scipy.signal._signaltools:resample

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import resample
n0, n1 = 20, 100  # number of samples
t0 = np.linspace(0, 10, n0, endpoint=False)  # input time stamps
x0 = np.cos(-t0**2/6)  # input signal
x1 = resample(x0, n1)  # resampled signal
t1 = np.linspace(0, 10, n1, endpoint=False)  # timestamps of x1
fig0, ax0 = plt.subplots(1, 1, tight_layout=True)

ax0.set_title(f"Resampling $x(t)$ from {n0} samples to {n1} samples")
ax0.set(xlabel="Time $t$", ylabel="Amplitude $x(t)$")
ax0.plot(t1, x1, '.-', alpha=.5, label=f"Resampled")
ax0.plot(t0, x0, 'o-', alpha=.5, label="Original")
ax0.plot(10, x0[0], 'rs', alpha=.5, label="Next Cycle")
ax0.legend(loc='best')

ax0.grid(True)
plt.show()

import matplotlib.pyplot as plt
import numpy as np
from scipy.fft import fftshift, fftfreq, fft, rfft, irfft
from scipy.signal import resample, resample_poly
fac, T0, T1 = 8, 1, 1/8  # upsampling factor and sampling intervals

for n0 in (15, 16):  # number of samples of input signal
    n1 = fac * n0  # number of samples of upsampled signal
    t0, t1 = T0 * np.arange(n0), T1 * np.arange(n1)  # time stamps
    x0 = np.zeros(n0)  # input signal has two non-zero sample values
    x0[n0//2], x0[n0//2+1] = n0 // 2, -(n0 // 2)

    x1n = irfft(rfft(x0), n=n1) * n1 / n0  # naive resampling
    x1r = resample(x0, n1)  # resample signal

    # Determine magnitude spectrum:
    x0_up = np.zeros_like(x1r)  # upsampling without antialiasing filter
    x0_up[::n1 // n0] = x0
    X0, X0_up = (fftshift(fft(x_)) / n0 for x_ in (x0, x0_up))
    XX1 = (fftshift(fft(x_)) / n1 for x_ in (x1n, x1r))
    f0, f1 = fftshift(fftfreq(n0, T0)), fftshift(fftfreq(n1, T1))  # frequencies
    df = f0[1] - f0[0]  # frequency resolution

    fig, (ax0, ax1) = plt.subplots(2, 1, layout='constrained', figsize=(5, 4))
    ax0.set_title(rf"Upsampling ${fac}\times$ from {n0} to {n1} samples")
    ax0.set(xlabel="Time $t$ in seconds", ylabel="Amplitude $x(t)$",
            xlim=(0, n1*T1))
    ax0.step(t0, x0, 'C2o-', where='post', alpha=.3, linewidth=2,
             label="$x_0(t)$ / $X_0(f)$")
    for x_, l_ in zip((x1n, x1r), ('C0--', 'C1-')):
        ax0.plot(t1, x_, l_, alpha=.5, label=None)
    ax0.grid()
    ax1.set(xlabel=rf"Frequency $f$ in hertz ($\Delta f = {df*1e3:.1f}\,$mHz)",
            ylabel="Magnitude $|X(f)|$", xlim=(-0.7, 0.7))
    ax1.axvspan(0.5/T0, f1[-1], color='gray', alpha=.2)
    ax1.axvspan(f1[0], -0.5/T0, color='gray', alpha=.2)
    ax1.plot(f1, abs(X0_up), 'C2-', f0, abs(X0),  'C2o', alpha=.3, linewidth=2)
    for X_, n_, l_ in zip(XX1, ("naive", "resample"), ('C0x--', 'C1.-')):
        ax1.plot(f1, abs(X_), l_, alpha=.5, label=n_)
    ax1.grid()
    fig.legend(loc='outside lower center', ncols=4)

plt.show()

import matplotlib.pyplot as plt
import numpy as np
from scipy.fft import rfftfreq, rfft
from scipy.signal import resample, resample_poly
n0 = 19937 # number of input samples - prime
n1 = 128  # number of output samples - fast FFT length
T0, T1 = 1/n0, 1/n1  # sampling intervals
t0, t1 = np.arange(n0)*T0, np.arange(n1)*T1  # time stamps
x0 = np.zeros(n0)  # Input has one non-zero sample
x0[0] = n0
x1r = resample(x0, n1)  # slow due to n0 being prime
x1p = resample(resample_poly(x0, 1, n0 // n1, padtype='wrap'), n1)  # periodic
x2p = resample(resample_poly(x0, 1, n0 // n1), n1)  # with zero-padding
X0 = rfft(x0) / n0
X1r, X1p, X2p = rfft(x1r) / n1, rfft(x1p) / n1, rfft(x2p) / n1
f0, f1 = rfftfreq(n0, T0), rfftfreq(n1, T1)
fig, (ax0, ax1) = plt.subplots(2, 1, layout='constrained', figsize=(5, 4))

ax0.set_title(f"Dowsampled Impulse response (from {n0} to {n1} samples)")
ax0.set(xlabel="Time $t$ in seconds", ylabel="Amplitude $x(t)$", xlim=(-T1, 1))
for x_ in (x1r, x1p, x2p):
    ax0.plot(t1, x_, alpha=.5)

ax0.grid()

ax1.set(xlabel=rf"Frequency $f$ in hertz ($\Delta f = {f1[1]}\,$Hz)",
        ylabel="Magnitude $|X(f)|$", xlim=(0, 0.55/T1))
ax1.axvspan(0.5/T1, f0[-1], color='gray', alpha=.2)
ax1.plot(f1, abs(X1r), 'C0.-', alpha=.5, label="resample")
ax1.plot(f1, abs(X1p), 'C1.-', alpha=.5, label="resample_poly(padtype='wrap')")
ax1.plot(f1, abs(X2p), 'C2x-', alpha=.5, label="resample_poly")

ax1.grid()

fig.legend(loc='outside lower center', ncols=2)

plt.show()