# 0.2 Measuring impulse responses using golay complementary sequences

 Page 1 / 2
Two impulse-response measurement methods are demonstrated, with source code provided in Matlab and Pure Data (PD).The measurement technique using Golay complementary sequences is particularly robust to additive white noise, while the swept sine measurementtechnique is robust to a weakly nonlinear motor exciting the linear system being measured.

## Introduction

[link] depicts a linear system characterized by an impulse response $h\left(n\right)$ , driven by an input signal $s\left(n\right)$ , and producing the output signal $r\left(n\right)$ . The system identification problem is to estimate $h\left(n\right)$ given known input/output signals $s\left(n\right)$ and $r\left(n\right)$ . This module illustrates the swept-sine and the Golay complementary sequence techniques for identifying finite impulse responses. The firstexample measures the impulse response of a highpass filter using the Golay method, and the second example measures the impulse response ofa weakly nonlinear loudspeaker driver using the swept-sine method.

## Summary of objectives

• To provide a general framework for characterizing single-input, single-output linear systems .
• To demonstrate how to measure the impulse response of a linear system using Golay complementary sequences .
• To explain some of the limitations of making measurements using standard sound interfaces.
• To demonstrate how to find the minimum-phase spectrum corresponding to a complex spectrum.
• To explain how to measure the impulse response of a system even if the excitation source motor is weakly nonlinear . This measurement technique uses a sine sweep test signal.

## Installation

1. Install a sound card, sound interface, or other full-duplex data acquisition card.
2. Consider testing the data acquisition card viewing the soundcard set-up instructions .
3. Install either MATLAB or Octave .
4. Install pd . (Alternatively, you may use other software that is capable of recording a system's output for a given inputexcitation signal. The software should also be capable of reading and writing WAV files. For example, any multitrack recordingsoftware should be fine.)
5. Download tf_meas.zip and unzip the contents into a conveniently located local directory.

## Linear system

Consider the causal, single-input single-output (SISO) system shown in [link] . For simplicity, we will take the system to be linear and discrete-time, so that it is characterized by its impulseresponse $h\left(n\right)$ or equivalently its transfer function $H\left(z\right)$ , which is the $z$ transform of $h\left(n\right)$ .

$h\left(n\right)↔H\left(z\right)$

We will assume that both $h\left(n\right)$ and $H\left(z\right)$ exist so that we can discuss measuring them interchangeably. We will further assume that $h\left(n\right)$ has finite length so that we can measure the response to an input signal in a finite amount of time. The goal of this document isto explain how to excite the system with a signal $s\left(n\right)$ , measure the response $r\left(n\right)$ , and use $s\left(n\right)$ and $r\left(n\right)$ to determine $h\left(n\right)$ (and equivalently $H\left(z\right)$ ). In particular, it is useful to pick a signal $s\left(n\right)$ that contains a large amount of energy so that measurement noise will not significantly corrupt the measurement results.

## Limitations of sound interfaces

Sound cards and sound interfaces are not designed for making transfer function measurements. They merely provide a cost-effective solutionsince almost all computers have sound cards. We demonstrate these weaknesses given measurements made on a PreSonus Firepod soundinterface. The output from channel 1 was directly connected to the line input on channel 1, and the sampling rate was ${f}_{S}=44.1$ kHz.

#### Questions & Answers

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!