Course code TUM21
Course title Manipulation of time series in time and frequency spectrum
Institution Technische Universität München
Course address Technische Universität München, Arcisstrasse 21, 80333 München
City Munich
Minimum year of study 1st year
Minimum level of English Fluent
Minimum level of French None
Key words Digital Signal Processing - Filtering - finite difference methods
Language English
Professor responsible apl. Prof. Dr.-Ing. Holger Waubke
Telephone +43-1-51581-2507
Fax +43-1-51581-2530
Participating professors
Number of places Minimum: 4, Maximum: 30, Reserved for local students: 0

An detailed understanding of side effects produced by operations based on time series. The differences that occur, if continuous operations are compared with operations for discrete series shall become obvious. This knowledge is needed whenever time series are used recorded during measurements.

Programme to be followed

1          Introduction

1.1       The generalized Dirac Delta Function

1.2       The generalized Heaviside Function

1.3       Sine and Cosine Functions

1.4       Sine Cardinalis and Sine Integralis Functions

1.5       The Fourier Transformation

1.6       Modified Plancherel's Theorem

1.7       Filter or the Convolution in Time Domain

1.8       Convolution in Frequency Domain and the Determination of RMS Values

1.9       The Laplace Transformation

1.10     The z-Transformation

1.11     Energetic Sum in the Spectral Domain

1.12     Aliasing

1.13     Remarks

2          Gibbs' Phenomenon

2.1       Gibbs' Phenomenon  in Time Domain

2.2       Gibbs' Phenomenon in Frequency Domain

2.3       Conclusion

3          Filter and Filterbanks

3.1       Kaiser Bessel Filter

3.2       Tschebycheff Approximation und Remez Algorithm

3.3       Filterbanks

3.4       Butterworth Filter

3.5       Bessel Filter

3.6       Conclusion

4          Manipulation of Discrete Time Series and Spectra and Definition of Blocks

4.1       Upsampling of Time Series

4.2       Extension of the Time Basis

4.3       Averaging of  Time Blocks

4.4       Conclusions

5          Hilbert Transformation, Demodulation and Envelope

5.1       Hilbert Transformation in Spectral Domain

5.2       Hilbert Transformation in Time Domain

5.3       Hilbert Transformation for Time Series

5.4       Estimation of the Envelope

5.5       Conclusions

6          Differentiation und Integration in Time Domain

6.1       Differentiation in Time Domain

6.2       Differentiation with Polynomial Interpolation

6.3       Integration with Polynomial Interpolation

6.4       Savitzky Golay Filter for smoothing and smoothed Differentiation

6.5       Savitzky Golay Filter for smoothed Integration

6.6       Differentiation with trigonometric Interpolation

6.7       Integration with trigonometric Interpolation

6.8       Conclusions

 7         Spectral Differentiation and Integration

7.1       Leakage

7.2       Investigations With a Tapered Window

7.3       Differentiation with and Without Tapered Window

7.4       Integration with and Without Tapered Window

7.5       Correction of the Spectral Integration

7.5.1    Procedure in Time Domain

7.5.2    Procedure in Frequency Domain

7.6       Conclusions

8          Correction of Integrating A/D Converters

8.1       Correction of Integrating A/D Converters in Frequency Domain

8.2       Correction of Integrating A/D Converters in Time Domain

8.3       Conclusions

9          Exponential Smoothing

9.1       Continuous Smoothing

9.2       Discrete Representation of Exponential Smoothing Functions

9.2.1    Discrete Approximation Based on the Assumption of Blocks Scaled With End Values

9.2.2    Discrete Approximation using Blocks Scaled With Average Value

9.2.3    Assumption of a Linear Interpolation of the Discrete Time Series

9.2.4    Stability of the Filter

9.2.5    Coefficients of  the Classical Filter

9.2.6    Coefficients of the Filter using Blocks Scaled With Average Value

9.2.7    Coefficients of the Filter With Linear Interpolation

9.2.8    Passing Level

9.3       Exponential Smoothing about a Continuous Fourier Transformation

9.3.1    Fourier Transformation

9.3.2    Plancherel's Theorem

9.3.3    Exponential Smoothing of the Continuous Spectrum

9.3.4    remarks on DFT

9.3.5    Simulation von Noise Immissions

9.3.6    Simulation based on Discrete Fourier Transformation

9.4       Conclusions

10        The Stationary Ergodic Process and Applications in Measurement Techniques

10.1     Estimation of the Transfer-Function of a Linear System

10.2     Estimation of the Propagation Time in a Linear System

Some knowledge about measurement techniques

Good basis in mathematics

Basic knowledge about Fourier transformation

Course exam Written test at the end of the course