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| import streamlit as st | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| def main(): | |
| st.set_page_config(layout="wide") | |
| st.title( | |
| "Procesamiento Digital de Señales - UNTREF \n ## Spectral Leakage en la DFT" | |
| ) | |
| st.divider() | |
| signal_expression, signal_settings = st.columns(2) | |
| with signal_settings: | |
| st.markdown("### Parámetros de la señal") | |
| num_samples = st.slider( | |
| "Cantidad de Muestras", min_value=4, max_value=64, value=8, step=1 | |
| ) | |
| freq = st.slider( | |
| r"Frecuencia angular $\omega_0$", | |
| min_value=-np.pi, | |
| max_value=np.pi, | |
| value=0.0, | |
| step=np.pi / 64, | |
| ) | |
| with signal_expression: | |
| freq_samples = int(np.round(64 * freq / np.pi)) | |
| st.markdown("### Señal analizada:") | |
| with st.columns(3)[1]: | |
| st.markdown(f"# $$e^{{j\\frac{{{freq_samples}}}{{64}}\pi n}}$$") | |
| samples = np.arange(num_samples) | |
| signal = np.exp(1j * (freq) * samples) | |
| dtft_samples = 2048 | |
| dtft_result = np.fft.fftshift(np.fft.fft(signal, dtft_samples)) / num_samples | |
| dtft_freqs = np.fft.fftshift(np.fft.fftfreq(dtft_samples)) | |
| dft_result = np.fft.fftshift(np.fft.fft(signal)) / num_samples | |
| dft_freqs = np.fft.fftshift(np.fft.fftfreq(len(signal))) | |
| dft_freqs_rad = 2 * np.pi * dft_freqs | |
| dtft_freqs_rad = 2 * np.pi * dtft_freqs | |
| # Plot the signals | |
| fig = plt.figure(figsize=(10, 4)) | |
| plt.axvline(np.pi, color="black", linestyle="--") | |
| plt.axvline(-np.pi, color="black", linestyle="--") | |
| plt.axvline(freq, color="black", alpha=0.5, linestyle=":", label=r"$\omega_0$") | |
| plt.plot(dtft_freqs_rad, np.abs(dtft_result), color="red", label="DTFT") | |
| plt.stem(dft_freqs_rad, np.abs(dft_result), markerfmt="C0o", label="DFT") | |
| plt.xlabel("Frecuencia angular [rad]") | |
| plt.ylabel("Magnitud de la transformada normalizada") | |
| plt.ylim(0, 1.1) | |
| plt.xlim(-np.pi - 0.1, np.pi + 0.1) | |
| plt.xticks( | |
| np.linspace(-np.pi, np.pi, 9), | |
| [ | |
| r"$-\pi$", | |
| r"$-\frac{3}{4}\pi$", | |
| r"$-\frac{\pi}{2}$", | |
| r"$-\frac{\pi}{4}$", | |
| r"0", | |
| r"$\frac{\pi}{4}$", | |
| r"$\frac{\pi}{2}$", | |
| r"$\frac{3}{4}\pi$", | |
| r"$\pi$", | |
| ], | |
| ) | |
| plt.grid() | |
| plt.legend(loc="upper right", framealpha=1, ncol=3, bbox_to_anchor=(0.65, 1.06)) | |
| plt.tight_layout() | |
| st.pyplot(fig, use_container_width=True) | |
| if __name__ == "__main__": | |
| main() | |