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Numpy Beginner's Guide (Update)

Numpy Beginner's Guide (Update)

By : Ivan Idris
2 (1)
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Numpy Beginner's Guide (Update)

Numpy Beginner's Guide (Update)

2 (1)
By: Ivan Idris

Overview of this book

This book is for the scientists, engineers, programmers, or analysts looking for a high-quality, open source mathematical library. Knowledge of Python is assumed. Also, some affinity, or at least interest, in mathematics and statistics is required. However, I have provided brief explanations and pointers to learning resources.
Table of Contents (16 chapters)
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14
C. NumPy Functions' References
15
Index

Time for action – fitting to a sine

In the previous Time for action section, we created a simple filter for detrended data. Now, let's use a more restrictive filter that will leave us only with the main frequency component. We will fit a sinusoidal pattern to it and plot our results. This model has four parameters—amplitude, frequency, phase, and vertical offset.

  1. Define a residuals function based on a sine wave model:
    def residuals(p, y, x):
       A,k,theta,b = p
       err = y-A * np.sin(2* np.pi* k * x + theta) + b
       return err
  2. Transform the filtered signal back to the original domain:
    filtered = -fftpack.irfft(fftpack.ifftshift(amps))
  3. Guess the values of the parameters of which we are trying to estimate a transformation from the time domain into the frequency domain:
    N = len(qqq)
    f = np.linspace(-N/2, N/2, N)
    p0 = [filtered.max(), f[amps.argmax()]/(2*N), 0, 0]
    print("P0", p0)

    The initial values appear as follows:

    P0 [2.6679532410065212, 0.00099598469163686377, 0, 0]
    
  4. Call...

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