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In order to obtain a smooth sine wave, the sampling rate must be far higher than the prescribed minimum required sampling rate, that is at least twice the frequency – as per Nyquist-Shannon theorem.
#SCIPY FFT SOFTWARE#
Python is an interpreter based software language that processes everything in digital. Plt.title('Sine wave f='+str(f)+' Hz') # plot title Plt.plot(t,x) # plot using pyplot library from matplotlib package
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(t,x) = sine_wave(f,overSampRate,phase,nCyl) #function call NCyl = 5 # desired number of cycles of the sine wave Phase = 1/3*np.pi #phase shift in radians
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Import matplotlib.pyplot as plt # library for plottingįrom signalgen import sine_wave # import the function Simulate a sinusoidal signal with given sampling rate Now that we have defined the sine wave function in signalgen.py, all we need to do is call it with required parameters and plot the output. This approach can be extended to object oriented programming. The intent is to hold all the related signal generation functions, in a single file. We will add more such similar functions in the same file. We note that the function sine wave is defined inside a file named signalgen.py. Return (t,g) # return time base and signal g(t) as tuple G = np.sin(2*np.pi*f*t+phase) # replace with cos if a cosine wave is desired (t,g) = sine_wave(f,overSampRate,phase,nCyl) (t,g) : time base (t) and the signal g(t) as tuple NCyl : number of cycles of sine wave to generate OverSampRate : oversampling rate (integer) Generate sine wave signal with the following parameters def sine_wave(f,overSampRate,phase,nCyl): Next, we define a function for generating a sine wave signal with the required parameters. Here, we are importing the numpy package and renaming it as a shorter alias np. In order to use the numpy package, it needs to be imported. Numpy is a fundamental library for scientific computations in Python. For a baseband signal bandwidth ( to ) and maximum frequency in a given band are equivalent).įor Python implementation, let us write a function to generate a sinusoidal signal using the Python’s Numpy library. By Nyquist Shannon sampling theorem, for faithful reproduction of a continuous signal in discrete domain, one has to sample the signal at a rate higher than at-least twice the maximum frequency contained in the signal (actually, it is twice the one-sided bandwidth occupied by a real signal. Given the frequency of the sinewave, the next step is to determine the sampling rate.įor baseband signals, the sampling is straight forward. For example, we wish to generate a sine wave whose minimum and maximum amplitudes are -1V and +1V respectively. In order to generate a sine wave, the first step is to fix the frequency f of the sine wave. This article is part of the book Digital Modulations using Python, ISBN: 978-1712321638 available in ebook (PDF) and Paperback (hardcopy) formats If you are inclined towards Matlab programming, visit here.
#SCIPY FFT SERIES#
I intend to show (in a series of articles) how these basic signals can be generated in Python and how to represent them in frequency domain using FFT. Often we are confronted with the need to generate simple, standard signals (sine, cosine, Gaussian pulse, squarewave, isolated rectangular pulse, exponential decay, chirp signal) for simulation purpose. Numerous texts are available to explain the basics of Discrete Fourier Transform and its very efficient implementation – Fast Fourier Transform (FFT). Plot one-sided, double-sided and normalized spectrum using FFT.
#SCIPY FFT HOW TO#
Key focus: Learn how to plot FFT of sine wave and cosine wave using Python.