Program

1. Introduction

Block diagram of a scan-and-record-type measurement device. Basic notions: instrumental function, convolution, analyzer and detector, inverse problem of measurement.

Classification of signals. Continuous-argument and discrete-argument signals. Signal transformations: inversion, shift, scaling. Model signals: Gaussian peak, Lorentzian peak. Elementary signals: Heaviside unit step, Dirac unit impulse, complex exponent. 

2. Fourier transform and spectral representation of signals.

Two synthetic representations of a signal: by delta-peaks and sinusoids. Continuous Fourier transform and its properties. Fourier spectra of model and elementary signals. "White" spectrum of the delta peak.

3. Measurement in spectral language

The convolution property of the FT. Impact of instrumental function in spectral language, resolution. The inverse problem of measurement and its solution by the FT. The sampling theorem. Noise suppression by filtering. Wiener filter. Signal-to-noise ratio. 

4. Wavelet transform

Continuous quadratic wavelet. Discrete wavelet transform. Example of data compression and retrieval by Daubechies wavelets and MC's built-in wavelet transform functions.

5. Solving inverse problem of measurement by parameter fitting

Signal models. Linear method of least squares -- example of usage on a 3-peak chromatogram/spectrogram.