Signal Processing Concepts

This section introduces some basic signal processing concepts that you need to know before working with signal data.

Removing Noise

A signal, by definition, contains information. Any signal obtained from a physical process also contains unwanted frequency components (noise). IDL provides several digital filter routines to remove noise.

Some noise can simply be removed by smoothing or masking an image or masking it within the frequency domain, but some noise requires more filtering. (See the definition for Wavelet, below.)

See Digital Filtering for more information.

Curve Fitting

Curve fitting is the process of finding various ways to fit a curve to a series of data points that best represents all points. Curve-fitting can also estimate points between values along a continuum. Curve fitting allows you to find intermediate estimates for these values. IDL's CURVEFIT function uses a gradient-expansion algorithm to compute a non-linear least squares fit to a user-supplied function with an arbitrary number of parameters.

See Curve and Surface Fitting for more information.

Convolution and Correlation

The term convolution refers to the relationship between the input signal, output signal, and impulse response. Correlation is a method of detecting a known waveform in the noisy background signals. Signals of any given type travel at a known rate, and correlation determines if the signal also occurs in another signal.

Mathematically, convolution and correlation are similar. They both use two signals to produce a third signal. In correlation, this third signal is called the cross-correlation of the input signals.

See Correlation and Covariance for more information.

Transforms

It is often difficult or impossible to make sense of the information contained in a digital signal by looking at it in its raw form—that is, as a sequence of real values at discrete points in time. Signal analysis transforms offer natural, meaningful, alternate representations of the information contained in a signal. Transforms make signal processing easier by changing the domain in which the underlying signal is represented.

Most signals can be decomposed into a sum of discrete (usually sinusoidal) signal components. The result of such decomposition is a frequency spectrum that can uniquely identify the signal. IDL provides three transforms to decompose a signal and prepare it for analysis: the Fourier transform, the Hilbert transform, and the wavelet transform.

See Signal Analysis Transforms for more information.

Wavelet Analysis

Wavelet analysis is a technique to transform an array of N numbers from their actual numerical values to an array of N wavelet coefficients. Since the wavelet functions are compact, the wavelet coefficients measure the variations around just a small part of the data array. Wavelet analysis is useful for signal processing because the wavelet transform allows you to easily pick out features in your data, such as noise or discontinuities, discrete objects, edges of objects, etc.

See Using the IDL Wavelet Toolkit for more information.