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, 201110 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...


Computing FFT Twiddle Factors

Rick Lyons August 8, 201017 comments

Some days ago I read a post on the comp.dsp newsgroup and, if I understood the poster's words, it seemed that the poster would benefit from knowing how to compute the twiddle factors of a radix-2 fast Fourier transform (FFT).

Then, later it occurred to me that it might be useful for this blog's readers to be aware of algorithms for computing FFT twiddle factors. So,... what follows are two algorithms showing how to compute the individual twiddle factors of an N-point decimation-in-frequency...


Computing an FFT of Complex-Valued Data Using a Real-Only FFT Algorithm

Rick Lyons February 9, 20103 comments

Someone recently asked me if I knew of a way to compute a fast Fourier transform (FFT) of complex-valued input samples using an FFT algorithm that accepts only real-valued input data. Knowing of no way to do this, I rifled through my library of hardcopy FFT articles looking for help. I found nothing useful that could be applied to this problem.

After some thinking, I believe I have a solution to this problem. Here is my idea:

Let's say our original input data is the complex-valued sequence...


Should DSP Undergraduate Students Study z-Transform Regions of Convergence?

Rick Lyons September 14, 201613 comments

Not long ago I presented my 3-day DSP class to a group of engineers at Tektronix Inc. in Beaverton Oregon [1]. After I finished covering my material on IIR filters' z-plane pole locations and filter stability, one of the Tektronix engineers asked a question similar to:

     "I noticed that you didn't discuss z-plane regions of      convergence here. In my undergraduate DSP class we      spent a lot of classroom and homework time on the  ...


Correcting an Important Goertzel Filter Misconception

Rick Lyons July 6, 201512 comments

Recently I was on the Signal Processing Stack Exchange web site (a question and answer site for DSP people) and I read a posted question regarding Goertzel filters [1]. One of the subscribers posted a reply to the question by pointing interested readers to a Wikipedia web page discussing Goertzel filters [2]. I noticed the Wiki web site stated that a Goertzel filter:

"...is marginally stable and vulnerable tonumerical error accumulation when computed usinglow-precision arithmetic and...

Implementing Impractical Digital Filters

Rick Lyons July 19, 20162 comments

This blog discusses a problematic situation that can arise when we try to implement certain digital filters. Occasionally in the literature of DSP we encounter impractical digital IIR filter block diagrams, and by impractical I mean block diagrams that cannot be implemented. This blog gives examples of impractical digital IIR filters and what can be done to make them practical.

Implementing an Impractical Filter: Example 1

Reference [1] presented the digital IIR bandpass filter...


Why Time-Domain Zero Stuffing Produces Multiple Frequency-Domain Spectral Images

Rick Lyons March 23, 2015

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...


"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:


Computing Translated Frequencies in Digitizing and Downsampling Analog Bandpass Signals

Rick Lyons October 31, 20131 comment

In digital signal processing (DSP) we're all familiar with the processes of bandpass sampling an analog bandpass signal and downsampling a digital bandpass signal. The overall spectral behavior of those operations are well-documented. However, mathematical expressions for computing the translated frequency of individual spectral components, after bandpass sampling or downsampling, are not available in the standard DSP textbooks. The following three sections explain how to compute the...


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...


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...


Multiplierless Exponential Averaging

Rick Lyons December 5, 20082 comments

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 relatively constant-amplitude signal measurements.

Figure 1 Exponential averaging: (a) standard network; (b) single-multiply network.

That exponential averager's difference equation is

y(n) = αx(n) + (1 –...

An Astounding Digital Filter Design Application

Rick Lyons July 7, 20169 comments

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 Designer

With typical filter design software packages the user enters numerical values for the...