## Microprocessor Family Tree

Below is a little microprocessor history. Perhaps some of the ol' timers here will recognize a few of these integrated circuits. I have a special place in my heart for the Intel 8080 chip.

Image copied, without permission, from the now defunct Creative Computing magazine, Vol. 11, No. 6, June 1985.

## A Markov View of the Phase Vocoder Part 2

IntroductionLast post we motivated the idea of viewing the classic phase vocoder as a Markov process. This was due to the fact that the input signal’s features are unknown to the computer, and the phase advancement for the next synthesis frame is entirely dependent on the phase advancement of the current frame. We will dive a bit deeper into this idea, and flesh out some details which we left untouched last week. This includes the effect our discrete Fourier transform has on the...

## A Markov View of the Phase Vocoder Part 1

IntroductionHello! This is my first post on dsprelated.com. I have a blog that I run on my website, http://www.christianyostdsp.com. In order to engage with the larger DSP community, I'd like to occasionally post my more engineering heavy writing here and get your thoughts.

Today we will look at the phase vocoder from a different angle by bringing some probability into the discussion. This is the first part in a short series. Future posts will expand further upon the ideas...

## 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 also need to apply a window function to the captured signal before taking the DFT [1 - 3]. There are many different window functions and each produces a different approximation of the spectrum. In this post, we’ll present Matlab code that...

## 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 the capabilities of the currently utilized Intel Cyclone V, the new Cyclone 10 GX and the upcoming Xilinx Versal floating-point FPGAs/ACAPs.

Fig 1. Making a Transmission Line, with the Circuit Emulator

Additional...

## Polar Coding Notes: A Simple Proof

For any B-DMC $W$, the channels $\{W_N^{(i)}\}$ polarize in the sense that, for any fixed $\delta \in (0, 1)$, as $N$ goes to infinity through powers of two, the fraction of indices $i \in \{1, \dots, N\}$ for which $I(W_N^{(i)}) \in (1 − \delta, 1]$ goes to $I(W)$ and the fraction for which $I(W_N^{(i)}) \in [0, \delta)$ goes to $1−I(W)^{[1]}$.

Mrs. Gerber’s Lemma

Mrs. Gerber’s Lemma provides a lower bound on the entropy of the modulo-$2$ sum of two binary random...

## Polar Coding Notes: Channel Combining and Channel Splitting

Channel Combining

Channel combining is a step that combines copies of a given B-DMC $W$ in a recursive manner to produce a vector channel $W_N : {\cal X}^N \to {\cal Y}^N$, where $N$ can be any power of two, $N=2^n, n\le0^{[1]}$.

The notation $u_1^N$ as shorthand for denoting a row vector $(u_1, \dots , u_N)$.

The vector channel $W_N$ is the virtual channel between the input sequence $u_1^N$ to a linear encoder and the output sequence $y^N_1$ of $N$...

## 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 posts. However this post serves as a guide to anyone who wishes to learn about the project or carry it forward. Hence I will go over the project details again.

Project overviewThe project “Digital Filter Blocks in MyHDL and PyFDA integration" aims...

## Sensors Expo - Trip Report & My Best Video Yet!

This was my first time at Sensors Expo and my second time in Silicon Valley and I must say I had a great time.

Before I share with you what I find to be, by far, my best 'highlights' video yet for a conference/trade show, let me try to entertain you with a few anecdotes from this trip. If you are not interested by my stories or maybe don't have the extra minutes needed to read them, please feel free to skip to the end of this blog post to watch the...

## Design a DAC sinx/x Corrector

This post provides a Matlab function that designs linear-phase FIR sinx/x correctors. It includes a table of fixed-point sinx/x corrector coefficients for different DAC frequency ranges.

A sinx/x corrector is a digital (or analog) filter used to compensate for the sinx/x roll-off inherent in the digital to analog conversion process. In DSP math, we treat the digital signal applied to the DAC is a sequence of impulses. These are converted by the DAC into contiguous pulses...

## Goertzel Algorithm for a Non-integer Frequency Index

If you've read about the Goertzel algorithm, you know it's typically presented as an efficient way to compute an individual kth bin result of an N-point discrete Fourier transform (DFT). The integer-valued frequency index k is in the range of zero to N-1 and the standard block diagram for the Goertzel algorithm is shown in Figure 1. For example, if you want to efficiently compute just the 17th DFT bin result (output sample X17) of a 64-point DFT you set integer frequency index k = 17 and N =...

## Phase and Amplitude Calculation for a Pure Real Tone in a DFT: Method 1

IntroductionThis is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving exact formulas for the phase and amplitude of a non-integer frequency real tone in a DFT. The linearity of the Fourier Transform is exploited to reframe the problem as the equivalent of finding a set of coordinates in a specific vector space. The found coordinates are then used to calculate the phase and amplitude of the pure real tone in the DFT. This article...

## Part 11. Using -ve Latency DSP to Cancel Unwanted Delays in Sampled-Data Filters/Controllers

This final article in the series will look at -ve latency DSP and how it can be used to cancel the unwanted delays in sampled-data systems due to such factors as Nyquist filtering, ADC acquisition, DSP/FPGA algorithm computation time, DAC reconstruction and circuit propagation delays.Some applications demand zero-latency or zero unwanted latency signal processing. Negative latency DSP may sound like the stuff of science fiction or broken physics but the arrangement as...

## Time Machine, Anyone?

Abstract: Dispersive linear systems with negative group delay have caused much confusion in the past. Some claim that they violate causality, others that they are the cause of superluminal tunneling. Can we really receive messages before they are sent? This article aims at pouring oil in the fire and causing yet more confusion :-).

IntroductionIn this article we reproduce the results of a physical experiment...

## Spectral Flipping Around Signal Center Frequency

Most of us are familiar with the process of flipping the spectrum (spectral inversion) of a real signal by multiplying that signal's time samples by (-1)n. In that process the center of spectral rotation is fs/4, where fs is the signal's sample rate in Hz. In this blog we discuss a different kind of spectral flipping process.

Consider the situation where we need to flip the X(f) spectrum in Figure 1(a) to obtain the desired Y(f) spectrum shown in Figure 1(b). Notice that the center of...

## A poor man's Simulink

Glue between Octave and NGSPICE for discrete- and continuous time cosimulation (download) Keywords: Octave, SPICE, Simulink

IntroductionMany DSP problems have close ties with the analog world. For example, a switched-mode audio power amplifier uses a digital control loop to open and close power transistors driving an analog filter. There are commercial tools for digital-analog cosimulation: Simulink comes to mind, and mainstream EDA vendors support VHDL-AMS or Verilog-A in their...

## Noise shaping

eywords: Quantization noise; noise shaping

A brief introduction to noise shaping, with firm resolve not to miss the forest for the trees. We may still stumble over some assorted roots. Matlab example code is included.

QuantizationFig. 1 shows a digital signal that is reduced to a lower bit width, for example a 16 bit signal being sent to a 12 bit digital-to-analog converter. Rounding to the nearest output value is obviously the best that can be done to minimize the error of each...

## How the Cooley-Tukey FFT Algorithm Works | Part 1 - Repeating Calculations

The Fourier Transform is a powerful tool, used in many technologies, from audio processing to wireless communication. However, calculating the FT can be computationally expensive. The Cooley-Tukey Fast Fourier Transform (FFT) algorithm provides a significant speedup. It exploits the repetitive nature of calculations within the Discrete Fourier Transform (DFT), the mathematical foundation of the FT. By recognizing patterns in the DFT calculations and reusing intermediate results, the FFT vastly reduces the number of operations required. In this series of articles, we will look at how the Cooley-Tukey FFT algorithm works.

## The Most Interesting FIR Filter Equation in the World: Why FIR Filters Can Be Linear Phase

This blog discusses a little-known filter characteristic that enables real- and complex-coefficient tapped-delay line FIR filters to exhibit linear phase behavior. That is, this blog answers the question:

What is the constraint on real- and complex-valued FIR filters that guarantee linear phase behavior in the frequency domain?I'll declare two things to convince you to continue reading.

Declaration# 1: "That the coefficients must be symmetrical" is not a correct

## 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...

## A New Related Site!

We are delighted to announce the launch of the very first new Related site in 15 years! The new site will be dedicated to the trendy and quickly growing field of Machine Learning and will be called - drum roll please - MLRelated.com.

We think MLRelated fits perfectly well within the “Related” family, with:

- the fast growth of TinyML, which is a topic of great interest to the EmbeddedRelated community
- the use of Machine/Deep Learning in Signal Processing applications, which is of...

## 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 time sequence's spectrum.

Background

The traditional way to interpolate (sample rate increase) an x(n) time domain sequence is shown in Figure 1.

Figure 1

The '↑ L' operation in Figure 1 means 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...

## Recruiting New Bloggers!

Previous calls for bloggers have been very successful in recruiting some great communicators - Rick Lyons, Jason Sachs, Victor Yurkovsky, Mike Silva, Markus Nentwig, Gene Breniman, Stephen Friederichs,

## An Astounding Digital Filter Design Application

I've recently encountered a digital filter design application that astonished me with its design flexibility, capability, and ease of use. The software is called the "ASN Filter Designer." After experimenting with a demo version of this filter design software I was so impressed that I simply had publicize it to the subscribers here on dsprelated.com.

What I Liked About the ASN Filter DesignerWith typical filter design software packages the user enters numerical values for the...

## 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 analog-to-digital converter (ADC) available, you can sync to the external clock using the scheme shown in Figure 2. This time-domain PLL model is similar to the one presented in Part 1 of this series on digital PLL’s [1]. In that PLL, we...

## 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...

## Dealing With Fixed Point Fractions

Fixed point fractional representation always gives me a headache because I screw it up the first time I try to implement an algorithm. The difference between integer operations and fractional operations is in the overflow. If the representation fits in the fixed point result, you can not tell the difference between fixed point integer and fixed point fractions. When integers overflow, they lose data off the most significant bits. When fractions overflow, they lose data off...

## The DSP Online Conference - Right Around the Corner!

It is Sunday night as I write this blog post with a few days to go before the virtual doors of the very first DSP Online Conference open..

It all started with a post in the DSPRelated forum about three months ago. We had just had a blast running the 2020 Embedded Online Conference and we thought it could be fun to organize a smaller event dedicated to the DSP community. So my goal with the post in the forum was to see if...

## Spline interpolation

A cookbook recipe for segmented y=f(x) 3rd-order polynomial interpolation based on arbitrary input data. Includes Octave/Matlab design script and Verilog implementation example. Keywords: Spline, interpolation, function modeling, fixed point approximation, data fitting, Matlab, RTL, Verilog

IntroductionSplines describe a smooth function with a small number of parameters. They are well-known for example from vector drawing programs, or to define a "natural" movement path through given...