A Direct Digital Synthesizer with Arbitrary Modulus

Neil Robertson June 3, 20195 comments

Suppose you have a system with a 10 MHz sample clock, and you want to generate a sampled sinewave at any frequency below 5 MHz on 500 kHz spacing; i.e., 0.5, 1.0, 1.5, … MHz.  In other words, f = k*fs/20, where k is an integer and fs is sample frequency.  This article shows how to do this using a simple Direct Digital Synthesizer (DDS) with a look-up table that is at most 20 entries long.   We’ll also demonstrate a Quadrature-output DDS.  A note on...


Somewhat Off Topic: Deciphering Transistor Terminology

Rick Lyons May 28, 20194 comments

I recently learned something mildly interesting about transistors, so I thought I'd share my new knowledge with you folks. Figure 1 shows a p-n-p transistor comprising a small block of n-type semiconductor sandwiched between two blocks of p-type semiconductor.

The terminology of "emitter" and "collector" seems appropriate, but did you ever wonder why the semiconductor block in the center is called the "base"? The word base seems inappropriate because the definition of the word base is:...


Reducing IIR Filter Computational Workload

Rick Lyons May 24, 20195 comments

This blog describes a straightforward method to significantly reduce the number of necessary multiplies per input sample of traditional IIR lowpass and highpass digital filters.

Reducing IIR Filter Computations Using Dual-Path Allpass Filters

We can improve the computational speed of a lowpass or highpass IIR filter by converting that filter into a dual-path filter consisting of allpass filters as shown in Figure 1.

...

A Lesson In Engineering Humility

Rick Lyons May 20, 20199 comments

Let's assume you were given the task to design and build the 12-channel telephone transmission system shown in Figure 1.

Figure 1

At a rate of 8000 samples/second, each telephone's audio signal is sampled and converted to a 7-bit binary sequence of pulses. The analog signals at Figure 1's nodes A, B, and C are presented in Figure 2.

Figure 2

I'm convinced that some of you subscribers to this dsprelated.com web site could accomplish such a design & build task....

IIR Bandpass Filters Using Cascaded Biquads

Neil Robertson April 20, 201911 comments

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.

A biquad section block diagram using the Direct Form II structure [3,4] is...


Controlling a DSP Network's Gain: A Note For DSP Beginners

Rick Lyons March 29, 201922 comments

This blog briefly discusses a topic well-known to experienced DSP practitioners but may not be so well-known to DSP beginners. The topic is the proper way to control a digital network's gain. Digital Network Gain Control Figure 1 shows a collection of networks I've seen, in the literature of DSP, where strict gain control is implemented.

              FIGURE 1. Examples of digital networks whose initial operations are input signal...


Generating Partially Correlated Random Variables

Harry Commin March 23, 201921 comments
IntroductionIt is often useful to be able to generate two or more signals with specific cross-correlations. Or, more generally, we would like to specify an $\left(N \times N\right)$ covariance matrix, $\mathbf{R}_{xx}$, and generate $N$ signals which will produce this covariance matrix.

There are many applications in which this technique is useful. I discovered a version of this method while analysing radar systems, but the same approach can be used in a very wide range of...


Free Goodies from Embedded World - Full Inventory and Upcoming Draw Live-Streaming Date

Stephane Boucher March 22, 20191 comment

Chances are that you already know that I went to Embedded World a few weeks ago and came back with a bag full of "goodies".  Initially, my vision was to do a single draw for one person to win it all, but I didn't expect to come back with so much stuff and so many development kits.   Based on your feedback, it seems like you guys agree that It wouldn't make sense for one person to win everything as no-one could make good use of all the boards and there would be lots of...


Angle Addition Formulas from Euler's Formula

Cedron Dawg March 16, 20199 comments
Introduction

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT), but only indirectly. The main intent is to get someone who is uncomfortable with complex numbers a little more used to them and relate them back to already known Trigonometric relationships done in Real values. It is essentially a followup to my first blog article "The Exponential Nature of the Complex Unit Circle".

Polar Coordinates

The more common way of...


Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT

Neil Robertson March 9, 201920 comments

One of the basic DSP principles states that a sampled time signal has a periodic spectrum with period equal to the sample rate.  The derivation of can be found in textbooks [1,2].  You can also demonstrate this principle numerically using the Discrete Fourier Transform (DFT).

The DFT of the sampled signal x(n) is defined as:

$$X(k)=\sum_{n=0}^{N-1}x(n)e^{-j2\pi kn/N} \qquad (1)$$

Where

X(k) = discrete frequency spectrum of time sequence x(n)


How Discrete Signal Interpolation Improves D/A Conversion

Rick Lyons May 28, 20121 comment
This blog post is also available in pdf format. Download here.

Earlier this year, for the Linear Audio magazine, published in the Netherlands whose subscribers are technically-skilled hi-fi audio enthusiasts, I wrote an article on the fundamentals of interpolation as it's used to improve the performance of analog-to-digital conversion. Perhaps that article will be of some value to the subscribers of dsprelated.com. Here's what I wrote:

We encounter the process of digital-to-analog...


Take Control of Noise with Spectral Averaging

Sam Shearman April 20, 20183 comments

Most engineers have seen the moment-to-moment fluctuations that are common with instantaneous measurements of a supposedly steady spectrum. You can see these fluctuations in magnitude and phase for each frequency bin of your spectrogram. Although major variations are certainly reason for concern, recall that we don’t live in an ideal, noise-free world. After verifying the integrity of your measurement setup by checking connections, sensors, wiring, and the like, you might conclude that the...


Spectral Flipping Around Signal Center Frequency

Rick Lyons November 7, 20074 comments

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...


TCP/IP interface (Matlab/Octave)

Markus Nentwig June 17, 201210 comments

Communicate with measurement instruments via Ethernet (no-toolbox-Matlab or Octave)

Purpose

Measurement 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...


A poor man's Simulink

Markus Nentwig January 24, 20153 comments

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

Introduction

Many 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...


Padé Delay is Okay Today

Jason Sachs March 1, 20166 comments

This article is going to be somewhat different in that I’m not really writing it for the typical embedded systems engineer. Rather it’s kind of a specialized topic, so don’t be surprised if you get bored and move on to something else. That’s fine by me.

Anyway, let’s just jump ahead to the punchline. Here’s a numerical simulation of a step response to a \( p=126, q=130 \) Padé approximation of a time delay:

Impressed? Maybe you should be. This...


Free Goodies from Embedded World - Full Inventory and Upcoming Draw Live-Streaming Date

Stephane Boucher March 22, 20191 comment

Chances are that you already know that I went to Embedded World a few weeks ago and came back with a bag full of "goodies".  Initially, my vision was to do a single draw for one person to win it all, but I didn't expect to come back with so much stuff and so many development kits.   Based on your feedback, it seems like you guys agree that It wouldn't make sense for one person to win everything as no-one could make good use of all the boards and there would be lots of...


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

Cedron Dawg May 21, 20151 comment
Introduction

This 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...


Generating Complex Baseband and Analytic Bandpass Signals

Rick Lyons November 2, 20112 comments

There are so many different time- and frequency-domain methods for generating complex baseband and analytic bandpass signals that I had trouble keeping those techniques straight in my mind. Thus, for my own benefit, I created a kind of reference table showing those methods. I present that table for your viewing pleasure in this blog.

For clarity, I define a complex baseband signal as follows: derived from an input analog xbp(t)bandpass signal whose spectrum is shown in Figure 1(a), or...


Sinusoidal Frequency Estimation Based on Time-Domain Samples

Rick Lyons April 20, 201719 comments

The topic of estimating a noise-free real or complex sinusoid's frequency, based on fast Fourier transform (FFT) samples, has been presented in recent blogs here on dsprelated.com. For completeness, it's worth knowing that simple frequency estimation algorithms exist that do not require FFTs to be performed . Below I present three frequency estimation algorithms that use time-domain samples, and illustrate a very important principle regarding so called "exact"...