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In this chapter we explore signal processing, which is a subject with applications in diverse branches of science and engineering. A signal in this context can be a quantity that varies in time (temporal signal), or as a function of space coordinates (spatial signal). For example, an audio signal is a typical example of a temporal signal, while an image is a typical example of a spatial signal in two dimensions. In reality, signals are often continuous functions, but in computational applications it is common to work with discretized signals, where the original continuous signal is sampled at discrete points with uniform distances. The sampling theorem gives rigorous and quantitative conditions for when a continuous signal can be accurately represented by a discrete sequence of samples.
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There are several alternative definitions of the Fourier transform, which vary in the coefficient in the exponent and the normalization of the transform integral.
There is also an implementation of FFT in the fft module in NumPy. It provides mostly the same functions as scipy.fftpack, which we use here. As a general rule, when SciPy and NumPy provide the same functionality, it is generally preferable to use SciPy if available, and fall back to the NumPy implementation when SciPy is not available.
Several other window functions are also available. See the docstring for the scipy.signal module for a complete list.
The data used in this example was obtained from https://www.freesound.org/people/guitarguy1985/sounds/52047 .
See the project’s web page at http://scikit-image.org for more information.
- Signal Processing
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- Chapter 17