def q2_4():
ipx_1 = [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]
ipx_2 = [
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
]
len_of_sample = len(ipx_1)
DTFS_result_1 = myDTFS(ipx_1, len_of_sample)
DTFS_magnitude_1 = [abs(result) for result in DTFS_result_1]
DTFS_phase_1 = [cmath.phase(result) for result in DTFS_result_1]
DTFS_result_2 = myDTFS(ipx_2, len_of_sample)
DTFS_magnitude_2 = [abs(result) for result in DTFS_result_2]
DTFS_phase_2 = [cmath.phase(result) for result in DTFS_result_2]
_, ax = plt.subplots(2, 1)
ax[0].stem(DTFS_magnitude_1)
ax[0].grid()
ax[1].stem(DTFS_phase_1)
ax[1].grid()
plt.show()
_, ax = plt.subplots(2, 1)
ax[0].stem(DTFS_magnitude_2)
ax[0].grid()
ax[1].stem(DTFS_phase_2)
ax[1].grid()
plt.show()
def q2_2_c():
ipx = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
len_of_sample = len(ipx)
DTFS_result = myDTFS(ipx, len_of_sample)
IDTFS_result = myIDTFS(DTFS_result)
DFT_result = myDFT(ipx, len_of_sample)
IDFT_result = myIDFT(DFT_result)
FFT_result = fft(ipx, len_of_sample)
print(np.allclose(np.array(DTFS_result) * len_of_sample, FFT_result))
print(np.allclose(DFT_result, FFT_result))
print(np.allclose(ipx, IDTFS_result))
print(np.allclose(ipx, IDFT_result))
def q2_4():
for N in [12, 24,48,96]:
ipx = [1, 1, 1, 1, 1, 1, 1]
ipx = np.pad(ipx, (0, N - len(ipx)), 'constant')
DTFS_result = myDTFS(ipx, N)
DTFS_magnitude = [abs(result) for result in DTFS_result]
DTFS_phase = [cmath.phase(result) for result in DTFS_result]
_, ax = plt.subplots(2, 1)
ax[0].stem(DTFS_magnitude)
ax[0].grid()
ax[1].stem(DTFS_phase)
ax[1].grid()
plt.show()
def q2_2_b():
ipx = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
len_of_sample = len(ipx)
DTFS_result = myDTFS(ipx, len_of_sample)
DTFS_magnitude = [abs(result) for result in DTFS_result]
DTFS_phase = [cmath.phase(result) for result in DTFS_result]
DFT_result = myDFT(ipx, len_of_sample)
DFT_magnitude = [abs(result) for result in DFT_result]
DFT_phase = [cmath.phase(result) for result in DFT_result]
_, ax = plt.subplots(2, 1)
ax[0].stem(DTFS_magnitude)
ax[0].grid()
ax[1].stem(DTFS_phase)
ax[1].grid()
plt.show()
_, ax = plt.subplots(2, 1)
ax[0].stem(DFT_magnitude)
ax[0].grid()
ax[1].stem(DFT_phase)
ax[1].grid()
plt.show()