Design IIR Bandpass Filters

Neil Robertson January 6, 201810 comments

In this post, I present a method to design Butterworth IIR bandpass filters.  My previous post [1] covered lowpass IIR filter design, and provided a Matlab function to design them.  Here, we’ll do the same thing for IIR bandpass filters, with a Matlab function bp_synth.m.  Here is an example function call for a bandpass filter based on a 3rd order lowpass prototype:

N= 3; % order of prototype LPF fcenter= 22.5; % Hz center frequency, Hz bw= 5; ...

Phase and Amplitude Calculation for a Pure Complex Tone in a DFT

Cedron Dawg January 6, 2018
Introduction

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving exact formulas to calculate the phase and amplitude of a pure complex tone from a DFT bin value and knowing the frequency. This is a much simpler problem to solve than the corresponding case for a pure real tone which I covered in an earlier blog article[1]. In the noiseless single tone case, these equations will be exact. In the presence of noise or other tones...


Feedback Controllers - Making Hardware with Firmware. Part 7. Turbo-charged DSP Oscillators

Steve Maslen January 5, 20187 comments
This article will look at some DSP Sine-wave oscillators and will show how an FPGA with limited floating-point performance due to latency, can be persuaded to produce much higher sample-rate sine-waves of high quality. 

Comparisons will be made between implementations on Intel Cyclone V and Cyclone 10 GX FPGAs. An Intel numerically controlled oscillator


Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals

Jason Sachs December 29, 20171 comment

Last time we looked at the use of LFSRs for pseudorandom number generation, or PRNG, and saw two things:

  • the use of LFSR state for PRNG has undesirable serial correlation and frequency-domain properties
  • the use of single bits of LFSR output has good frequency-domain properties, and its autocorrelation values are so close to zero that they are actually better than a statistically random bit stream

The unusually-good correlation properties...


An Efficient Linear Interpolation Scheme

Rick Lyons December 27, 201725 comments

This blog presents a computationally-efficient linear interpolation trick that requires at most one multiply per output sample.

Background: Linear Interpolation

Looking at Figure 1(a) let's assume we have two points, [x(0),y(0)] and [x(1),y(1)], and we want to compute the value y, on the line joining those two points, associated with the value x. 

       Figure 1: Linear interpolation: given x, x(0), x(1), y(0), and y(1), compute the value of y. ...


An Alternative Form of the Pure Real Tone DFT Bin Value Formula

Cedron Dawg December 17, 2017
Introduction

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving alternative exact formulas for the bin values of a real tone in a DFT. The derivation of the source equations can be found in my earlier blog article titled "DFT Bin Value Formulas for Pure Real Tones"[1]. The new form is slighty more complicated and calculation intensive, but it is more computationally accurate in the vicinity of near integer frequencies. This...


Design IIR Butterworth Filters Using 12 Lines of Code

Neil Robertson December 10, 201712 comments

While there are plenty of canned functions to design Butterworth IIR filters [1], it’s instructive and not that complicated to design them from scratch.  You can do it in 12 lines of Matlab code.  In this article, we’ll create a Matlab function butter_synth.m to design lowpass Butterworth filters of any order.  Here is an example function call for a 5th order filter:

N= 5 % Filter order fc= 10; % Hz cutoff freq fs= 100; % Hz sample freq [b,a]=...

Feedback Controllers - Making Hardware with Firmware. Part 6. Self-Calibration Related.

Steve Maslen December 3, 20177 comments

This article will consider the engineering of a self-calibration & self-test capability to enable the project hardware to be configured and its basic performance evaluated and verified, ready for the development of the low-latency controller DSP firmware and closed-loop applications. Performance specifications will be documented in due course, on the project website here.

  • Part 6: Self-Calibration, Measurements and Signalling (this part)
  • Part 5:

Simplest Calculation of Half-band Filter Coefficients

Neil Robertson November 20, 20179 comments

Half-band filters are lowpass FIR filters with cut-off frequency of one-quarter of sampling frequency fs and odd symmetry about fs/4  [1]*.  And it so happens that almost half of the coefficients are zero.  The passband and stopband bandwiths are equal, making these filters useful for decimation-by-2 and interpolation-by-2.  Since the zero coefficients make them computationally efficient, these filters are ubiquitous in DSP systems.

Here we will compute half-band...


Feedback Controllers - Making Hardware with Firmware. Part 5. Some FPGA Aspects.

Steve Maslen November 14, 2017
This part of the on-going series of articles looks at a variety of aspects concerning the FPGA device which provides the high-speed maths capability for the low-latency controller and the arbitrary circuit generator application. In due course a complete specification along with  application  examples will be maintained on the project website here.

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...

The Swiss Army Knife of Digital Networks

Rick Lyons June 13, 20168 comments

This blog describes a general discrete-signal network that appears, in various forms, inside so many DSP applications. 

Figure 1 shows how the network's structure has the distinct look of a digital filter—a comb filter followed by a 2nd-order recursive network. However, I do not call this useful network a filter because its capabilities extend far beyond simple filtering. Through a series of examples I've illustrated the fundamental strength of this Swiss Army Knife of digital networks...


Online DSP Classes: Why Such a High Dropout Rate?

Rick Lyons October 7, 201718 comments

Last year the IEEE Signal Processing Magazine published a lengthy article describing three university-sponsored online digital signal processing (DSP) courses [1]. The article detailed all the effort the professors expended in creating those courses and the courses' perceived values to students. 

However, one fact that struck me as important, but not thoroughly addressed in the article, was the shocking dropout rate of those online courses. For two of the courses the article's...


Half-band filter on Xilinx FPGA

Lyons Zhang November 30, 20105 comments
1. DSP48 Slice in Xilinx FPGA

There are many DSP48 Slices in most Xilinx® FPGAs, one DSP48 slice in Spartan6® FPGA is shown in Figure 1, the structure may different depending on the device, but broadly similar.

Figure 1: A whole DSP48A1 Slice in Spartan6 (www.xilinx.com)

2. Symmetric Systolic Half-band FIR

Figure 2: Symmetric Systolic Half-band FIR Filter

3. Two-channel Symmetric Systolic Half-band FIR

  Figure 3: 2-Channel...


Some Observations on Comparing Efficiency in Communication Systems

Eric Jacobsen March 17, 2011
Introduction

Engineering is usually about managing efficiencies of one sort or another. One of my favorite working definitions of an engineer says, "An engineer is somebody who can do for a nickel what any damn fool can do for a dollar." In that case, the implication is that the cost is one of the characteristics being optimized. But cost isn't always the main efficiency metric, or at least the only one. Consider how a common transportation appliance, the automobile, is optimized...


An Astounding Digital Filter Design Application

Rick Lyons July 7, 201613 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...


Frequency Translation by Way of Lowpass FIR Filtering

Rick Lyons February 4, 20175 comments

Some weeks ago a question appeared on the dsp.related Forum regarding the notion of translating a signal down in frequency and lowpass filtering in a single operation [1]. It is possible to implement such a process by embedding a discrete cosine sequence's values within the coefficients of a traditional lowpass FIR filter. I first learned about this process from Reference [2]. Here's the story.

Traditional Frequency Translation Prior To Filtering

Think about the process shown in...


Two jobs

Stephane Boucher December 5, 201223 comments

For those of you following closely embeddedrelated and the other related sites, you might have noticed that I have been less active for the last couple of months, and I will use this blog post to explain why. The main reason is that I got myself involved into a project that ended up using a better part of my cpu than I originally thought it would.

edit - video of the event:

I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other...


Benford's law solved with DSP

Steve Smith February 22, 20087 comments

I have a longtime interest in the mystery of 1/f noise. A few years ago I came across Benford’s law, another puzzle that seemed to have many of the same characteristics.

Suppose you collect a large group of seemingly random numbers, such as might appear in a newspaper or financial report. Benford’s law relates to the leading digit of each number, such as "4" in 4.268, "3" in 0.0312, and "9" in -932.34. Since there are nine possible leading digits...


Time-Domain Periodicity and the Discrete Fourier Transform

Eric Jacobsen July 13, 2012

Introduction

The Discrete Fourier Transform (DFT) and it's fast-algorithm implementation, the Fast Fourier Transform (FFT), are fundamental tools for processing and analysis of digital signals. While the continuous Fourier Transform and its inverse integrate over all time from minus infinity to plus infinity, and all frequencies from minus infinity to plus infinity, practical application of its discrete cousins can only be made over finite time and frequency intervals. The discrete nature...