How do I plot an fft in python using scipy and modify the frequency range so that it shows the two peaks frequencies in the center?

The following Python code uses numpy to produce a frequency plot of a sinusoid graph :

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

# Number of samplepoints
N = 600
# sample spacing
T = 1.0 / 800.0
x = np.linspace(0.0, N*T, N)
y = np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x)
yf = scipy.fftpack.fft(y)
xf = np.linspace(0.0, 1.0/(2.0*T), N//2)

fig, ax = plt.subplots()
ax.plot(xf, 2.0/N * np.abs(yf[:N//2]))
plt.show()

Based on the code above , we are plotting a sine wave with two frequencies, one at 50Hz and another at 80 Hz. You can clearly see the Fourier transform plot shows peaks at those two frequencies.

My question: How do I modify the above code so that the x-axis ranges from 0-100Hz ?

If I change

xf = np.linspace(0.0, 1.0/(2.0*T), N//2)

to

xf = np.linspace(0.0, 100, N//2)

Then my graph looks like:

But the graph now shows my peaks at around 11 and 20Hz, which is not correct. When I change my axis, the peak values should not change.

What am I doing wrong?

Answer

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

# Number of samplepoints
N = 600
# sample spacing
T = 1.0 / 800.0
x = np.linspace(0.0, N*T, N)
y = np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x)
yf = scipy.fftpack.fft(y)
xf = np.linspace(0.0, 1.0/(2.0*T), N//2)

fig, ax = plt.subplots()
ax.plot(xf, 2.0/N * np.abs(yf[:N//2]))
ax.set(
    xlim=(0, 100)
)
plt.show()

simply add the xlim