Spectral Parameter Estimation of Noisy Complex Exponential data Records

What is SPENCER?

SPENCER is a Matlab Graphic User Interface (GUI) for spectral analysis of 1D complex exponential signals. The software was primarily intended to process NMR spectroscopy signals, but it may used to analyze any process involving damped or undamped sinusoids.

Signals may be visualized either in the time domain or the frequency domain via FFT. But the main object of SPENCER is to process a signal in the time domain using parametric methods. So, SPENCER relies on specific estimation routines written in the Matlab programming language. The estimation algorithms implemented are:

  • Backward linear prediction with singular value decomposition (SVD), also known as the Kumaresan-Tufts method [1]
  • Matrix Pencil method [2]
  • State-space or Kung's direct data approximation method [3]
  • High-order Yule-Walker approach (HOYW-SVD) [4,5]

SPENCER includes features such as line listing, signal reconstruction, comparison between the original and estimated signal, etc (see poster).

A special feature offered by SPENCER is the possibility to select a frequency interval in which to proceed to a spectral estimation. In some situations (signals with a large number of lines and samples) a direct estimation made on the whole frequency band may be difficult and sometimes inefficient. In this case, it is possible to generalize the previous operation: the whole frequency band is decomposed in multiple subbands in which the estimation process is repeated. This enables one to divide a complex estimation problem into several simpler ones.

Two decomposition schemes are included:

  • In the uniform decomposition, the signal is split into adjacent spectral bands with the same frequency width [5].
  • The adaptive decomposition leads to an automatic selection of the frequency bands with relevant information according to some criterion [6].

Once the decomposition is effective, the user may choose between the same estimation methods given before.


SPENCER is a free software. It can be distributed and modified without limitation for personal and academic purposes only. Proper reference to the software must be given if it is used in a published work.
Commercial or industrial use is not allowed without permission of the authors. To get an agreement, simply send an email to the authors.


This software is available in zip format.
Unzip the package and launch Matlab. To run the software, type 'Spencer' in the Matlab prompt.

System Requirements

  • Matlab version 6 or higher with the Signal Processing Toolbox
  • Operating systems: Windows, Linux, MacOS X
  • Supported data formats: Matlab, text and Bruker.


  • Estimation and decomposition routines: E.H. Djermoune, M. Tomczak, P. Mutzenhardt
  • Matlab GUI: E.H. Djermoune, M. Tomczak, J. Tan Luong Ann
  • Baseline estimation routine: V. Mazet
  • NMR advisor: P. Mutzenhardt


The authors of this freeware accept no responsibility for damages resulting from the use of this product. It is provided AS IS, and you, its user, assume all risks when using it.

Bug reports may be returned to the authors.


[1]      R. Kumaresan, D. W. Tufts, Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise, IEEE Trans. Acoust. Speech Signal Process., vol. 30, pp. 833-840, 1982.

[2]      Y. Hua, T. K. Sarkar, Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise, IEEE Trans. Acoust. Speech Signal Process., vol. 38, no. 5, pp. 814-824, 1990.

[3]      R. Kung, K. S. Arun, D. V. Bhaskar Rao, State-space and singular value decomposition-based approximation methods for the harmonic retrieval problem, J. Opt. Soc. America, vol. 73, no. 12, pp. 1799-1811, 1983.

[4]      P. Stoica, R. L. Moses, T. Söderström, J. Li, Optimal HOYW estimation of sinusoidal frequencies, IEEE Trans. Signal Process., vol. 39, pp. 1360-1368, 1991.

[5]      M. Tomczak, E. H. Djermoune, A subband ARMA modeling approach to high-resolution NMR spectroscopy, J. Magn. Reson. Vol. 158, pp. 86-98, 2002.

[6]      E. H. Djermoune, M. Tomczak, P. Mutzenhardt, A new adaptive subband decomposition approach for automatic analysis of NMR data, J. Magn. Reson. Vol. 169, pp. 73-84, 2004.