfanidis, the well-known professor with the ECE Department of Rutgers University, has made two of his signal processing textbooks available for downloading on the Internet. The first textbook is: "Introduction to Signal Processing" available at: http://eceweb1.rutgers.edu/~orfanidi/intro2sp/
Happily, also available at the above web site are:
- Errata for the textbook.
- Homework Solutions Manual
- Errata for Solutions...
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...
Discrete Wavelet Transform Filter Bank Implementation (part 1)
UPDATE: Added graphs and code to explain the frequency division of the branches
The focus of this article is to briefly explain an implementation of this transform and several filter bank forms. Theoretical information about DWT can be found elsewhere.
First of all, a 'quick and dirty' simplified explanation of the differences between DFT and DWT:
The DWT (Discrete Wavelet Transform), simply put, is an operation that receives a signal as an input (a vector of data) and...
Analytic Signal
In communication theory and modulation theory we always deal with two phases: In-phase (I) and Quadrature-phase (Q). The question that I will discuss in this blog is that why we use two phases and not more.
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 absolute power, it would be nice to be able to display it on a PSD plot. Unfortunately, you can’t read the power directly from the plot. For example, the plotted spectral peak of a narrowband signal, such as a sinewave, is lower than the...
Multi-Decimation Stage Filtering for Sigma Delta ADCs: 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 automate the process of designing the multi-stage decimation filter(s). The toolbox is published as an open-source at the MathWorks web-site. My dissertation is open for public online as well. The toolbox has a wide set of examples to guide the user...
Constrained Integer Behavior
The wheels go round and round, round and round ...Integer arithmetic is ubiquitous in digital hardware implementations, it's prolific in the control and data-paths. When using fixed width (constrained) integers, overflow and underflow is business as usual.
Building with IntegersThe subtitle of this post mentions a wheel - before I get to the wheel I want to look at an example. The recursive-windowed-averager (rwa, a.k.a moving average)...
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...
DSPRelated and EmbeddedRelated now on Facebook & I will be at EE Live!
I have two news to share with you today.
The first one is that I finally created Facebook pages for DSPRelated.com and EmbeddedRelated (DSPRelated page - EmbeddedRelated page). For a long time I didn't feel that this was something that was needed, but it seems that these days more and more people are using their Facebook account to stay updated with their favorite websites. In any event, if you have a Facebook account, I would greatly appreciate if you could use the next 5 seconds to "like"...
Stereophonic Amplitude-Panning: A Derivation of the 'Tangent Law'
In a recent Forum post here on dsprelated.com the audio signal processing subject of stereophonic amplitude-panning was discussed. And in that Forum thread the so-called "Tangent Law", the fundamental principle of stereophonic amplitude-panning, was discussed. However, none of the Forum thread participants had ever seen a derivation of the Tangent Law. This blog presents such a derivation and if this topic interests you, then please read on.
The notion of stereophonic amplitude-panning is...
Simultaneously Computing a Forward FFT and an Inverse FFT Using a Single FFT
Most of us are familiar with the processes of using a single N-point complex FFT to: (1) perform a 2N-point FFT on real data, and (2) perform two independent N-point FFTs on real data [1–5]. In case it's of interest to someone out there, this blog gives the algorithm for simultaneously computing a forward FFT and an inverse FFT using a single radix-2 FFT.
Our algorithm is depicted by the seven steps, S1 through S7, shown in Figure 1. In that figure, we compute the x(n) inverse FFT of...
How the Cooley-Tukey FFT Algorithm Works | Part 3 - The Inner Butterfly
At the heart of the Cooley-Tukey FFT algorithm lies a butterfly, a simple yet powerful image that captures the recursive nature of how the FFT works. In this article we discover the butterfly’s role in transforming complex signals into their frequency components with efficiency and elegance. Starting with the 2-point DFT, we reveal how the FFT reuses repeated calculations to save time and resources. Using a divide-and-conquer approach, the algorithm breaks signals into smaller groups, processes them through interleaving butterfly diagrams, and reassembles the results step by step.
Simple Discrete-Time Modeling of Lossy LC Filters
There are many software applications that allow modeling LC filters in the frequency domain. But sometimes it is useful to have a time domain model, such as when you need to analyze a mixed analog and DSP system. For example, the system in Figure 1 includes an LC filter as well as a DSP portion. The LC filter could be an anti-alias filter, a channel filter, or some other LC network. For a design using undersampling, the filter would be bandpass [1]. By modeling...
'z' as in 'Zorro': Frequency Masking FIR
An efficient way to implement FIR filters. Matlab / Octave example included. Keywords: Frequency masking FIR filter implementation
IntroductionAn "upsampled" FIR filter uses multiple-sample delays between the taps, compared to the unity delays in a conventional FIR filter. The resulting frequency response has steeper edges, but contains periodic images along the frequency axis (Fig. 1). Due to the latter, it is typically not too useful on its own.
Figure 1: Conventional and 'upsampled'...
