# Sine sweep vs impulse response

What kind of pros and cons does these method for identifying a system have? I seem to have a hard time finding literature discussion in this issue.

I am operating on a linear system, or the linear area of the system. So non linearity isn't an issue here.

• the issue is mostly about putting enough energy into the system so that the S/N ratio in the measurement is good, while avoiding saturating or clipping the driving input. i would suggest looking up the term "crest factor". the lower the crest factor the better and it cannot get lower than 1. May 25, 2015 at 18:52
• besides impulsing your input (terrible crest factor) and sinusoidal sweep, there is another technique called "maximum length sequences" (MLS). long ago i wrote a tutorial regarding the math involved. May 25, 2015 at 18:58
• If it's a digital system you simulate (i.e. in Simulink) then a Kronecker's (Dirac's) delta is a best choice. In the result you will get an exact system's IR. In real world applications it is rather impossible to get the exact impulse and you will generally find sweep as a better solution - you can even calculate the THD with it. It all depends what is the system that you are trying to identify. Like @robertbristow-johnson mentioned, there is also a MLS, but I suggest to not use it out of many reasons. Unless you want to average your results in noisy environment and you know what you are doing
– jojeck
May 25, 2015 at 19:36
• @robertbristow-johnson: what can I say Robert - I was raised in hatred to MLS and love to sweep's ;) sasd: Regarding SNR performance, here is some over 10 yr. old article that contains the comparison.
– jojeck
May 25, 2015 at 20:08
• @sasd, if you were using an impulse driver, you would want to make it periodic so that you could synchronously measure the response each impulse, overlay them on top of each other, and average (maybe kicking out outliers before averaging). and you would want the period to be longer than any possible impulse response to avoid time-aliasing. problem with the impulse driver is that the driving function is 0 for N-1 out of N samples and you're not putting in as much energy into the system as you could and you have to pay for that with either a longer measurement time or with lower S/N. May 25, 2015 at 20:09

A good starting point to better help you understand the differences between several available methods for Transfer Function measurements is the Müller and Massarani paper entitled "Transfer-Function Measurements with Sweeps". Whilst the title eludes to coverage of only the ESS method, it does do a good job at covering other techniques too.

Angelo Farina has also contributed many works regarding Transfer Function measurements for a variety of applications, all of which he makes freely available here: http://pcfarina.eng.unipr.it/Public/Papers/list_pub.htm

I hope that this assists with your literature quest. Following reading these papers you should have a better understanding of the different methods, along with their respective pro's and con's, so you can make an educated decision regarding which technique best suits your application.

• Any books describing it?
– sasd
May 27, 2015 at 18:24
• Good question. Various books talk about the measurement process, but generally they don't go into a comprehensive comparative analysis of the different methods. Section 8.2 of "Room Acoustics (5th Ed)" - Heinrich Kuttruff, does present some different techniques and gives some high level analysis of pro's and con's between them. That could be a good starting point for you. I hope this helps.
– MDT
May 27, 2015 at 22:14

Personally:The impulse response gives a visual way of understanding the system response and can be used in a convolution calculation. But you will find a vast number of distinct systems yield very similar waveforms for the impulse response; requiring great precision to identify.

The sine wave response makes up for this by redundancy in measurements and provides information for various regulations, requirements, and control design.

Just for your information: you should be aware that things with long intricate time constants confound simple measurements; like thermal control systems where every little edge and connection slowly heats up and "reflects" energy back. For these systems I threw in the towel and used pulse response over a long time and then constructed approximation models and then worked from the approximations when they were good enough. The truth is that all of this is approximations to "reality" anyway.

My background is related to structural system analysis, so my answer will take into account the input usually used during structural testing.

The effects of sine-sweep excitation on the system response have been analyzed, among the others, in the paper listed below:

G. Gloth, M. Sinapius, Detection of Non-Linearities in Swept-Sine Measurements, XXI International Modal Analysis Conference - IMAC, Orlando, Florida, 2003 (here it talks also about non-linearities identification, which is not your case, but still it can give you useful infos about the effect of this type of excitation)

J.A. Lollock, The effect of swept sinusoidal excitation on the response of a single degree of freedom oscillator, 43rd AIAA Structures, Structural Dynamics and Materials Conference, Denver, Colorado, 2002

P. Nali, A. Bettacchioli, Beating phenomena in spacecraft sine tests and an attempt to include the sine sweep rate effect in the test-prediction

Impulse excitation is usually give by means of an impact and this makes it a simple and fast way for measuring frequency response functions. Impact testing produces responses with high crest factors, but it suffers of the same problems as those of random excitation: the input is a broad spectrum and the energy associated with an individual frequency is small.

Both are transient excitations.