Gain insights into Python for scientific computing. Explore arrays, plotting, linear equations, and algorithms using NumPy, Matplotlib, SciPy. Delve into applying tools with practical exercises.

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Python3

If you're a scientist or an engineer interested in learning scientific computing, this is the place to start.

In this course, you'll learn to write your own useful code to perform impactful scientific computations. Along the way, your understanding will be tested with periodic quizzes and exercises.

Topics covered in this course include arrays, plotting, linear equations, symbolic computation, scientific algorithms, and random variables. You’ll also be exposed to popular Python packages like NumPy, Matplotlib, SciPy, and others. In the last part of the course, the application section will test your ability to recall and apply the tools you have studied into newly learned scientific concepts.

At the end of this course, you'll be equipped with the tools necessary for everyday scientific computation.

Python for Scientists and Engineers

# Introduction

Fourier transform is a method for expressing a function as a weighted sum of sinusoids. Fourier transforms are computed on a time domain signal to check its components in the frequency domain. Fourier transform has vast applications including signal, noise, image, and audio processing. 

When both the function and its Fourier transform are replaced with their discretized counterparts, it is called the discrete Fourier transform (DFT). The `fftpack` module in  SciPy helps the user compute the DFT using the algorithm Fast Fourier Transform (FFT).

The FFT $y[k]$ (length $N$) of sequence $x[n]$ (length $N$) is defined as:

$$y[k]=\sum_{n=0}^{N-1}e^{-2 \pi j \frac{kn}{N}}x[n]$$

We can go from the frequency domain to the time domain using an inverse Fourier transform. This is defined as: 

$$x[n]=\frac{1}{N}\sum_{k=0}^{N-1}e^{2 \pi j \frac{kn}{N}}y[k]$$


The FFT is computed using `fft()` and inverse transform is computed using `ifft()`.

This lesson describes the implementation of Fourier transform. 

Introduction

Python Refresher

Arrays

Plotting

Systems of Linear Equations

Symbolic Computation

Scientific Algorithms

Random Variables

Applications

Conclusion

Appendix

Python for Scientists and Engineers Exam

Fourier Transforms

Introduction