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...


How Not to Reduce DFT Leakage

Rick Lyons May 23, 201211 comments

This blog describes a technique to reduce the effects of spectral leakage when using the discrete Fourier transform (DFT).

In late April 2012 there was a thread on the comp.dsp newsgroup discussing ways to reduce the spectral leakage problem encountered when using the DFT. One post in that thread caught my eye [1]. That post referred to a website presenting a paper describing a DFT leakage method that I'd never heard of before [2]. (Of course, not that I've heard...


The History of CIC Filters: The Untold Story

Rick Lyons February 20, 20124 comments

If you have ever studied or designed a cascaded integrator-comb (CIC) lowpass filter then surely you've read Eugene Hogenauer's seminal 1981 IEEE paper where he first introduced the CIC filter to the signal processing world [1]. As it turns out, Hogenauer's famous paper was not the first formal document describing and proposing CIC filters. Here's the story.

In the Fall of 1979 Eugene Hogenauer was finalizing his development of the CIC filter, the filter now used in so many multirate signal...


Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data

Rick Lyons December 14, 201112 comments

There are two code snippets associated with this blog post:

Flat-Top Windowing Function for the Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data

and

Testing the Flat-Top Windowing Function

This blog discusses an accurate method of estimating time-domain sinewave peak amplitudes based on fast Fourier transform (FFT) data. Such an operation sounds simple, but the scalloping loss characteristic of FFTs complicates the process. We eliminate that complication by...


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...


Orfanidis Textbooks are Available Online

Rick Lyons July 12, 2011

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...

Do Multirate Systems Have Transfer Functions?

Rick Lyons May 30, 20112 comments

The following text describes why I ask the strange question in the title of this blog. Some months ago I was asked to review a article manuscript, for possible publication in a signal processing journal, that presented a method for improving the performance of cascaded integrator-comb (CIC) decimation filters [1].

Thinking about such filters, Figure 1(a) shows the block diagram of a traditional 2nd-order CIC decimation filter followed by downsampling by the sample rate factor R. There we...


Multiplying Two Binary Numbers

Rick Lyons March 16, 20117 comments

I just encountered what I think is an interesting technique for multiplying two integer numbers. Perhaps some of the readers here will also find it interesting.

Here's the technique: assume we want to multiply 18 times 17. We start by writing 18 and 17, side-by-side in column A and column B, as shown at the top of Figure 1. Next we divide the 18 at the top of column A by two, retaining only the integer part of the division, and double the 17 at the top of column B. The results of those two...


"Neat" Rectangular to Polar Conversion Algorithm

Rick Lyons November 15, 20105 comments

The subject of finding algorithms that estimate the magnitude of a complex number, without having to perform one of those pesky square root operations, has been discussed many times in the past on the comp.dsp newsgroup. That is, given the complex number R + jI in rectangular notation, we want to estimate the magnitude of that number represented by M as:

On August 25th, 2009, Jerry (Mr. Wizard) Avins posted an interesting message on this subject to the comp.dsp newsgroup (Subject: "Re:


Improved Narrowband Lowpass IIR Filters

Rick Lyons November 6, 20101 comment

Here's a neat IIR filter trick. It's excerpted from the "DSP Tricks" chapter of the new 3rd edition of my book "Understanding Digital Signal Processing". Perhaps this trick will be of some value to the subscribers of dsprelated.com.

Due to their resistance to quantized-coefficient errors, traditional 2nd-order infinite impulse response (IIR) filters are the fundamental building blocks in computationally-efficient high-order IIR digital filter implementations. However, when used in...


A Useful Source of Signal Processing Information

Rick Lyons March 23, 20168 comments

I just discovered a useful web-based source of signal processing information that was new to me. I thought I'd share what I learned with the subscribers here on DSPRelated.com.

The Home page of the web site that I found doesn't look at all like it would be useful to us DSP fanatics. But if you enter some signal processing topic of interest, say, "FM demodulation" (without the quotation marks) into the 'Search' box at the top of the web page

and click the red 'SEARCH...


The DFT of Finite-Length Time-Reversed Sequences

Rick Lyons December 20, 201910 comments

Recently I've been reading papers on underwater acoustic communications systems and this caused me to investigate the frequency-domain effects of time-reversal of time-domain sequences. I created this blog because there is so little coverage of this topic in the literature of DSP.

This blog reviews the two types of time-reversal of finite-length sequences and summarizes their discrete Fourier transform (DFT) frequency-domain characteristics.

The Two Types of Time-Reversal in DSP

...

Implementing Simultaneous Digital Differentiation, Hilbert Transformation, and Half-Band Filtering

Rick Lyons November 24, 20152 comments

Recently I've been thinking about digital differentiator and Hilbert transformer implementations and I've developed a processing scheme that may be of interest to the readers here on dsprelated.com.

This blog presents a novel method for simultaneously implementing a digital differentiator (DD), a Hilbert transformer (HT), and a half-band lowpass filter (HBF) using a single tapped-delay line and a single set of coefficients. The method is based on the similarities of the three N =...


Handy Online Simulation Tool Models Aliasing With Lowpass and Bandpass Sampling

Rick Lyons May 4, 20151 comment

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 tool shows four important characteristics of periodic sampling:

  Characteristic# 1: All input analog spectral components, regardless of their center frequencies, show up (appear) below half the sample rate in the digitized...

Complex Down-Conversion Amplitude Loss

Rick Lyons March 3, 20157 comments

This blog illustrates the signal amplitude loss inherent in a traditional complex down-conversion system. (In the literature of signal processing, complex down-conversion is also called "quadrature demodulation.")

The general idea behind complex down-conversion is shown in Figure 1(a). And the traditional hardware block diagram of a complex down-converter is shown in Figure 1(b).

Let's assume the input to our down-conversion system is an analog radio frequency (RF) signal,...


A Table of Digital Frequency Notation

Rick Lyons August 5, 2013

When we read the literature of digital signal processing (DSP) we encounter a number of different, and equally valid, ways to algebraically represent the notion of frequency for discrete-time signals. (By frequency I mean a measure of angular repetitions per unit of time.)

The various mathematical expressions for sinusoidal signals use a number of different forms of a frequency variable and the units of measure (dimensions) of those variables are different. It's sometimes a nuisance to keep...


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.

...

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...


A Fast Real-Time Trapezoidal Rule Integrator

Rick Lyons June 13, 20204 comments

This blog presents a computationally-efficient network for computing real‑time discrete integration using the Trapezoidal Rule.

Background

While studying what is called "N-sample Romberg integration" I noticed that such an integration process requires the computation of many individual smaller‑sized integrations using the Trapezoidal Rule integration method [1]. My goal was to create a computationally‑fast real‑time Trapezoidal Rule integration network to increase the processing...


Somewhat Off Topic: Deciphering Transistor Terminology

Rick Lyons May 28, 20193 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:...