import numpy as np
from scipy.fftpack import fft as sfft
from scipy.fftpack import dct as sdct
from scipy.fftpack import dst as sdst
from scipy.fftpack import idst as sidst
from scipy.fftpack import idct as sidct

y_1d = np.zeros(8)
y_1d[1] = 1
x_1d = np.zeros_like(y_1d)
x_1d[3] = 1
y_1d_fft = sdst(y_1d, type=1)
x_1d_fft = sdct(x_1d, type=1)
o_1dfft = x_1d_fft * y_1d_fft
out_1d = sdst(o_1dfft, type=1)