I just computed an DFT and FFT of a sinc function, but when I visualise them the results are strangely different? what am I missing

Question

The idea here is to improve a Sinc function by manipulating its Fourier transform.

As you can see, the tophat has ripples in the bands of interest and I want to eliminate them by smoothing them with a window or some filtering method, then take the DFT of the smoothed tophat to get the Sinc.

I want to compare the Sinc obtained from the smoothed tophat with the actual Sinc used to get the rippled tophat.

import numpy as np
import matplotlib.pyplot as plt
def fft(p):
  return np.fft.fftshift(np.fft.fft(np.fft.fftshift(p)))

##define discrete Fourier transform
def DFT(x):
    N = x.size
    #Create vector to store result in
    X = np.zeros(N, dtype=complex)
    for k in range(N):
        for n in range(N):
            X[k] += np.exp(-1j * 2.0* np.pi* k * n / N) * x[n]
    return X
x = np.array([-2.81131875e-02, -3.96997713e-02, -4.21368144e-02, -3.44452846e-02,
 -1.80464821e-02,  3.47617152e-03  ,2.51429695e-02,  4.17113849e-02,
  4.89232237e-02,  4.45735920e-02,  2.91392108e-02,  5.79606030e-03
, -2.02066174e-02, -4.26991128e-02, -5.60228061e-02, -5.64157843e-02,
 -4.30215932e-02, -1.82621467e-02 , 1.25480044e-02,  4.22981416e-02,
  6.36705197e-02,  7.08779634e-02,  6.11503378e-02,  3.56057506e-02,
 -7.36946338e-04, -3.98641156e-02, -7.24435298e-02, -8.99361403e-02,
 -8.66871186e-02, -6.15139083e-02, -1.83898004e-02,  3.40030403e-02,
  8.38410834e-02,  1.18587835e-01,  1.27818064e-01,  1.05851694e-01,
  5.36133160e-02, -2.07428262e-02, -1.02672849e-01, -1.73486957e-01,
 -2.13645119e-01, -2.06513036e-01, -1.41864949e-01, -1.84298219e-02,
  1.55066260e-01,  3.60639086e-01,  5.73509978e-01,  7.65904176e-01,
  9.11528887e-01,  9.89928563e-01,  9.89928563e-01,  9.11530481e-01,
  7.65911712e-01,  5.73528030e-01,  3.60669975e-01,  1.55108326e-01,
 -1.83838723e-02, -1.41826535e-01, -2.06494808e-01, -2.13657425e-01,
 -1.73533710e-01, -1.02749119e-01, -2.08345369e-02 , 5.35272126e-02,
  1.05793985e-01,  1.27807692e-01 , 1.18633975e-01,  8.39393878e-02,
  3.41351502e-02, -1.82532023e-02, -6.14064529e-02, -8.66385973e-02,
 -8.99643861e-02, -7.25486656e-02, -4.00269498e-02, -9.22081286e-04,
  3.54422496e-02,  6.10504637e-02,  7.08711442e-02,  6.37651928e-02,
  4.24781826e-02,  1.27749970e-02, -1.80408041e-02 ,-4.28604510e-02,
 -5.63580073e-02, -5.60886911e-02, -4.28797388e-02, -2.04643427e-02
 , 5.51990784e-03,  2.89109493e-02,  4.44513443e-02,  4.89421251e-02,
  4.18738004e-02,  2.54163255e-02,  3.79921602e-03, -1.77499417e-02,
 -3.42484465e-02 ,-4.20918559e-02, -3.98241253e-02, -2.83838352e-02])
def sinc(x):
        xu =  np.sin(x)/x
        xu[x==0] = 1
        return xu
xx = sinc(x)
dft = DFT(xx)
plt.plot(xx)
plt.figure()
plt.plot(dft/np.max(dft),label='DFT')
plt.plot(fft(xx)/np.max(fft(xx)),label='FFT')

where xx is some 1D Sinc function.