The Discrete Fourier Transform and the Need for Window Functions
The Discrete Fourier Transform (DFT) is used to find the frequency spectrum of a discrete-time signal. A computationally efficient version called the Fast Fourier Transform (FFT) is normally used to calculate the DFT. But, as many...
Project Report : Digital Filter Blocks in MyHDL and their integration in pyFDA
The Google Summer of Code 2018 is now in its final stages, and I’d like to take a moment to look back at what goals were accomplished, what remains to be completed and what I have learnt. The project overview was discussed in the previous blog...
Modeling Anti-Alias Filters
Digitizing a signal using an Analog to Digital Converter (ADC) usually requires an anti-alias filter, as shown in Figure 1a. In this post, we’ll develop models of lowpass Butterworth and Chebyshev anti-alias filters, and compute the time...
Multiplierless Exponential Averaging
This blog discusses an interesting approach to exponential averaging. To begin my story, a traditional exponential averager (also called a "leaky integrator"), shown in Figure 1(a), is commonly used to reduce noise fluctuations that contaminate...
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...
The correct answer to the quiz of @apolin
The correct answer to the @apolin quiz can be easily explained using the following Simulink model: In MATLAB you have to initialize the two filters: h = dftmtx (8); h1 = h (3, :); % The filter of the quiz h2 = h (7, :); % The...
Setting Carrier to Noise Ratio in Simulations
When simulating digital receivers, we often want to check performance with added Gaussian noise. In this article, I’ll derive the simple equations for the rms noise level needed to produce a desired carrier to noise ratio (CNR or...
Bank-switched Farrow resampler
Bank-switched Farrow resampler Summary A modification of the Farrow structure with reduced computational complexity.Compared to a conventional design, the impulse response is broken into a higher number of segments. Interpolation accuracy is...
Digital PLL’s, Part 3 – Phase Lock an NCO to an External Clock
Sometimes you may need to phase-lock a numerically controlled oscillator (NCO) to an external clock that is not related to the system clocks of your ASIC or FPGA. This situation is shown in Figure 1. Assuming your system has an...
Update to a Narrow Bandpass Filter in Octave or Matlab
Following my earlier blog post (June 2020) featuring a Narrow Bandpass Filter, I’ve had some useful feedback and suggestions. This has inspired me to come up with an updated version, incorporating the following changes compared to the earlier...
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...
A Fast Real-Time Trapezoidal Rule Integrator
This article presents a computationally-efficient network for computing real?time discrete integration using the Trapezoidal Rule.
Third-Order Distortion of a Digitally-Modulated Signal
Analog designers are always harping about amplifier third-order distortion. Why? In this article, we'll look at why third-order distortion is important, and simulate a QAM signal with third order distortion.
A Narrow Bandpass Filter in Octave or Matlab
The design of a very narrow bandpass FIR filter, coded in either Octave or Matlab, can prove challenging if a computationally-efficient filter is required. This is especially true if the sampling rate is high relative to the filter's center...
IIR Bandpass Filters Using Cascaded Biquads
In an earlier post [1], we implemented lowpass IIR filters using a cascade of second-order IIR filters, or biquads. This post provides a Matlab function to do the same for Butterworth bandpass IIR filters. Compared to conventional implementations, bandpass filters based on biquads are less sensitive to coefficient quantization [2]. This becomes important when designing narrowband filters.
Second Order Discrete-Time System Demonstration
Discrete-time systems are remarkable: the time response can be computed from mere difference equations, and the coefficients ai, bi of these equations are also the coefficients of H(z). Here, I try to illustrate this remarkableness by converting a continuous-time second-order system to an approximately equivalent discrete-time system. With a discrete-time model, we can then easily compute the time response to any input. But note that the goal here is as much to understand the discrete-time model as it is to find the response.
A Beginner's Guide To Cascaded Integrator-Comb (CIC) Filters
This article discusses the behavior, mathematics, and implementation of cascaded integrator-comb filters.
The correct answer to the quiz of @apolin
The correct answer to the @apolin quiz can be easily explained using the following Simulink model: In MATLAB you have to initialize the two filters: h = dftmtx (8); h1 = h (3, :); % The filter of the quiz h2 = h (7, :); % The...
A Free DSP Laboratory
Getting Started In Audio DSPImagine 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...
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...
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...
A Differentiator With a Difference
Some time ago I was studying various digital differentiating networks, i.e., networks that approximate the process of taking the derivative of a discrete time-domain sequence. By "studying" I mean that I was experimenting with various...
Python scipy.signal IIR Filter Design
Introduction The following is an introduction on how to design an infinite impulse response (IIR) filters using the Python scipy.signal package. This post, mainly, covers how to use the scipy.signal package and is not a thorough...
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...
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...
A Recipe for a Basic Trigonometry Table
Introduction This is an article that is give a better understanding to the Discrete Fourier Transform (DFT) by showing how to build a Sine and Cosine table from scratch. Along the way a recursive method is developed as a tone generator for a...
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...
Update to a Narrow Bandpass Filter in Octave or Matlab
Following my earlier blog post (June 2020) featuring a Narrow Bandpass Filter, I’ve had some useful feedback and suggestions. This has inspired me to come up with an updated version, incorporating the following changes compared to the earlier...
An Efficient Full-Band Sliding DFT Spectrum Analyzer
In this blog I present two computationally efficient full-band discrete Fourier transform (DFT) networks that compute the 0th bin and all the positive-frequency bin outputs for an N-point DFT in real-time on a sample-by-sample basis. An Even-N...
Find Aliased ADC or DAC Harmonics (with animation)
When a sinewave is applied to a data converter (ADC or DAC), device nonlinearities produce harmonics. If a harmonic frequency is greater than the Nyquist frequency, the harmonic appears as an alias. In this case, it is not at once...
