我有一个5000个点x和y的信号当我手动使用离散傅立叶变换时，可以创建一个控制系数数量的系数列表，系数越多，对原始信号的近似度越大。
在下面的示例中，存在5000 points的信号，其在经过DFT之后生成具有201 coefficients的列表。
但是当使用fft()函数时，我无法控制系数的数量。
有没有办法使用numpy或scipy，或者它们的fft functions来生成同样的201个系数，而不是生成5000个系数？

import matplotlib.pyplot as plt
import numpy as np
from math import tau
from scipy.integrate import quad_vec
from scipy.fft import fft

def f(t, t_list, x_list, y_list):
    return np.interp(t, t_list, x_list + 1j*y_list)

N = 5000
t_list = np.linspace(0, 2*np.pi, N)

r = (((0.0*np.pi<=t_list) * (t_list<=0.5*np.pi)) * 1/np.cos(t_list-0.25*np.pi) +
    ((0.5*np.pi<t_list) * (t_list<=1.0*np.pi)) * 1/np.cos(t_list-0.75*np.pi) +
    ((1.0*np.pi<t_list) * (t_list<=1.5*np.pi)) * 1/np.cos(t_list-1.25*np.pi) +
    ((1.5*np.pi<t_list) * (t_list<=2.0*np.pi)) * 1/np.cos(t_list-1.75*np.pi))

# create de signal a square form

x_list, y_list = np.cos(t_list) * r, np.sin(t_list) * r

fig, ax = plt.subplots(figsize=(5, 5))
ax.set_aspect('equal')
ax.plot(x_list, y_list)

print('x length list: ', len(x_list)) #5000 points
print('y length list: ', len(y_list)) #5000 points

order = 100 # -order to order i.e -100 to 100

# you can change the order to get proper figure

# too much is also not good, and too less will not produce good result

print("generating coefficients ...")

# lets compute fourier coefficients from -order to order

c = []

# we need to calculate the coefficients from -order to order

for n in range(-order, order+1):
    # calculate definite integration from 0 to 2*PI
    # formula is given in readme
    coef = 1/tau*quad_vec(lambda t: f(t, t_list, x_list, y_list)*np.exp(-n*t*1j), 0, tau, limit=100, full_output=1)[0]
    c.append(coef)

print("completed generating coefficients.")

c = np.array(c)

print('c length list: ', len(c))

# convert x and y to complex number

z = x_list + 1j*y_list

# get coeff of all element of list

coeff_fft = fft(z)

print('coeff_fft length list: ', len(coeff_fft))

输出

x length list:  5000
y length list:  5000
generating coefficients ...
completed generating coefficients.
c length list:  201
coeff_fft length list:  5000