python - Plot a fourier transform of a sin wav with matplotlib

Question

I am trying to plot a fourier transform of a sign wave based on the scipy documentation

import numpy as np
import matplotlib.pyplot as plt
import scipy.fft

def sinWav(amp, freq, time, phase=0):
    return amp * np.sin(2 * np.pi * (freq * time - phase))

def plotFFT(f, speriod, time):
    """Plots a fast fourier transform

    Args:
        f (np.arr): A signal wave
        speriod (int): Number of samples per second
        time ([type]): total seconds in wave
    """

    N = speriod * time
    # sample spacing
    T = 1.0 / 800.0
    x = np.linspace(0.0, N*T, N, endpoint=False)

    yf = scipy.fft.fft(f)
    xf = scipy.fft.fftfreq(N, T)[:N//2]
    plt.plot(xf, 2.0/N * np.abs(yf[0:N//2]))
    plt.grid()
    plt.xlim([1,3])
    plt.show()


speriod = 1000
time  = {
    0: np.arange(0, 4, 1/speriod),
    1: np.arange(4, 8, 1/speriod),
    2: np.arange(8, 12, 1/speriod)
}

signal = np.concatenate([
    sinWav(amp=0.25, freq=2, time=time[0]),
    sinWav(amp=1, freq=2, time=time[1]),
    sinWav(amp=0.5, freq=2, time=time[2])
])   # generate signal

plotFFT(signal, speriod, 12)

---

Desired output

I want to be getting a fourier transform graph which looks like this

Current output

But instead it looks like this

---

Extra

This is the sin wave I am working with

question from:https://stackoverflow.com/questions/65660991/plot-a-fourier-transform-of-a-sin-wav-with-matplotlib

Answer 1

import numpy as np
import matplotlib.pyplot as plt
import scipy.fft

def sinWav(amp, freq, time, phase=0):
    return amp * np.sin(2 * np.pi * (freq * time - phase))

def plotFFT(f, speriod, time):
    """Plots a fast fourier transform

    Args:
        f (np.arr): A signal wave
        speriod (int): Number of samples per second
        time ([type]): total seconds in wave
    """

    N = speriod * time
    # sample spacing
    T = 1.0 / 800.0
    x = np.linspace(0.0, N*T, N, endpoint=False)

    yf = scipy.fft.fft(f)
    xf = scipy.fft.fftfreq(N, T)[:N//2]

    amplitudes = 1/speriod* np.abs(yf[:N//2])
  
    plt.plot(xf, amplitudes)
    plt.grid()
    plt.xlim([1,3])
    plt.show()


speriod = 800
time  = {
    0: np.arange(0, 4, 1/speriod),
    1: np.arange(4, 8, 1/speriod),
    2: np.arange(8, 12, 1/speriod)
}

signal = np.concatenate([
    sinWav(amp=0.25, freq=2, time=time[0]),
    sinWav(amp=1, freq=2, time=time[1]),
    sinWav(amp=0.5, freq=2, time=time[2])
])   # generate signal

plotFFT(signal, speriod, 12)

You should have what you want. Your amplitudes were not properly computed, as your resolution and speriod were inconsistent.

Longer data acquisition:

import numpy as np
import matplotlib.pyplot as plt
import scipy.fft

def sinWav(amp, freq, time, phase=0):
    return amp * np.sin(2 * np.pi * (freq * time - phase))

def plotFFT(f, speriod, time):
    """Plots a fast fourier transform

    Args:
        f (np.arr): A signal wave
        speriod (int): Number of samples per second
        time ([type]): total seconds in wave
    """

    N = speriod * time
    # sample spacing
    T = 1.0 / 800.0
    x = np.linspace(0.0, N*T, N, endpoint=False)

    yf = scipy.fft.fft(f)
    xf = scipy.fft.fftfreq(N, T)[:N//2]

    amplitudes = 1/(speriod*4)* np.abs(yf[:N//2])
  
    plt.plot(xf, amplitudes)
    plt.grid()
    plt.xlim([1,3])
    plt.show()


speriod = 800
time  = {
    0: np.arange(0, 4*4, 1/speriod),
    1: np.arange(4*4, 8*4, 1/speriod),
    2: np.arange(8*4, 12*4, 1/speriod)
}

signal = np.concatenate([
    sinWav(amp=0.25, freq=2, time=time[0]),
    sinWav(amp=1, freq=2, time=time[1]),
    sinWav(amp=0.5, freq=2, time=time[2])
])   # generate signal

plotFFT(signal, speriod, 48)